Lecture 1 | Modern Physics: Special Relativity (Stanford)

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Lecture 1 of Leonard Susskind’s Modern Physics course concentrating on Special Relativity. Recorded April 14, 2008 at Stanford University.

This Stanford Continuing Studies course is the third of a six-quarter sequence of classes exploring the essential theoretical foundations of modern physics. The topics covered in this course focus on classical mechanics. Leonard Susskind is the Felix Bloch Professor of Physics at Stanford University.

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this program is brought to you by Stanford University please visit us at stanford.edu this quarter we're going to learn about field theory classical field theory fields such as the electromagnetic field gravitational field other fields in nature which I won't name right now propagate which means they change according to rules which give them a wave-like character moving through space and one of the fundamental principles of field theory in fact more broadly nature in general is the principle of relativity the principle the special printless the the principle of special relativity in this particular case the principle of special relativity well let's just call it the principle of relativity goes way back there was not an invention of Einstein's I'm not absolutely sure when it was first announced or articulated in the form which I'll spell it out I don't know whether it was Galileo or Newton or those who came after them but those early pioneers certainly had the right idea it begins with the idea of an inertial reference frame now inertia reference frame this is something a bit tautological about an inertial reference frame Newton's equations F equals MA are satisfied in an inertial reference frame what is an inertial reference frame it's a frame of reference in which Newton's equations are satisfied I'm not going to explain any further what an inertial reference frame is except to say that the idea of an inertial reference frame is by no means unique a reference frame first of all was a reference frame in tale of a reference frame first of all entails a set of coordinate axes in ordinary space X Y & Z and you know how to think about those but it also entails the idea that the coordinate system may be moving or not moving relative to whom relative to whomever we sitting here or you sitting here in this classroom here define a frame of reference we can pick the vertical direction to be the z axis the horizontal direction along my arms here to be the x axis X plus that way X my X is minus in that direction and which one have I left out I've left out the y axis which points toward you from me so there are some coordinate axes for space XY and Z and I didn't this in addition to specify a frame of reference one also imagines that this entire coordinate system is moving in some way relative to you sitting there presumably with a uniform velocity in a definite direction if your frame of reference is an inertial frame of reference in other words if when you throw balls around or juggle or do whatever is supposed to do in an inertial frame of reference if you find yourself in an inertial frame of reference then every other frame of reference that's moving with uniform velocity relative to you now remember what uniform velocity means it doesn't just mean with uniform speed it means with uniform speed in an unchanging direction such a frame of reference is also inertial if it's accelerated or if it starts standing still and then suddenly picks up some speed then it's not an inertial frame of reference all inertial frames of reference according to Newton and also I think also Galileo Galileo was often credited with the idea but I never read enough of Galileo to know whether he actually had it or not neither did I read enough of Newtons they both wrote in languages that I don't understand what was I saying oh yes right according to both Newton and anybody else who thought about it very hard the laws of physics are the same in all inertial reference frames laws of physics meaning F equals MA the forces between objects all the things that we would normally call laws of nature or laws of physics don't distinguish between one frame of reference of and another if you want a kind of pictorial example that I like to use a lot when I'm explaining this to the children or to grownups I like to think about the laws of juggling there are very definite procedures that you train your body to do uh in order to be able to juggle balls correctly now you can imagine yourself being in a railroad car moving with perfectly uniform velocity down the x axis and trying to juggle do you have to compensate for the fact that the train is moving and for particular when you throw a ball up into the air that you have to reach over to the right to compensate for the fact that the train is moving to the left my left your right the answer is no you don't the laws of juggling are the same in every reference frame and every inertial reference frame whatever you do in one reference frame you do exactly the same thing and you'll succeed or fail depending on whether you're a good juggler or not but it will not depend on whether you're moving with uniform velocity so the laws of juggling are the same in every inertial reference frame the laws of mechanics are the same in every inertial reference frame the laws Newtonian laws of gravity are the same in every inertial frame according to Newton what about the laws of electrical phenomena well there there was a clash the clash had to do with Maxwell's equations Maxwell's equations were the field equations the field theory that governed the electromagnetic field and the way that it propagated and sent waves electromagnetic waves that we ordinarily call light or radio waves or so forth and the fundamental dilemma as you all know I'm sure you all know the fundamental dilemma was both according to well here was the dilemma Maxwell's equations said light moves with a certain velocity if you take the various constants that appear in Maxwell's equations and put them together in the right way you get the velocity of waves moving down an axis and that velocity comes out to be a certain number out of Maxwell's equations you have two choices one is to believe that Maxwell's equations are true laws of nature as good as any other laws of nature in which case the principle of relativity says they should be the same in every reference frame but if it follows from Maxwell's equations that the speed of light is three times ten to the eighth meters per second which is about what it is if it follows from Maxwell's equations that light moves that fast and if Maxwell's equations are laws of physics fundamental laws of physics and if the laws of physics are the same in every reference frame then the speed of light must be the same in every reference frame but that was very hard to swallow because if a light beam is going down that axis and you chase it and run along with it that lets say three-quarters of the speed of light then you want to see that light ray moving much more slowly than three times ten to the eighth meters per second relative to you on the other hand the light ray going in the other direction since you're sort of running into it you should see going even faster so all these possibilities could not simultaneously be correct that the laws of nature are the same in every reference frame and that Maxwell's equations are laws of physics in the same sense that Newton's laws of physics namely the same in every reference frame something had to give well the point was of course that they were good laws of nature and that they were the same in every reference frame the thing that had to give is our concepts of velocity space and time and how we measure velocity especially velocities were up which are up near the speed of light now I'm not going to spend the full amount of time that I did previously on the special theory of relativity that can be found on lectures from how long ago and there on the Internet I believe relativity and electromagnetism I think that was maybe about three quarters ago I've lost track yeah they're up there they're on the net and they're the lectures on relativity special relativity and electromagnetic theory we're just going to cut through it real fast we're going to cut through the basic ideas of relativity a little more mathematically than I would do if I were teaching it for the first time I teach it the first time I tend to teach it the way Einstein first conceived of it how do you measure distances how do you measure velocities how do how does the propagation of light influence these things instead I'm going to take a more mathematical view of it and think about the properties of various kinds of coordinate transformations coordinates now consists not only of XY and Z but also time T so imagine every event in the world is characterized by just like every particle would be characterized by a position x y&z every event taking place in space-time is characterized by four coordinates X Y Z and T let's suppress for the moment y&z let's just forget I forget them for the moment and concentrate on X and T that would be appropriate if we were mainly interested in motion along one axis let's focus on that motion along the x axis let's suppose there is no motion along y&z then we can forget y&z for the moment momentarily we'll come back to them and think of motion along X and T and the various reference frames that might be moving along the x axis alright here's here's time vertically is space horizontally physicists always draw space horizontally and time vertically I found out that mathematicians are at least certain computer scientists always draw time going horizontally I didn't know that and I got into an enormous argument with a quantum computer scientist which was ultimately resolved by the fact that he had time going horizontally and I had it going vertically these are traditions I guess traditions grow up around subjects but time is north and X is east I guess or at least time is upward yeah yeah yeah that's what that that that's the point that is the point yes they're thinking of time is the independent variable and everybody knows that it's a law of nature that the independent variable should be horizontal ok all right now let's in let's imagine a moving observer moving down the x axis with a velocity V let's take his origin of spatial coordinates his origin of spatial coordinates at time T equals zero is just the same let's assume that my I'll be the moving observer I move down the x-axis I am my own origin there's nobody who was your origin that seat is vacant over there so that absent a human over there is the center of the x-coordinates in your frame I'm the X prime coordinates and of course I being very egocentric will take my x-acto is origin to be where I am there I do I move down the x-axis we pass each other our origins pass each other at t equals 0 so that means at T equals 0 your axis and my axes are the same or your origin in my origin is the same but then as I move down the x axis my core my coordinate center moves to the right most of the right that's supposed to be a straight line that's as good as I can do under the circumstances that's a straight line and it's moving with velocity V which means it's X prime equals SR it means x equals VT but it's also that's the way you describe it in terms of your coordinates my centre you described by saying x equals VT how do I describe it I just say X prime my coordinate X prime is 0 X prime equals 0 is the same as x equals VT all right what's the relationship between X Prime and X and T well it's easy to work out if you believe this picture the X prime coordinate is the distance from my origin the x coordinate is the distance from your origin so one of these is X the other is X prime the upper one here is X prime the low and here is X and the relationship between them is that they differ by an amount VT in particular X is equal to X prime minus VT or X prime is equal to X plus VT will have it wrong yes I do X prime is X minus BT and X is X prime plus VT yeah I think I have that's correct now all right what about time itself well according to Newton and according to Galileo and according to everybody who came afterward up until Einstein time is just time is just time is just time there was no notion that time might be different in different reference frames Newton had the idea of a universal time sort of God's time God upon his cloud ticking off with his with his super accurate watch and that time was universal for everybody no matter how they were moving and so everybody would agree on what on the time of any given event in this map of space and time here and so the other equation that went with this is that T prime is equal to T let's forget the top equation here let's just forget it one might say that this was the Newtonian or the Galilean transformation properties between X and T your coordinates and the coordinates that I ascribe to a point in space-time now let's examine a light ray moving down the plus x axis if it starts at the origin here then it moves along a trajectory which is x equals CT C being the speed of light now shortly I'm going to set C equal to 1 we're going to work in units in which C is equal to 1 but not quite yet incidentally once you understand a bit of relativity working in coordinates in which C is not equal to 1 is about as stupid as using different units for x and y are if we used yards for x and feet for y then we will have all kinds of funny factors in our equations which would be conversion factors from X which is measured in feet to Y which is measured in our yards the cycle has its uses log scale has its uses no long skilling long scale well let common interest yep I'm not sure we good but okay I'm just saying it is quite often in practical circumstances that one uses different scales yeah you sometimes you might there might be a good reason I mean um it wouldn't be totally unreasonable for a sailor to use different units for horizontal direction and vertical direction hmm I mean he's used to moving around horizontally he might use what miles miles versus fathoms or something nautical miles versus paddles yeah Persian is relative but um when you talk about a frame of reference you need to specify a period of time because obviously goes that 15 billion years there is no yeah we're ignoring now the fact that the universe began at some time and we're imagining now as Newton did and as the early Einstein did that the universe has just been here forever and ever and ever unchanging totally static and space and time have properties which don't change with time now of course that's incorrect in the real world and at some point we will take up the subject of cosmology and find that's not right but as long as we're interested in time intervals which are not I suspect this is what you're getting at as long as we're interested in time intervals which are not too long in particular time intervals over which the universe doesn't expand very much and so forth we can mainly say the properties of space don't change over a period of time and so everything just stays the same as always was is that what you're asking it seems that that this assumption if it is made it needs to what you're describing so well so the question is without imagining to some point as it doesn't lead it doesn't lead to what I'm describing where is this this room for different formulas here this is a formula which is based on an assumption the assumption being that time is universal that's what Einstein found was wrong basically what he found is that when you're in a moving frame of reference to different the observers will not agree about what time a particular event takes place this is the culprit here this one and some modifications to this one but in any case to see what's wrong let's go to Maxwell's equations Maxwell's equations say that light always moves with this velocity C being some numbers in meters per second okay 3 times 10 to the 8th meters per second we will later as I said say C equals 1 let's imagine a light beam moving down the x axis let's describe how X prime sees it in other words you see the light move this way to the right how do I see the light well let's see what I see let's just work it out X prime will be X which is CT for that light ray minus VT which is the same as C minus VT all this says is that I see the light moving with a diminished velocity a velocity C minus V why is that because I'm moving along with the light so naturally I see it move slowly the slow compared to what you see it what about the light going in the other direction supposing it was a light beam going in the other direction then how would you describe it you would describe it as x equals minus CT and if I do exactly the same thing I will find that X prime is equal to X that's minus CT – VT which is the same as minus C plus V times T so what this says is that I will see the light moving also in the negative direction that's the minus sign but I'll see it moving with an enhanced velocity C plus V if this were the right story and if these were the right transformation laws for space and time then it could not be the case that Maxwell's equations are laws of physics or laws of nature in the sense that they were true in every reference frame they would have to be corrected in moving frames just like the juggler who had to reach to the right who didn't actually but who thought he had to reach to the right to collect the ball when train is moving the physicist interested in light beams would have to correct things for the motion of his reference frame now it's an experimental fact that this is not the case that you don't have to correct for motion was the famous Michelson Morley experiment Einstein he just rejected he just felt this can't be right Maxwell's equations were much too beautiful to be relegated to the approximate or to the contingent on which reference frame and so he said about to find a framework in which the speed of light would be the same in every reference frame and he basically focused on these equations and after various very very beautiful Gedanken experiments thought experiments about light and about measuring and so forth he came to a set of formulas called the Lorentz transformations I'm going to explain them the Lorentz transformations in a more mathematical way not fancy mathematics but just get we want to get right to the heart of it and not spend the three weeks doing it the best way is to a mathematical problem but before I do let me set up a different mathematical problem which is for most of you you've seen me do this before but nonetheless let's go through it again the problem of rotation of coordinates we're going to do this quickly let's just take spatial coordinates now for the moment two dimensional spatial coordinates let's forget X and T and just concentrate on X&Y two coordinates in space instead of events in space-time concentrate on a point in space a point in space has coordinates and we can determine those coordinates the x and y coordinates just by dropping perpendicular to the x axis in the y axis and we would describe this point as the point at position let's just call it X Y now there's nothing sacred about horizontal and vertical so somebody else may come along some crazy mathematician a really nutty one who wants to use coordinates which are at an angle relative to the vertical maybe a couple of beers and you don't know the difference between vertical and worth worth worth we should give this direction a name oblique yeah all right the oblique observer the blue observer can blue be seen everybody can see blue okay good ah the blue observer also characterizes points by coordinates which he calls X Prime and Y Prime the X Prime and the Y prime coordinates are found by dropping perpendicular to the X Prime and the Y prime axis so here's X prime is y prime and given a point X Y there's a role it must be a role if you know the value of x and y you should be able to deduce the value of X I'm in y-prime if you know the angle between the two coordinates between the x coordinate and the X prime coordinate and the formulas simple we've used it least in these classes many times I'll just remind you what it is that's X prime is equal to x times cosine of the angle between the two frames between the two coordinate systems minus y times sine of the angle and Y prime is equal to minus plus I think X sine of theta plus y cosine theta I just want to remind you about a little bit of trigonometry all of trigonometry is encoded in two very simple formulas I've used them this signs on these signs of are on the right let's Ella and X prime is bigger than X for small theta since ours here are all so it's Auto Expo Rhine is bigger than it is is it yeah let's see if you rotate it to the next so that y is y prime is zero it's further out X prime rook will have it backward yeah what's your gift I'm not gonna fit nobody so let's say just make sure the links take survive is the little perpendicular there no my life primary so that's y prime y prime is this is why I'm here right right that's why I'm in X prime is bigger than X so there has to be a plus sign on the second you know its prime is bigger than X let's see um yeah X prime is bigger than X yeah X prime is bigger than X looks like that's probably right probably sign but then this one must be man negative yeah okay there's an easy way to correct for it another way to correct for it just call this angle minus theta that would also do the trick because cosine of minus theta is the same as cosine of theta and sine changes sign when you change theta 2 minus theta so if instead of calling this angle theta I called it minus theta then my previous formulas would be right it's true true but the it's an excuse all right what do we know about sine and cosine it's important to understand sine and cosine everything you ever learned about trigonometry can be codified in two very simple formulas if you know about complex numbers the two very simple formulas are that cosine of theta is e to the I theta plus e to the minus I theta over 2 and sine of theta is e to the I theta minus e to the minus I theta over 2i those two formulas contain everything about trigonometry you don't have to know any other formulas other than these for example I will assign you the homework problem of using these two formulas to find cosine of the sum of two angles but the way you would do it is just write the sum of two angles in here and then reexpress the Exponential's in terms of cosine and sine that's easy to do e to the I theta is equal to cosine of theta plus I sine theta and e to the minus I theta is cosine of theta minus I sine theta so work through these formulas get familiar with them they're extremely useful formulas once you know them you will never have to remember any trigonometric formulas again the other thing to know is that e to the I theta times e to the minus I theta is 1 all right e to the anything times e to the minus the same thing is one those things characterize all trigonometric formulas in particular as was explained to me by Michael a number of times if we multiply e to the I theta times e to the minus I theta we will get one on this side but on this side we will get cosine squared of theta plus sine squared of theta naught minus sine squared but plus sine squared cosine squared and then ice minus I squared sine squared that gives us cosine squared plus sine squared cosine squared theta plus sine squared theta so that's equivalent to the fact that e to the I theta times e to the minus I theta is 1 all right now the most important fact that again follows from the simple trigonometry is that when you make the change of coordinates from XY to X prime Y prime something is left unchanged namely the distance from the origin to the point XY that's something which is you know you count the number of the molecules along the blackboard from here to here and that doesn't change when I change coordinates so the distance from the origin to the point XY has to be the same independent of which coordinate axes we use well let's take the square of that distance the square of that distance we know what it is let's call it s squared I'm not sure why I use s but s for distance s s for distance s for space I think it must be for space that I'm using it for the spaces for the spatial distance from the origin to the point XY we know what that is it's Pythagoras theorem x squared plus y squared but as I said there's nothing special about the XY axes we also ought to be able to calculate it as X prime squared plus y prime squared well it's not too hard to work out that X prime squared plus y prime squared is x squared plus y squared it's easy to use do X prime squared plus y prime squared will have x squared cosine squared theta it will also have x squared sine squared theta when you add them you'll get x squared plus y squared you know you know the rigmarole so it follows from cosine squared plus sine squared equals 1 that X prime squared plus y prime squared equals also equal is equal to x squared plus y squared work that out make sure that you have this on the control that you understand why from the trigonometry not from the the basic physics of it or the basic geometry of it is clear make sure that you understand that you can see that from the trigonometry okay one last thing about sines and cosines if I plot on the blackboard for every angle if I plot sine or cosine along the horizontal axis supposing I plot cosine of theta along the horizontal axis and sine of theta along the vertical axis then if I plot all possible angles they will correspond to a bunch of points that lie on a unit circle Y on a unit circle because sine squared plus cosine squared equals 1 so one might call the properties of sine and cosine the properties of circular functions circular in that they're convenient for rotating they're convenient for describing unit circles points on unit circles are described in terms of coordinates which are cosines and sines of angles and so forth it's natural to call them circular functions these are these are not the functions that come in to the transformation the new transformation properties first of all these are wrong and I don't want to use X what's X ya ya now just wrong Newton had it wrong Newton or Galileo however it was postulated who postulated it Einstein modified it now we're going to have to make sure that Einstein's modification doesn't change things in situations where Newton knew where Newton's equations were good approximations the situations where I'm Stan's modifications are important is when we're talking about frames of reference moving very rapidly up near the speed of light before the 20th century nobody or nothing had ever moved faster than a hundred miles an hour probably well of course some things did light did but for all practical purposes light didn't travel at all it's just when you turned on the switch the light just went on so light didn't travel nothing and anybody's experienced direct experience traveled faster than 100 or 200 miles an hour and well I should say nothing travels faster than 100 miles an hour and then live to tell about it so all of experience was about very slow velocities on the scale of the speed of light on the scale of such velocities newton's formulas must be correct they work they're they're very useful they work Nutan got away with it so there must be good approximations it better be that whatever einstein did to the equations in particular to these two equations here had been a reduced to newton's equations in the appropriate limit okay let's come back now to light light according to the Newton formulas doesn't always move with the speed of light but let's let's try to figure out what it would mean of a better formula of a replacement for this but light always moves with the speed of light first of all let's set the speed of light equal to one that's a choice of units in particular it's a choice of the relation between space units and time units if we work in our light years for spent for a distance and years for time then light moves one light year per year the speed of light is one if we use seconds and light seconds it's also one whatever whatever scale we use for space if we use for time the time that it takes light to go that distance one unit of space if we use that for time units then the speed of light is equal to one now from the ordinary point of view of very slowly moving things those are odd units but if we were electrons with neutrinos and whizzing around like photons they would be the natural units for us speed of light equals one so let's set the speed of light equal to one as I said it's just the choice of units and then a light ray moving to the right just moves along a trajectory x equals T C is just equal to one a light ray moving to the left is x equals minus T how can we take both of these equations and put them together sorry x equals minus T can I write a single equation which if it's satisfied is a light ray either moving to the left or to the right yes here's an equation x squared equals T squared it has two solutions x equals T and X equals minus T the two square roots or x squared equals T squared is equivalent to either x equals T or x equals minus T in other words this equation here has the necessary and sufficient condition for describing the motion of a light ray either to the right or to the left supposing we found a replacement for this equation which had the following interesting property that whenever let's let's write it this way X square minus T squared equals 0 this is even better for our purposes x squared minus T squared equals 0 that's the necessary and sufficient condition to describe the motion of a light ray supposing we found a new set of rules a new set of transformation properties which which um had the property that if x squared minus T squared is equal to 0 then we will find that X prime squared minus T prime squared is equal to 0 in other words supposing this implied this and vice-versa then it would follow that what the unprimed observer you and your seats see is a light ray the primed observer me moving along also see as a light ray both of us agreeing that light rays move with unit velocity now this doesn't work for Newton's formula here it just doesn't work if X is equal to T it does not follow that X prime is equal to the T prime in fact it says something quite different okay so the form of these equations must be wrong let's look for some better equations now at this point let's in fact let's even be a little bit more ambitious it turns out being a little bit more ambitious actually simplifies things let's not only say that when X square minus T squared is equal to zero then X prime squared minus T prime squared is equal to zero let's say something even bolder let's say the relation between XT and X prime T prime is such that x squared minus T squared is equal to X prime squared minus T prime squared in other words pick any X and any T and calculate X square minus T squared then take the same point except reckoned in the primed coordinates in other words we take a certain event a light bulb goes off someplace you say that corresponds to X and T I say it corresponds to X Prime and T Prime but let's require just to try it out see if we can do it let's look for transformations so that X square minus T squared will always be equal to X prime squared minus T's prime squared that would be enough to ensure that everybody will agree about the speed of light why if x squared minus T squared equals X prime minus T prime squared for all X and T and so forth then when X square minus T squared equals zero X prime minus T prime squared will be zero and then if this is a light ray so is this a light ready everybody get the logic ok good so let's assume now that let's ask can we find transformations which have this particular property now it's not so different from looking for transformations which preserve x squared plus y squared equals x prime squared plus y prime squared it's just a little minus sign other than a minus sign here X square minus T squared look of these two is very similar and the mathematics is quite similar here are the transformations which preserve x squared plus y squared what are the transformations which preserve x squared minus T squared well they are the Lorentz transformations they are the fundamental transformations of the special theory of relativity they're not this but they're closely related or perhaps one should say closely analogous to these equations here but we have to substitute for circular trigonometry hyperbolic trigonometry so let's go back and remember a little bit about hyperbolic functions instead of circular functions well I didn't want to erase that all right these are the basic rules governing circular functions cosine theta this sine theta is equal to this and the e to the I theta in terms of cosine and sine all right let's see if we have a yeah we do have a blank blackboard here let me write whoops what did I do here I erased something I didn't mean to erase incidentally does everybody see how I got this side from the side you just add and subtract the equations appropriately and you isolate it to the I theta e to the minus R theta that's elementary exercise alright hyperbolic functions what are hyperbolic functions alright those are functions of the form hyperbolic cosine cosh hyperbolic cosine first of all the angle theta is replaced by a variable called Omega which I will call Omega Omega is called a hyperbolic angle it doesn't go from zero to two pi and then wind around on a circle it goes from minus infinity to infinity goes from minus infinity to infinity so it's a variable that just extends over the entire real axis but it's defined in a manner fairly similar to cosine and sine cosh Omega is by definition you're not allowed to ask why this is definition e to the Omega plus e to the minus Omega over 2 all we do is substitute for theta or for Omega theta I theta substitute Omega and that gives you hyperbolic functions likewise or similarly there's the hyperbolic sine and that's given by e to the Omega minus e to the minus Omega over 2 essentially you throw away all eyes out of that formula out of the top formulas just throw away all Sun all eyes the equations on the right-hand side become e to the Omega equals hyperbolic cosh Omega plus sin Chi Omega and e to the minus Omega equals cosh so mega- cinch Omega I think that's right is it right gosh – cinch it is yeah it is right okay now what about the analog of cosine squared plus sine squared equals one that simply came by multiplying this one by this one so let's do the same operation multiplying e to the Omega by each by e to the minus Omega gives one and now that gives cosh squared minus cinch squared you see we're getting a minus what we want we want that minus the minus is important we want the well somewhere is under here was a formula with a minus sign yeah we want to get that – into play here that's cos Omega squared knockouts Prakash squared Omega minus sin squared Omega so it's very similar everything you want to know about hyperbolic trigonometry and the theory of these functions is called hyperbolic trigonometry everything you ever want to know is codified in these simple formulas these in these and they're more or less definitions but there are the useful definitions now yeah go ahead yeah not only is it worth mentioning I was just about to mention it so I squared minus y squared is what hyperbola yeah right exactly so if I were to play the same game that I did here namely plot on the horizontal and vertical axis the values not of cosine of theta and sine of theta but cosine cosine cosh of that of Omega and since Omega what's in other words on the x-axis now we're going to plot cos Omega and on the y-axis cinch Omega then this is a hyperbola not a circle but a hyperbola and it's a hyperbola with asymptotes that are at 45 degrees you can see let me show you why why the asymptotes are at 45 degrees when Omega is very large when Omega is very large then e to the minus Omega is very small right when Omega is very large e to the minus Omega is very small and that means both cosh and cinch are both essentially equal to e to the plus Omega in other words when Omega gets very big cosh and cinch become equal to each other and that's this line here cash equals cinch along this line here so when Omega gets very large the curve asymptotes to to a curve which is a 45 degrees it's not hard to see that in the other direction when Omega is very negative that that it asymptotes to the other asymptotic line here so that's why it's called hyperbolic geometry it the hyperbolic angle the hyperbolic angles the caches the cinches play the same role relative to hyperbolas as sines and cosines do two circles any questions No so cosh Omega equals zero how would you plot that hi purple okay show me hmm Oh cos squared minus sin squared equals zero no that's no no cos squared minus sin squared equals one in the same sense that sine squared plus cosine square it never equals zero I think what I think you want to ask a different question I think oh well since Omega equals zero is the horizontal axis the costume a equals zero is the vertical eyebrows right okay well this is the x-intercept yeah it's it's the vertex I just think here's one point on a minute oh man the x-intercept there is one yeah because Kostroma cost of zero is one to see that just plug one r 0 in here 1 plus 1 divided by 2 is 1 at least it was yesterday yeah stores okay so now we we're sort of starting to cook a little bit we're starting to see something that has that nice minus sign in it but what's it got to do with X and T and X Prime and T prime we're now set up to make let's call it a guess but it's a guess which is based on the extreme similarity between hyperbolas and circles cautions and cosines and so forth he is the guess I'm going to make and then we'll check it we'll see if it does the thing we wanted to do my formula instead of being this has gotten with and we're now going to have instead of x and y we're going to have x and t time and x later on we'll put back y&z we're going to have to put back y&z but they're very easy okay so let's start with X prime X prime is the coordinate given to a point of space-time by the moving observer namely me and I'm going to guess that it's some combination of X and T not too different but not the same as where is it X prime equals X minus VT I'm going to try cosh Omega X let's write X cos Omega minus T sin Omega sort of in parallel with this I could put a plus sign here but you can go back and forth between the plus and the minus by changing the sign of Omega just as you did here so this let's do it this way X cos Omega minus T sin Omega and T prime going to look similar but without the extra minus sign here this you know the relation between sines cosines and cautious and cinches is one of just leaving out an eye you go from sines and cosines the clashes and cinches by leaving out the I well if you track it through carefully you'll find that this minus sign was really an I squared it's not going to matter much I will just tell you it was really came from some I squared and if you leave out I I squared just becomes one squared is no minus sign so here's the guess for the formula connecting X prime T Prime with X and T it equals let's say X since Omega – no – plus T cos Omega in this case there are two minus signs in this case there was only one minus sign okay but but let's check what do we want to check we want to check that X prime squared minus T prime squared is equal to x squared minus T squared your ask you're probably asking yourself what is this Omega what does it have to do with moving reference frames I'll tell you right now what Omega is it's a stand-in for the velocity between the frames we're going to find the relationship between Omega and the relative velocity of the reference frames in a moment there has to be a parameter in the lower end these are the lines in these are the Lorentz transformations connecting two frames of reference in the Lorentz transformations as a parameter it's the velocity the relative velocity that parameter has been replaced by Omega it's a kind of angle relating the two frames a hyperbolic angle but we'll we'll come back to that for the moment let's prove that with this transformation law here that X prime squared minus T prime squared is equal to zero ah is equal to X square minus T squared I'm getting to that point in the evening where I'm going to make mistakes all right this is easy you just work it out you use all you have to use is that cosine squared minus sine squared is 1 you can work that out by yourself but we can just see little pieces of it here X prime squared will have x squared cos squared Omega t prime squared will have x squared sin squared Omega if I take the difference between them I'll get a term with an x squared times cos squared minus sin squared but cos squared minus sin squared is one fine so we'll find the term with an x squared when we square take the square of the difference between the squares of this and this and likewise will also find the T squared the cross term when you square X Prime you'll have XT cost cinch when you square T Prime you'll have XT costs inch when you subtract them it'll cancel and it's easy to check that's our basically one liner to show that with this transformation here x prime squared minus T's prime squared is x squared minus T squared which is exactly what we're looking for let me remind you why are we looking for it if we find the transformation for which the left-hand side and the right-hand side are equal then if x squared equals T squared in other words if the right-hand side is 0 the left-hand side will also be 0 but x squared but x equals T that's the same as something moving with the speed of light in the X frame of reference if this being 0 is equivalent to the left hand side being 0 it says that in both frames of reference the light rays move with the same velocity so that's the basic that's the basic tool that we're using here X prime squared minus T prime squared is equal to x squared minus T squared all right that does follow by a couple of lines using cos squared minus N squared equals 1 but what I want to do let's take another couple of minutes now let's take a break for five minutes and then come back and connect these variables Omega with the velocity of the moving frame of reference somebody asked me a question about the ether and what it was that people were thinking somehow Einstein never got trapped into this mode of thinking um well what were they thinking about when they were thinking about the ether what exactly was the michelson-morley experiment well I'll just spend the minute or two mentioning it certainly Maxwell understood that his equations were not consistent with with Newtonian relativity he understood that but his image of what was going on is that the propagation of light was very similar to the propagation of sound in a material or water waves propagating on water and of course it is true that if you move relative to the atmosphere or move relative to the substance that sound is propagating in you'll see sound move with different velocities depending on your motion if you're at rest in a gas of material isn't there's a natural sense in which is a particular rest frame the rest frame is the frame in which on the average the molecules have zero velocity if you're in that reference frame then first of all light has the same velocity that way as that way number one and it has a velocity that's determined by the properties of the fluid that the sound is moving in okay Maxwell more or less thought that light was the same kind of thing that there was a material and the material had a rest frame and that particular rest frame was the frame in which light would move with the same velocity to the left as to the right and he thought that he was working out the mechanics or the behavior of this particular material and that we were pretty much at rest relative to this material and that's why we saw light moving the same way to the left of the right one would have to say then that Maxwell did not believe that his equations were a universal set of laws of physics but that they would change when you moved from frame to frame just happened by some luck we happen to be more or less at rest relative to the ether to this strange material um of course you could do an experiment with sound if you're moving through the sound you can check that the velocity in different directions is different you do let's not worry exactly how you do that that's what the Michelson Morley experiment was Michelson and Morley I suppose said look the earth is going around in an orbit maybe at one season of the year we just happen to be at rest relative to the ether by accident and some other season six months later we're going to be moving in the opposite direction and we won't well we won't be at rest only at one point in the orbit could we be at rest relative the–this or at any other point in the orbit we wouldn't be so if we measure in November that light moves the same than all possible directions then in what's what's the opposite of November May then in May we should find that light is moving with great with the different velocities in different directions and he tried it and a very fancy and sophisticated way of measuring the relative velocity in different directions but he found that there was no discrepancy that the light traveled the same velocity in every direction at every time of year there were all sorts of ways to try to rescue the ether but none of them worked none of them work and the result was one had to somehow get into the heart of space and time and velocity and mid distance and all those things in a much deeper way in a way that didn't involve the idea of a material at rest in some frame of reference that that propagated the light okay oh where are we I forgotten where we were when we stopped somebody remind me whoo-hah Omega yeah what is Omega forgotten Omega Oh how Omega is really metal speed of light but to the velocity of the moving reference frame here we have two reference frames X T and X Prime and T prime what's the relationship between them well the whole goal here was to understand the relationship between frames of reference moving with relative velocity between them Omega is not exactly the relative velocity but it is closely related to it okay let's say let's see if we can work out the relationship we know enough to do it let's see if we can work out the relationship between Omega and the velocity of the moving frame all right again let's go back to this picture there's a frame of reference moving let's redraw it here's my origin moving along okay what does it mean to say that from your perspective my frame of reference so my origin is moving with velocity V well by definition this is not a law now this is a definition and says that this line here has the equation x equals VT that's the definition of this V here my origin moves relative to your origin it moves with a uniform constant velocity that's an assumption that we're talking about two inertial frames of reference and you in your frame of reference will write x equals VT that's the definition of V if you like what will I call it I will call it X prime equals zero all along there I will say X prime is equal to zero it's my origin of coordinates okay now let's come to this transformation law here and see if we can spot how to identify V well X prime equals zero that's this trajectory moving at an angle with a velocity V X prime equals zero is the same as saying X cos Omega equals T sin Omega X prime equals zero set this side equal to zero and that says that X cos Omega equals T sin Omega all right so whatever the connection between velocity and Omega is it must be such that when X prime is equal to zero X cos Omega equals T sin Omega well let's look at that equation it also says that X is equal to sin CH Omega over cos Omega times T well that's interesting because it's also supposed to be equivalent to x equals VT now I know exactly how to identify what the velocity is as a function of Omega the velocity of the moving transformation the moving coordinate system must just be sin Chi Omega over cos Omega that's the only way these two equations can be the same x equals VT x equals sin Chi Omega over cos Omega times T so now we know it we know what the relationship between velocity and Omega is write it down the velocity of the moving frame now this is not the velocity of light it's just the velocity of the moving frame must just be cinch Omega over cos omega well actually i want to invert this relationship i want to find sin and cos omega in terms of the velocity i want to rewrite these Lorentz transformations where are they i want to rewrite these Lorentz transformations in terms of the velocity that's the familiar form in which you learn about it in in elementary relativity books X prime is equal to something with velocities in it to exhibit that all we have to do is to find Cinch and cosh Omega in terms of the velocity that's not very hard let's let's work it out the first step is to square it and to write V squared is equal to cinch Omega squared over cosh Omega squared that was easy next I'm going to get rid of since Omega squared and substitute where is it I lost it one is equal to cos Omega squared minus cinch Omega squared alright so wherever I see cinch Omega squared I can substitute from here namely cosh squared Omega minus one is equal to sine squared Omega so here we are this is just equal to hash of Omega squared minus one divided by cost of Omega squared or let's multiply by what I want to do is solve for cost Omega in terms of velocity I want to get rid of all these cautions and cinches of Omega and rewrite it in terms of velocity so first x cost Omega squared we have cosh squared Omega times V squared equals cosh squared Omega minus one or it looks to me like this is cosh squared Omega times one minus V squared equals one what I've done is transpose yeah cos squared times V squared minus cos squared itself that gives you cos squared 1 minus V squared equals 1 change the sign can everybody see that the second line follows from the first I'll give you a second yeah yeah yeah it's clear ok finally we get that cos Omega is equal to 1 divided by 1 minus V squared but now I have to take the square root cos Omega / one minus V squared and then take the square root and that gives you cos Omega now we've all seen these square roots of 1 minus V squared in relativity formulas here's where it begins the kayne we begin to see it materializing what about sin Chi Omega let's also write down sin Chi Omega well from here we see that sin Chi Omega is just equal to V times cos Omega this is easy since Omega equals V times cos Omega sorrow sin Chi Omega is V divided by square root of 1 minus V squared let's go back to these Lorentz transformations over here and write them getting rid of the trigonometric functions the hyperbolic trigonometric functions and substituting good old familiar velocities let's get rid of this and substitute the good old ordinary velocities ok so we have here X prime equals x times cos Omega and that's divided by square root of 1 minus V squared then this minus T times sin Omega which is V over the square root of 1 minus V squared or if I put the two of them together and combine them over the same denominator it's just X minus VT divided by square root of 1 minus V squared I think most of you have probably seen that before maybe slightly different let's let's clean it up a little bit X prime equals X minus VT divided by the square root of 1 minus V squared what about T prime T Prime is equal to t minus V X over square root of 1 minus V squared T prime is equal to T times cos cost is just 1 over square root and then x times sin CH that gives us the extra V in other words the formulas are more or less symmetrical and those are all good old Lorentz transformations now what's missing is the speed of light let's put back the speed of light the put back the speed of light is an exercise in dimensional analysis there's only one possible way the speed of light can fit into these equations they have to be modified so that they're dimensionally correct first of all one is dimensionless has no dimensions it's just one velocity is not dimensionless unless of course we use dimensionless notation for it but if velocity is measured in meters per second then it's not dimensionless how do we make V squared dimensionless we divide it by the square of the speed of light in other words this V squared which is here which has been defined in units in which the speed of light is 1 has to be replaced by V squared over C squared likewise over here V squared over C squared now velocity times time does have notice first of all the left hand side has units of length the right hand side this is dimensionless X has units of length but so does velocity times time so this is okay this is dimensionally consistent as it is but over here it's not the left hand side has dimensions of time that's all right 1 minus V squared over C square that's dimensionless this has units of time but what about velocity times X velocity times X does not have units of time in order the given units of time you have to divide it by C square okay let's check that velocity is length all the time times length divided by C squared that's length square R which gets correct but it's correct all right this is probably familiar to most of you who've seen relativity once or twice before these are the equations relating to different moving coordinate systems moving relative to the x axis but you see the deep mathematics or the mathematical structure of it in many ways is best reflected by this kind of hyperbolic geometry here and you know most physicists by now never write down the Lorentz transformations in this form much more likely to write them in this form easier to manipulate easier to use trigonometry or or hyperbolic trigonometry it's a little exercise it's a nice little exercise to use this the hyperbolic trigonometry to compute their to compute the compounding of two Lorentz transformations if frame two is moving relative to frame one with velocity V and frame three Israel moving relative to two with velocity V Prime how is three moving relative to one the answer is very simple in terms of hyperbolic angles you add the hyperbolic angles not the velocities but the hyperbolic angles the hyperbolic angle of three moving relative to one is the hyperbolic angle of three moving relative to two plus two moving relative to one and then you use a bit of trigonometry or hyperbolic trigonometry to figure out how you do the inches and kosh's of the sum of 2 hyperbolic angles very straightforward and I'll leave it as an exercise to see if you can work that out much easier than anything else ok so there there we have the Lorentz transformations yeah oh oh absolutely yes that's that's that's a good point yeah when we that's right if we have frame 1 let's call this x1 and y1 x2 and y2 and finally x3 and y3 well then the angle of – let's call F of 3 relative to 1 let's call it theta 1 3 is just equal to theta 1 2 plus theta 2 3 the angle connecting frame one with frame 3 is just the sum of the angle theta 1 2 plus theta 2 3 so in that respect the Lorentz transformations are much simpler in terms of the Omegas it's the Omegas which combined together to add when you add velocities now how different is omega from the velocity let's work in units in which the speed of light is equal to 1 where is our formula for velocity all right let's take this formula over here what a cinch Omega 4 small Omega let's put the C squared there a let's not put the C square there or not put the C square there since Omega is essentially Omega when Omega is small just like sine is omega where is theta when theta is small the cinch function the cost function looks like like this the cinch function looks like this but it but it crosses the axis with a slope of 1 for small Omega cinch Omega is proportional to Omega for small velocity one minus V squared is very close to 1 if the velocity is a hundredth of the speed of light then this to within one ten-thousandth is just 1 if we're talking about velocities a millionth of the speed of light then this is very close to 1 and so since Omega and velocity are very close to each other it's what's going on here Thanks okay so for small velocities Omega and velocity are the same the actual correct statement is that V over C is like Omega the dimensionless velocity over the speed of light is like Omega for small Omega and small velocity so for small velocity adding velocities and adding omegas are the same things but when the velocities get large the right way to combine them to find relationships between different frames is by adding Omega and not adding velocities when you add Omega like compounding velocities as you've got it there I guess you won't go greater than 45 degrees that guess because that would be faster than light no but Omega no more you see this bit the speed of light is V equals one that corresponds to Omega equals infinity yeah yeah so Omega Omega runs over the whole range from minus infinity to infinity but when it does V goes from minus the speed of light to the speed of light so you can add any omegas and still add any omegas Omega that's right there's no there's no speed limit on Omega is this like we just go on that diagram it looks like it's greater than 45 degrees if here where where I make a and I guess they use the definition of state along the hyperbola yeah that's right sorry where are we right there today I guess that's theta though isn't it this is Theta that's a good oh god yeah right right yeah Omega is the distance along hyperbola that's right distances that's right Omega is a kind of distance along the hyperbola all right now let's let's talk about that a little bit all right now that we've established the basic mathematics structure of the transformations I think we should go back and talk about some simple relativity phenomena and derive them oh one thing which is important which I yeah well let's see we're here are my Lorentz transformations over here I said we should we ought to at the end make sure that our transformations are not too dissimilar from Newton's in particular when the velocities are small they should reduce to Newton that's all we really know that's or at least that's all that Newton really had a right to assume that when the velocities are smaller than something or other that his equations should be good approximations isn't adding velocity good enough isn't velocities adding good enough in fact you're right in fact you're right but let's just look at the transformations themselves all right as long as the velocity is a small percentage of the speed of light an ordinary velocities are what a hundred miles an hour versus 186,000 miles an hour what is that it's small right and it's doubly small when you square it so for typical ordinary velocities even the velocities of the earth around the Sun and so forth fairly large velocities what 60 kilometers per second or something like that 60 kilometers per second is pretty fast that's the that's the orbital earth around the Sun it's pretty fast but it's nowhere near 300,000 kilometers per No yeah looks here on a thousand meters per second we're I'm sorry three times ten to the eighth no three times three hundred thousand kilometers per second right 60 kilometers per second three hundred thousand kilometers per second small fraction and then square it so for ordinary motions this is so close to one that the deviation from one is negligible so let's start with the top equation for the top equation this is negligible and it's just x prime equals X minus VT the bottom equation here you have a C squared in the denominator whenever you have a C squared in the denominator that's a very very large thing in the denominator this is negligible compared to T so here the speed of light is also in the denominator just forget this and it's just T but it's just T prime equals T it's just D prime equals T so in fact Newton's formulas are essentially correct for slow velocities no no significant departure from Newton until the velocities get up to be some some appreciable fraction of the speed of light okay let's talk about proper time proper time and then let's do a couple of relativity examples yeah question the bottom equation when X is very large yes that's right when X is exceedingly large you get a correction but that correction that X has to be very large look let's let's discuss before we do anything else let's let's let's talk about that a little bit X minus VT one minus V squared over C squared yeah let's alright in my drawings I'm going to sitt C equal to one but in the equations you can leave the C there okay this equation we understand apart from this one minus V squared over C squared in the denominator it's just this x equals V T or X minus V X minus X minus VT that's Newton let's look at this one over here okay let's look at the surface T prime equals zero T prime equals zero is the set of points that I in my moving reference frame call T call time equals zero it's what I call the set of points which are all simultaneous with the origin T prime equals zero is just everyplace in space-time which has exactly the same time according to my frame of reference and I will therefore call all those points synchronous at the same time what do you say about them if T prime is equal to zero that says that T is equal to V over C squared X now let's set C equal to one for the purpose of drawing just for the purpose of drawing I don't want this huge number C squared to distort my drawings too much it says the T equals V X what does the surface T equals V X look like it looks like this T equals V X which is also X is equal to 1 over V T so it's just a uniform line like that all of these points are at different times from your reckoning this ones later this ones later this ones later and so forth according to my reckoning all these points are at the same time so we disagree about what's simultaneous this was this was the hang-up incidentally this was the basic hang-up that took so long to overcome that took Einstein to overcome it the idea that simultaneity was the same in every reference frame nobody in fact it was so obvious that nobody even thought to ask a question is simultaneous does it mean the same thing in every reference frame no it doesn't in more in your reference frame the horizontal points are all simultaneous with respect to each other in my reference frame what I call horizontal what I call simultaneous you do not okay so simultaneity had to go let me point out one more thing about these equations I'm not going to solve them for you but I will tell you the solution anyway how do you solve for X and T in terms of X Prime and T Prime well think about it in the case of angles supposing I have a relationship like X prime is equal to X cosine theta what is it plus plus y sine theta and y prime is equal to X minus X sine theta plus or Y cosine theta and supposing I want to solve for x and y in terms of X Prime and Y Prime you know what the solution is just change theta 2 minus theta and write that X is equal to X prime cosine of minus theta but what's cosine of minus theta right cosine theta plus y sine of minus theta what's sine of minus theta minus sine theta times y and likewise for y prime Y prime is equal to minus x times sine of minus theta so that becomes plus X sine theta plus y cosine of minus theta which is cosine theta you don't have to go through the business of solving the equations you know that if one set of axes is related to the other by rotation by angle theta the second one is related to the first one or vice versa the first one is related to the second one by the negative of the angle if to go from one frame to another you rotate by angle theta and to go from the second frame back to the first you rotate by angle minus theta so you just write down exactly the same equations interchange Prime and unprimed and substitute for theta minus theta same thing for the Lorentz transformations exactly the same thing if you want to solve these for X and T write down the same equations replace primed by unprimed and change the sign of omegas to minus the sines of omegas change sinus rgn of all the sign all the cinches okay in other words just send Omega 2 minus Omega and that will solve the equations in the other direction yeah yes it's also the same as changing V 2 minus V yes the way to see that is to go right what was it what do we have cosh Omega yep yeah that's right via sign yes that was correct yeah you just well you change Omega 2 minus Omega it has the action of changing V 2 minus V you can just check that from the equations good alright let's let's talk about proper time a little bit proper time if you're doing ordinary geometry you can measure the length along a curve for example and the way you do it is you take a tape measure and you you know sort of take off you take off equal intervals equal equal little separations you can think of these separations as differential distances DS squared small little differential distances and that differential distance is d x squared plus dy squared with the x squared and the y squared are just the differential increments in x and y DX and dy this is d s alright so that's the way and you add them up you add them up that's the way you compute distances along curves it's quite obvious that if you take two points the distance between those two points depends on what curve not the same for every curve so I'll measure the longer curve you have to know not only the two points but you have to know the curve in order to say what the distance between those points are of course the distance between its longer straight line that's that's well-defined but the distance along a curve depends on the curve in any case D s squared equals the x squared plus dy squared is the basic defining notion of distance between two neighboring points if you know the distance between any two neighboring points in a geometry you basically know that geometry almost essentially completely so given this formula for the distance between two points you can compute if you like the distance along a curve because you've got to take the square root of this and then add them up don't anhedonia the squares add the differential distances all right the important thing is here that square root of DX squared plus dy squared which is the distance between neighboring points doesn't depend on your choice of axes I could choose X Y axes I could choose X prime y prime axes if I take a little differential displacement the X and the y or I just take two points two neighboring points don't even give them labels and measure the distance between them the distance between them should not depend on conventions such as which axes are used and so when I make rotational transformations the X square plus dy squared doesn't change the X and the y may change but the x squared plus dy squared does not change the same thing is true in relativity or the analogous thing we don't measure distances along the paths of particles let's say now that this curve here is the path of a particle moving through space-time there's a particle moving through space-time and we want some notion of the distance along it the notion of distance along it another example would just be a particle standing still as a particle standing still particle standing still is still in some sense moving in time I wouldn't want to say that the distance between these two points and space-time is zero they're not the same point I wouldn't like to say it's zero I would like to say there's some kind of notion of distance between them but it's quite clear that that distance is not measured with a tape measure this point and this point are the same point of space boom here at this point of space and that at a later time boom again at the same point of space two events at the same point of space how do I characterize and some nice way the distance between those two events that occurred in the same place you don't do it with a tape measure all right what do you do with a clock a clock you take a clock and you start it at this point tic tic tic tic tic tic tic a stopwatch you press it at this point tic tic tic tic tic it picks off intervals and then you stop it at that point and you see how much time has evolved that's a notion of distance along a particle trajectory it's not the distance the particle moves in space it's a kind of distance that it's moved through space-time and it's not zero even if the particle is moving standing perfectly still in fact what it is is it's the time along the trajectory what about a moving particle well you can imagine that a moving particle carries a clock with it of course not all particles carry clocks but we can imagine they carry clocks with them as they move and we can start the clock over here and then the clock over here what is the time read off by this moving clock the time read off by a moving clock is much like the distance along a curve measured by a tape measure in particular it should not depend on the choice of coordinates why not this is a question that has nothing to do with coordinates I have a clock made in the standard clock Factory the standard clock Factory and I don't know we're in Switzerland someplace makes a certain kind of clock that clock gets carried along with a particle and we ask how much time evolves or how much time elapses or how much the clock changes between here and here that should not depend on a choice of coordinates it shouldn't depend on a choice of coordinates because it's a physical question that only involves looking at the hands of the clock in fact we can ask it for little intervals along along the trajectory we could ask how much time elapses according to the clock between here and here well the answer again should not depend on what coordinates you use which Lorentz frame you use and there's only one invariant quantity that you can make out of the D X's and DTS describing this point describing these two points there's a little interval DT and there's a little interval DX now we're in space and time not ordinary not ordinary space and the quantity which is invariant there's really only one invariant quantity that you can make out of it it is DT squared minus DX squared it's the same quantity x squared minus T squared for a whole you know for a whole interval the T squared minus DX squared that's the quantity which is invariant it's minus D it's the negative of what I wrote over here x squared minus T squared okay this quantity is equal to the X prime squared minus DT power sorry DT prime squared minus the X prime squared the same algebra goes into this as goes into showing that X prime squared minus T prime squared equals x squared minus T squared incidentally this is the same as saying T prime squared minus X prime squared equals T squared minus x squared doesn't matter which way you write it all right so that suggests that suggests that the time read off the invariant time read off along a trajectory between two points separated by DX and DT is just the square root of DT squared minus DX squared why the square-root incidentally okay you're going to integrate in detail I can integrate DT yeah well alright why not just DT square minus the x squared for the time between here and here is it here's an answer supposing we go to you two intervals exactly the same as the first one we go an interval over here DX and DT and then we go another DX in DT what happens when we double the interval to DT squared minus DX squared it gets multiplied by four because everything is squared well I wouldn't expect a clock when it goes along you know when it goes along a trajectory for twice the the interval here to measure four times the the time I expected to measure twice the time so for that reason the square root is the appropriate thing here okay that's called D tau squared the tau squared the proper time along the trajectory of an object you're right that's just the towel or D tau squared being the x squared minus DT squared the Tau is called the proper time let's go I think we'll let's see the towel is called the proper time and it is the time read by a clock moving along a trajectory it's not just DT that's the important thing it's not just DT the T squared minus the x squared let's do one last thing let's just do the twin paradox in this language I think I think I've had it I'm going to finish you can do the twin paradox in this language all you have to do is to compute the proper time along two trajectories one that goes out with a uniform velocity turns around and comes back with the same uniform velocity versa a trajectory which just goes from one point to the st. the another point along a straight line and it's no more weird it's no weirder really from this perspective than saying the distance from one point to another along two different curves do not have to agree the proper time along two different curves in general will not agree what is a little bit weird is that because of this minus sign the proper time this way is less than the proper time this way that's the consequence of this minus sign here moving with some DX decreases the proper time all right we'll do a little bit more next time but then I want to get to the principles of field theory and and connect some of this with field equations for interesting wave fields the preceding program is copyrighted by Stanford University please visit us at stanford.edu

Historical Lies That Will Make You Rethink Your Entire Education

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The Real Meaning of E=mc² | Space Time | PBS Digital Studios

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You’ve probably known OF E=mc² since you were born, and were also probably told that it meant that it proved Mass equaled Energy, or something along those lines. BUT WAIT. Was E=mc² explained to you properly? Mass equalling energy is mostly true, but E=mc² actually describes a much more interesting, and frankly mind-blowing aspect of reality that likely wasn’t covered in your high school physics class. Join Gabe on this week’s episode of PBS Space Time he discusses THE TRUE MEANING OF E=mc²

Extra Credit:

Einstein’s 1905 E=mc^2 paper (English translation):

(more modern notation)

Veritasium: Your Mass is NOT From the Higgs Boson



Ryan Brown

David Shi


Jay Perrin


Movement 3 – Janne Hanhisuanto (
miracle – slow (
Secret Society – Logical Disorder (
Saw Slicing – Patternbased (
Dr Dreidel – Patternbased (
Earth Breath – Human Terminal (
Pinball Beat – Patternbased (
Heisse Luft – Thompson and Kuhl (

New SpaceTime episodes every Wednesday!

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What Happens At The Edge Of The Universe?

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What Happens At The Edge Of The Universe?

Voice over:

What Would Happen If The Sun Suddenly Disappeared?

Have you ever wondered what might lie at the end of the universe? It’s amazing to imagine what it could be like at the very edge of the universe, what it looks like, what is out there. If it were possible to see this part of space, we would see the beginning of the universe as it began. But once something slips past the event horizon, it becomes lost to our sight, no longer giving off light signals.

Spacetime is a fascinating subject. One that needs to be explored to fully understand just how big the known universe is. So let’s take a journey to the outside of the known universe and answer: What Happens at The Edge of the Universe.

Lee Smolin Public Lecture Special: Einstein’s Unfinished Revolution

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On April 17, in a special webcast talk based on his latest book, Einstein’s Unfinished Revolution, Perimeter’s Lee Smolin argued that the problems that have bedeviled quantum physics since its inception are unsolved and unsolvable for the simple reason that the theory is incomplete. There is more to quantum physics waiting to be discovered.

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Oxbridge Philosophy – John Cleese & Jonathan Miller

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From the second Amnesty gala “An Evening Without Sir Bernard Miles” which took place in 1977.

Originally written for the 1960s British comedy stage revue “Beyond the Fringe” which starred Peter Cook, Dudley Moore, Alan Bennett, and Jonathan Miller.

hmm victim Stein says doesn't it John says blue and brown looks every well the statement fetch me that /w saying statement it for that snap going if I is lab is a snap you stab such that where I to fit you the statements pitch with that slab will be disjunctive Lee tonight Oh God yes well she gave me a keep me keep me baby try to favorite roller primitive camp stake yeah yeah rather pretty thick in the sense it the unfit slabs you see young bitch slap snap and claim to exist if they really know more than the unseat three in the quad no I think you're making a rather primitive kappa runescape no you're not it's me yes yes I love it coming are you using here yeah in the affirmative say hey did you I like the paper like because it has to bear on something that I'm considering myself at the moment namely what what part what what and know me as philosophers how to play in this business and confusing heterogeneous confusing and confused on the political social economical societies one other people have jobs to do I mean what what what what what jobs do people do these days they chop down trees they choke countries they drive buses they play game now we also play games but as philosophers if we play languages goes um at language now when you and I go to the cricket pitch we do so secure in the knowledge that a game of cricket is in the offing but when we play language games we do so rather in order to find out what game it is that we're pain in other words him why do philosophy at all in yeah what yeah what yeah what no no the neck agency I think the burden is fair and square on your shoulders b/c it restrains me in the exact road the philosophy has in everyday life yes waiting I can do this no this morning I walked into a shop yeah and a shop assistant was having an argument with a customer the shop assistant said yes and a customer said what do you mean yes and the shop assistants head I mean yes now here we have let me have a splendid example to to do then you only people are asking each other what are innocents them the metaphysical question mmm what do you mean yes I mean yes as ever that's almost where I as a philosopher a good'n welcome yeah did you well never they were in rather a hurry

Philosophy of Science with Hilary Putnam

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Bryan Magee and Hilary Putnam discuss some of the basic issues in the philosophy of science and the philosophy of mathematics including the nature of scientific knowledge, scientific method, demarcation, objectivity, the notion of truth (e.g. the correspondence theory), inductive logic, reductionism, the fact-value dichotomy, materialism, the nature of mathematics, etc.

Hilary Putnam was an American philosopher, mathematician, and computer scientist who was a central figure in analytic philosophy. He made important contributions to many fields, including logic, philosophy of mind, mathematics, philosophy of language, epistemology, and the philosophy of science.

Check out Putnam’s book “Reason, Truth, and History”:

This interview is from a 1978 BBC program, transcript/subtitles available.

Read more about some of these issues:
Scientific Realism & Antirealism:
Scientific Revolutions:
Social Dimensions of Scientific Knowledge:
Theory & Observation in Science:
Science & Pseudo-Science:
Scientific Objectivity:

The connection between philosophy and the
mathematical sciences has always been very close. Plato had written over the door
of his academy the words: "Let no one into here who
is ignorant of geometry". It was Aristotle who codified the
basic sciences into the categories and gave them the names
that we use to this day. Some of the greatest philosophers have
been themselves great mathematicians who invented new branches of mathematics. Descartes is an obvious example, and so is Leibniz
and Pascal. In fact, most of the great philosophers, not all, but most, came to philosophy from
mathematics or the sciences. And this tendency has continued into our present century. Bertrand
Russell was trained first as a mathematician. Wittgenstein was trained first as an engineer.
The reason for this persisting connection is I think obvious, and that is that the basic
urge which has driven most of the greatest philosophers has been the urge to deepen our
understanding of the world and of its structure. And this is also what creative scientists
are doing. For most of the past, too, people thought that mathematics was the most
indubitable knowledge as well as being utterly precise and clear that human beings possessed. So
there have always been plenty of philosophers examining mathematics to try & find out what
was so special about it, and whether this was something that could be applied to the acquisition
of other sorts of knowledge. Ditto with the sciences, which were also thought to yield a very
specially safe and certain kind of knowledge. What was it about science that made its results
so reliable? And could its methods, whatever these were, be used in other fields? These
investigations into the concepts and methods, procedures and models that are involved in
mathematics & science have come to be known as the philosophy of mathematics and the
philosophy of science. And it’s with these that we're going to be concerned in this program.
Chiefly, with the philosophy of science, though in fact, we have someone taking part who
is expert in both: Professor Hilary Putnam of Harvard University. Professor Putnam, I'd
like to start our discussion from a standpoint which I think a very large number of our viewers
occupy anyway, and it's really this. Since the 17th century I suppose, there's been a spectacular
decline in religious belief, especially in the west and especially among educated people.
And for millions, the role that used to be taken in life by a worldview based on religion
has been increasingly supplanted by a worldview based on science or at least purporting to
be derived from science, anyway. And this is still enormously powerful in the hold that
it has on people's minds throughout the west, probably it effects all of us. So I think I'd
like to start this discussion by getting you to pin-down that scientific world outlook
which is so influential in the modern world which will be underlying a lot of what we're going
to have to talk about. Let me dodge the question a little bit by talking not about scientists
think now but what many scientists thought 100 years ago or 75 years ago. Think of
doing a crossword puzzle. You might have to change a few things as you go along,
but towards the end, everything fits and things get added on one step at a time. That's the
way the progress of science looked for 300 years. In 1900, a famous mathematician, David
Hilbert, gave a list of 50 mathematical problems to a world congress of mathematicians which
are still very famous. And it's very interesting that he included one problem which we would
not call a mathematical problem very early in the list (I think problem 3) which was to put
the foundations of physics on a satisfactory basis. And that was for mathematicians, not for
physicists! The idea's—tiny it up. That's right. The idea is Newton, Maxwell, Dalton, and
so on, had all put in all the parts of the story, and now it was just for mathematicians
to basically clean up the logic, as it were. I think in a conversation we had a couple of days
ago, you described this as a "treasure chest" view, and I like that picture, because here's
this big chest that we're just filling up. It's an accumulation. You don't have to subtract,
you don't have to take out. Occasionally you make a little mistake, but basically the idea is
— or to shift the metaphor — like building a pyramid: you put down the ground floor,
then the next floor, and the next floor, it just goes up. That's part of this, a view
of knowledge as growing by accumulation. The other part of it is the idea that the special
success of the sciences — obviously what we're impressed by is success. This culture values
success and science is a successful institution. But there's the idea that science owes
its success to using a special method and that comes partly from the history of science,
from the fact Newton, for example, lived after Bacon and was influenced by Bacon. And the idea
that empirical science has grown up together with something called "inductive logic". And this
idea that there's a method, the inductive method, and that the sciences can be characterized
by the fact that they use this method and use it explicitly and consciously, as it were,
not unconsciously as maybe someone who's learning cooking might be using it, but pretty
deliberately and explicitly. So I think that these two things, the idea of knowledge as
growing by accumulation & growing by the use of a special method, the inductive method,
are the key elements of the old view. Yes, and if I were going to put the same thing
I suppose slightly differently, I think I'd say this: For two or three hundred years, educated western
man thought of the universe and everything in it as consistently of matter in motion. And that
was all there was, whether from the outermost galaxies of the stars into ourselves and our
bodies, and the cells of which we're made up, and so on. And that science was finding
out more and more about this matter and its structure and its motion by a method which
you just characterized as "scientific method". And the idea was that if we went on long enough,
we'd simply — as you said with your crossword puzzle metaphor — we'd find out everything
there was to find out. We could, eventually, by scientific methods, completely explain
and understand the world. Now, that has been abandoned by scientists, though, in fact,
this hasn't got through yet to the non-scientist. There are still large numbers of
non-scientists who go on thinking that that's how scientists think, but of course, they no
longer do, do they? This has started to break down. I think it started to break down with Einstein. If I
can drag in a bit of history of philosophy, screaming by the hair: Kant did something in philosophy
which I think has begun to happen now in science. He challenged a certain view of truth. Before Kant
no philosopher really doubted that truth was simply correspondence to reality — there are different
words, some philosophers spoke of "agreement". But the idea is a "mirror theory" of knowledge… Well Kant said it isn't so simple, there's a
contribution of the thinking mind. Sure, it isn't made up by the mind, Kant was no
Idealist; it isn't all a fiction, it isn't something we make up, but it isn't just a copy either.
What we call "truth" depends both on what there is, on the way things are, and on the
contribution of the thinker, the mind. I think that today scientists have come to a somewhat
similar view. That is, since the beginning of the 20th century, the idea that there's a
human contribution, a mental contribution to what we call "truth"; the theories aren't
simply dictated to us by the facts, as it were. I'd like to ask you to unpack that a little
because I think that some of our viewers will find this idea a little puzzling. "How can
it be" some people will ask themselves, "that what is and is not true could depend not only
on what the facts are, but on the human mind?" Well, let me use an analogy with vision. We
tend to think that what we see just depends on what's out there. But the more one studies
vision, either as a scientist or as a painter, one discovers that what's called vision
involves an enormous amount of interpretation. The color we see as red is not the same color
in terms of wavelengths at different times of the day. So that even in what we think of
as our simplest transaction with the world, just looking at it, we are interpreting. In other
words, we bring a whole number of things to the world that we're not directly conscious of
usually unless we turn inwards & start examining them. That's right. I think the world must've
looked different in the Middle Ages to someone who looked up and thought of the
stars as "up" and us at the bottom, for example. Today when we look out into space, I think
we have a different experience than somebody with the Medieval worldview. And what you're
saying is that the very categories in which we see the world & interpret our experience, and the
ideas within which we organize our observations and the facts around us and so on, are provided
by us. So that the world as conceived by science is partly contributed by external facts,
but also partly contributed by categories and ways of seeing things which come
from the human observer. That's right. And an example of that in science–I'll oversimplify, but
it's not basically falsified–is this wave-particle business. It's not that there's something, an electron,
which is some half a wave and half a particle, that would be meaningless. But that
there are many experiments which can be described two ways. You can either think
of the electron as a wave or you can think of it as a particle, and both descriptions
are in some crazy way true and adequate. They're alternative ways of describing the same
facts and both descriptions are accurate? That's right. Philosophers have started talking of 'equivalent
descriptions'. That's a term used in philosophy of science. But now, for a couple of hundred
years after Newton, educated western man thought that what Newton had produced was objective
fact and he had discovered laws which governed the workings of the world and the workings
of the universe, and this was just objectively true independently of us; that Newton and
other scientists had read these facts off of nature by observing it, and looking at it, and so on.
And these statements which made up science were simply true. Now, there came, didn't
there, a period in the development of science beginning in the late 19th century, when people
began to realize that these statements were not entirely true, that this wasn't just a
body of objective fact which had been read-off from the world. In other words, that
science was corrigible, scientific theories could be wrong. And that raises some very profound
questions. I mean, if science isn't just an objectively true description of the way
things are, what is it? And if we don't get it from observing the world, where do we get it from?
Well, I don't wanna say that we don't get it from observing the world at all. Obviously,
part of this Kantian image is that there IS a contribution which is not us, there's something
"out there". But that also there's a contribution from us. And even Kant, by the way, thought
that Newton science was indubitable. In fact, he thought we contributed its indubitability.
The step beyond Kant is the idea that not only is reality partly mind-dependent, but
that there are alternatives. And that the concepts we impose on the world may not be
the right ones and we may have to change them; that there's an interaction between what
we contribute and what we find out. But now, what was it that made people begin to realize that
this basic conception of science as objective truth was wrong? That science was corrigible,
that science was fallible? I think it's that the older science turned out to be wrong when
no one expected it to be wrong, not in detail but in the big picture. It's not that we find
out that, say, the Sun isn't 93 million miles from the Earth but only 20 million from the
Earth. That's not going to happen. I mean, sometimes it makes blunders even about
things like that, but that's like making a blunder about whether there's a chair in the room.
Wholesale skepticism about whether numerical values are right in science would be as
unjustified as wholesale skepticism about anything. But where the newer theories don't agree
with Newton is not over the approximate truth of the mathematical expressions in Newton's
theory — those are still perfectly good for calculation — it's over the big picture. We've replaced the
picture of an absolute space and an absolute time by the picture of a four-dimensional spacetime.
We've replaced the picture of a Euclidean world by a picture of a world which obeys a geometry
Euclid never dreamed of. We've swung back to the picture of the world as having a
beginning in time which is really a shocker. It's not even that things once refuted stay
refuted forever. So it means really that a whole conception of science has been superseded.
Instead of thinking of science as a body of knowledge which is being added to all the
time by further scientific work. That whole conception of science has been dispensed
with really, and we now think of it as a set of theories which are themselves constantly being
replaced by better theories, by more accurate theories, by richer, more explanatory theories.
And even the theories we now have like those of Einstein and his successors will
probably be replaced in the course of time by other better theories, by scientists yet
unknown, isn't that so? That's exactly right. In fact, scientists themselves make this prediction.
That is, that the main theories of the 20th century, relativity and quantum mechanics, will give
way to some other theory which will interpret both of them and so on forever. Now, this
raises a very fundamental question: namely, the question "What is truth?". I mean, when we
say that this or that scientific statement is true, or this or that scientific theory is true, what,
in these newly understood circumstances of ours, can we mean by "truth"? There are
still two views as there have been since Kant. One is this old correspondence view,
still has its adherents. But I think the view that's coming in more and more is that one
cannot make a total separation between what's true and what our standards of assertability are.
That the way in which the–what I called using the Kantian picture the "mind-dependence of
truth" comes in–is the fact that what's true and what's false is in part a function of
what our standards of truth and falsity are. And that depends on our interests, which
again change over time of course. That's right. I'd like you to say a little more about this question
of truth because, this again, I think is puzzling to the layman. I think that people who are
not trained in science or philosophy are apt to think there are a certain set of facts and a
true statement is a statement that accurately describes those facts. I'd like you to talk
a little about some of the difficulties that are actually involved in this. I think the
biggest difficulty in science itself comes from the fact that, even within one scientific
theory, you often find different accounts can be given of so-called facts. This came in
with the special theory of relativity when it turned out that facts about simultaneity,
whether two things happen at the same time, could be described differently by different
observers. One could say "boy-scout A fired his starter's pistol before boy-scout B", the other
could say "no, boy-scout B fired his starter's pistol before boy-scout A". And if the distance
is sufficiently large so that a light signal can't travel from one to the other without
exceeding the speed of light, then it may be both descriptions are correct, both are
admissible. Of course, this leads to profound conceptual difficulties in understanding some
modern scientific theories. This prompts the thought that a scientific theory can be useful
and meaningful, it can work, even if nobody really quite understands what it means. This
is the case with quantum mechanics, isn't it? I mean, nobody is really sure what quantum
mechanics actually means, and yet it works. That's right. And again, I wanna say one shouldn't
push that too far because I think we don't wanna give up our standards of intelligibility altogether.
We want to say quantum mechanics works and the very fact that it works means that there's
something fundamentally right about it. And with respect to its intelligibility, we're willing to
say, in part, that may be that we have the wrong standards of intelligibility, that we have
to change our intuitions. But in part, there are real paradoxes in the theory and I
think that more work has to be done to really get a satisfactory resolution of these paradoxes.
I think somebody hearing our discussion and to whom perhaps some of these ideas are new,
might find himself thinking, well, if all this is so, how is it that science works? If traditional
scientific theories are breaking down; if science is turning out not to be a body of
reliable, permanent, firm objective knowledge; if a significant proportion of every scientific
theory is subjective anyway in the sense that it's contributed by the human mind, by the observer,
by the scientist–how is it in these circumstances that we can actually build bridges, fly airplanes,
make rockets go to the moon, and actually make all this soft, fuzzy, changing, partly
subjective body of theory work for us? It must fit the world in some very basic way, in
spite of everything that we've been saying. That's true, but I think the contrast between being
subjective and fitting the world isn't altogether right. I'm not saying that scientific knowledge
is subjective or that "anything goes". I'm saying we're in the difficult position
that we often are in life of thinking there is a difference between good and bad
reasoning, but we don't have a mechanical rule. In everyday life, we use interest-loaded terms.
We wouldn't say that there's a policeman on the corner if we didn't have a whole network
of social institutions. Somebody coming from a primitive tribe which didn't have policemen
might say there's a man in blue on the corner. But the fact that the notion of a policeman
is shaped by our interests doesn't mean that it can't be objectively true that there's a
policeman on the corner. Also, I think science works precisely because of this corrigibility
in large part, as Professor Popper's pointed out. The difference between science and previous
ways of trying to find out truth is, in large part, that scientists are willing to test their ideas
because they don't regard them as infallible, in a way that was known at the beginning and then in
the success of Newton science somewhat forgotten. And we've had to be reminded again of what
Bacon knew, that you have to put questions to nature and be willing to change your
ideas if they don't work. In some respects, the traditional opposition between science and
religion has–the two parties have crossed places haven't they? I mean, many religious people
now believe they have certain knowledge about the world–that it was created by a God, that He
made us in His own image, gave us immortal souls which will survive our death, and so on–
certain very fundamental propositions which they hold with absolute certainty. And it's
the scientist who believes that everything is fallible, that the world is a mysterious
place, that we'll never get to the end of the mystery of, and so on. Isn't there
something in that? Maybe. I'm not sure… Well, let's not pursue that. But one point
I do want to take up with you, leaving even religion aside, is that, now that science is
seen in this entire different way that you've been describing, by virtually all scientists,
doesn't it mean that the difference between science and non-science isn't what it was
always thought of as being? In other words, since science is so subjective, indefinite,
changing, & so on, it's no longer a clearly-cut and different kind of human activity or kind of
human knowledge from other sorts of human knowledge and other sorts of human activity?
I think that's both true & culturally very important. I think the harm that the old picture
of science does is that if there is this realm of absolute fact that scientists are
gradually accumulating, then everything else appears somehow as non-knowledge, something
to which even words like 'true' and 'false' can't properly apply. I think that the so-called
fact-value dichotomy is a very good example of this. It's hard to have a discussion on
politics, for example, without someone very quickly saying, at least in my country, "Is
that a fact or a value judgment?", as though it can't be a fact that Hitler was a bad man,
for example, or a fact that Farrah Fawcett is a beautiful woman. And do you think that it
is a fact that Hitler was a bad man? Oh yes I do. [LAUGHTER] I do too! But then, if this is so, if
we are abandoning so many of these comfortable clear-cut distinctions of the past, what's
the point of continuing to use the category or the notion or the term 'science' anyway? I mean,
does it any longer clearly demarcate something differentiable from everything else? I don't
think it does. I think that if you're going to distinguish science from non-science, that
makes a lot of sense if you still have this old view that there's this inductive method
and what makes something science is that it uses it and uses it pretty consciously
and pretty deliberately, and that what makes something non-science is either it uses it
entirely unconsciously, as in learning how to cook, you're not consciously thinking about
inductive logic, or perhaps doesn't use it at all as metaphysics was alleged not to use
it at all, I think unfairly. But once you say, both say that there's a sharp line between,
say, practical knowledge & science, and to say that the method which is supposed to draw
this line is rather fuzzy, something that we can't state exactly. And attempts to state it,
by the way, have been very much a failure still. Inductive logic cannot be, say, programmed
on a computer the way deductive logic can be programed on a computer. I think the development
of deductive logic in the last hundred years and the development of the computer have
really brought home very dramatically just what a difference state we are in with respect to
"proof" in the mathematical sciences which we can state rigorous canons for, and "proof" in
what used to be called the "inductive sciences", where we can state general maxims but you
really have to use intuition, general know-how, and so on in applying them. One of the two
categories that you described the old-fashion way of looking at science in terms of was
that there was a particular scientific method; that you observe the facts and on the basis
of these observed instances, you generalized to form scientific theories which you then
verified by experiment. That was the old view. Now that that has been abandoned, is there
any longer any single method which is thought of as being scientific method? I don't think
there should be. People talk of scientific method as a sort of fiction, but I think that,
even in physics, where you do get experiments and tests which pretty much fit the textbooks
— there's a great deal that does and then a great deal that shouldn't. And I think, in fact, in the
culture I don't really believe there's an agreement on what's a science & what isn't. Any university
will tell you in its catalogue there are things called "social sciences" and that sociology
is a science and that economics is a science. I bet if you ask anyone in the physics department
whether sociology is a science, he'll say "no". But why would he say "no"? That's interesting.
I think the real reason is not that the sociologist don't use the inductive method–they probably
use it more conscientiously, poor things, than the physicists do–I think it's because
they're not as successful. So in other words, science has become almost a name for successful
pursuit of knowledge. That's right. Yeah. Well now, I think you've given a very good description
of the way in which this age-old view of what science was has broken down in our century
and been replaced by something much more fluid and perhaps much more difficult to get hold of.
But you have, I think, described it very clearly. Can we now come against this background to
what philosophers of science are actually doing. You are a philosopher of science, what do
you and your colleagues do? Well, part of what we do, which I won't try to describe on
this broadcast, is fairly technical investigation of specific scientific theories. We look at
quantum mechanics very closely, both to learn what lessons we can from it for philosophy,
and to see what contributions we can make as philosophers to clarifying its foundations.
We look at relativity theory very closely, we look at Darwinian evolution very closely,
and so on. This is the part of philosophy of science that provides the data for the rest.
But much philosophy of science shades over into general philosophy. And I think the
best way to describe it is in terms of what we've been talking about. That is, each of
the issues we've been talking about divides philosophers of science. There are philosophers
of science who have a correspondence view of truth and try to show this came be made
precise, the objections can be overcome, you can still view science somehow in the old
way. And there are others who try to sketch what another view of truth would come to.
There are philosophers who still think there is an inductive method that can be
rigorously stated & who work on inductive logic. By the way, I think it's important there should
be, because we won't make progress trying to state the inductive method if there aren't. And
that there are others who view the development of science more culturally, more historically.
And then, people like myself, who have a sort of in between position; that there's
something to the notion of a scientific method, there are clear examples, but that it's more
or less a continuum, you mustn't think of it as a kind of mechanical rule, an algorithm
that you can apply to get scientific knowledge. So that I'd say each of these issues: the nature of
truth, the nature of the scientific method, whether there's any necessary truths in science, any
conceptual contribution which is permanent and can't be subject to revision is a big question.
And who are you, plural, doing all this work for? I don't ask that in an irreverent way,
but what I have in mind is this. I've myself taking part in attempts to bring scientists
and philosophers together for discussions of precisely the issues that you've raised,
and these attempts have usually failed and failed for the same reason: namely, that the
scientists lose interest. They go back to their laboratories and get on with doing more
science. And the great bulk of working scientists, it seems to me, don't in fact take very much of
an interest in the issues you've been talking about. I think it's conspicuous that the greatest of all
scientists are exceptions. The really blockbusting, the path-breaking scientists who've actually
made the revolution in this century that you've been talking about: people like Einstein, Max Planck,
Neils Bohr, Max born, Schrödinger, de Broglie… These people were enormously interested in the
conceptual questions that you've raised, but these were the pioneering geniuses, and the great mass of
thousands of scientists who follow on behind them and put their work to its practical application,
they don't seem to care. So, who is listening to you? Who is reading the stuff that you publish?
Well I'd say, first of all, I think we are basically writing for the philosophically interested
layman, for the reader of philosophy. I don't view philosophy of science as giving direct
advice to scientists, just as I think moral philosophers are ill-advised to think that
they're giving at least immediately current, contemporary advice on how to live your
life or what bills to pass in Parliament. On the other hand, I do think that scientists tend
to know the philosophy of science of 50 years ago. And perhaps this isn't a bad thing. That is,
perhaps this time lag, this culture lag has some value in weeding out what they shouldn't pay
attention to. I mean, it's annoying for a philosopher to encounter a scientist who's both sure that
he needn't listen to any philosophy of science and then who produces verbatim ideas which you
can recognize as coming from what was popular in 1928. Is there a direct parallel here between
what you're saying about scientists and Keynes, the economist Keynes' famous remark that
nearly all businessmen who thought that they were indifferent to airy-fairy economic theory,
were in fact the slaves of the economic theorists of yesterday and the previous generation?
That's exactly true. I suppose another parallel one could make would be to say that the account
that ordinary language users give of language and their use of language would be extremely
unsophisticated simply because they take it for granted and never thought about it. That too
would probably apply to the account that most scientists would give of what they
were doing when they were doing their science. That's right. That is, it's a mistake to think
that merely because one practices an activity, one can give a theory of it. One criticism that's
often been made about philosophers of science is that although they talk of "science" in
this general way, what they're nearly always referring to, in fact, is one science: namely,
physics. Now, it's true, isn't it, that the science in which the most exciting developments have
probably taken place in the last 20 years anyway has been not physics but biology. Are
philosophers of science genuinely open to the criticism of being too physics-based in their
view of science & having ignored biology too much? I think I would defend us against that
on the grounds that, although the theories in biology are of great scientific importance
–Darwin's theory of evolution, Crick-Watson on DNA, and so on–they don't, by and large,
pose big methodological problems of a kind that don't arise in physical science. I'm not
sure whether you're going to agree with that. Well, I mean, you mentioned the word
'evolution' just now & it seems to me that here is a concept which originated in one of the sciences,
namely, biology, and which over a comparatively short period of time has spread throughout
the whole of our culture. So that the way almost everybody thinks is influenced by the
notion of evolution, not only about the origins of man, but about institutions, or the arts,
or all kinds of other things. I mean, evolution has become a dimension of western man's thinking
about almost anything, is that not so? That's right. And perhaps there has not been enough
attention to this theory. Though what strikes me as interesting is that the possibility of explanations
of what we think of as the biological kind– explanations in terms of function rather
than in terms of physics and chemistry, what you're made of–have come under more
attention recently as a result of computer science. Now, this does raise something I'm particularly
interested in when you talk of computer science & that is the interaction between our technology
in the case of computers and philosophy; not just science and philosophy, but technology
and philosophy. I mean, computers were originally constructed on the basis of a self-conscious
analogy with the human mind. But as they became more and more sophisticated, we began to
learn things from them about the human mind. So our construction of computers & what they
then tell us about ourselves seems to actually precede by interactive growth, isn't that so?
That's right. And today—this is one area, by the way, in which philosophers are in
close contact with scientists. That is, the fields of linguistics, cognitive psychology, computer
science, and philosophy of language today interact constantly, people send papers to one
another, not because someone tells them to, there are conferences in which specialists in these
fields meet together, again not because someone decided there should be some cross-fertilization.
The interesting thing about the computer case is one might've thought that the computer,
the rise of the computer, would encourage a certain kind of vulgar Materialism.
The idea: so after all, we are machines, so after all, everything about us can be
explained in terms of physics & chemistry. Paradoxically, the real effect of the computer on
psychology and on philosophy of mind has been a decrease in that kind of Reductionism.
See, the thing about the computer is that when you work with computers, you very rarely have
to think about their physics and chemistry. There's a distinction that people draw between their
"software", meaning their program, their instructions, their rules, the way they do things, & their "hardware".
And generally you ignore their hardware, you talk about computers at the software level, and
you wouldn't really be able to explain what they do in a way that would be of any use
to anyone in terms of the hardware level. There is a kind of emergence here, although
it's not a mystical kind of emergence, it's not that they're violating the laws of physics.
It's just that higher-level facts about organization have a kind of autonomy. The fact that it's
following this program explains why it does this and I don't need to know how it's built,
I only need to know it can be built in such a way that it will follow this program…
If you apply this to the mind, it suggests a return to a view of the mind that I associate
with Aristotle. It's the view that we are not "ghosts in a machine", not spirits which are
only temporarily in bodies, but that the relation between the mind & the body is a relation
of function to what has that function. Aristotle said that, if you use the word "soul"
in connection with an axe–of course he said you don't– you'd say the soul of an axe is cutting.
And he said the soul of the eye is seeing, and he thought of man as a thing that thinks.
You're talking now of the alternative to Materialism and, say, a religious view that this gives
us, puts me in mind instantly of the most significant of all the Materialist philosophies
in the modern world: namely, Marxism, which after all, is the official state philosophy
of about a third of mankind as we sit here discussing this. Marxism claims to be scientific
and this is a very important thing about it. Is there a significant Marxist contribution
to the philosophy of science? I don't think there's a significant Marxist contribution,
but I don't think that the Marxists were all wrong either. I think Engels was one of the
most scientifically learned men of his century. He got a number of things wrong, but he
had an immense general scientific knowledge. And Anti-Dühring, his big book on philosophy of
science, although it contains some rather strange ideas, some of which he gets from Hegel by the way,
is, on the whole, a sensible book on philosophy of science, among other things. On the other
hand, it's not specifically Marxist. I'd say that Engels views in the philosophy of science
are in large part influenced by the standard philosophy of science of the time. They're
a fairly sophisticated inductive account. And what about subsequent Marxists thinkers
who also had some pretension to be philosophers, like Lenin, for example? Lenin, I think, is on the
whole, one of the worst. He says, for example, that theories are "copies" of motion. I mean, there
you have the copy theory; science is just copying off the reality in its crudest view. Mao is
more sophisticated. Mao was very influenced by John Dewey who was widely read in China
in the 1920s. Do you think it's actually made a contribution to the subject as it is
today or not really? I think that it anticipated –it perhaps might've made a contribution if
people had been less ideologically divided because I think non-Marxists could've learned–the
Marxists were among the first people to try to somehow combine a Realist view with a
stress on practice, with a stress on corrigibility. And they were very hostile to the notion of
a priori truth & today many mainline philosophers of science are very hostile to a priori truth.
As it is, they play somewhat the role in philosophy of science, I think, that Keynes said
they'd play in economics. He described Marx as one of his sort of underground predecessors. Yes, yes.
When I was introducing this program, I mentioned not only the philosophy of science, but also the
philosophy of mathematics. And before we close, I would like us to say something about that anyway.
I suppose one could really say that the central problem in the philosophy of mathematics
is a direct parallel to the central problem in the philosophy of science: namely, how does
it fit the world? With science, it's how does science fit the world? In mathematics, it's how
does mathematics fit the world? Is that right? That's right and it's even worse, because if you're
trying to defend a "copy view", a correspondence view of truth in empirical science, you can
answer the question "well how do we build-up this picture in such a way that corresponds?" by
saying that we have sense organs. As I mentioned before that's not a total answer because
there's a tremendous amount of interpretation involved in simple seeing & simple hearing.
But if you're talking about numbers and sets, and someone says okay if mathematical knowledge
is simply some kind of a copy of the way numbers ARE and the way sets are, and the way other
abstract objects that mathematicians study are, the question [is] then: what SENSE enables us
to see how they are? What is a number? Yes, yes. A deeply problematic question but still an
important one. On the other hand, I don't want to say that the anti-correspondence
view has it very easy either. It seems to me that mathematical knowledge is a real puzzle. And
I think that philosophers should concentrate more on philosophy of mathematics than they
do now because it seems to be an area where no theory works very well. Isn't there another
very important parallel between mathematics and science? I mean, throughout the history of
science, one of the conflicts has been between one camp who thought that it was all about
objects in the world which existed independently of human experience, and another camp which
thought no it's human beings and observers who actually contribute most of this.
And as you pointed out much earlier in our discussion, the truth is almost certainly a
combination of both. There is a long standing dispute in mathematics between one body of
people who think that mathematical knowledge is something that's, sort of speak,
inherent in the structure of the world, and we derive it from the world by experience
& observation, and another body of mathematical thought that says no, mathematics is a creation
of the human mind which we then try to impose on reality like a grid, as it were, on a landscape.
Isn't that so? That's right. The latter story is attractive because of the sense organ problem,
but it doesn't seem to work either because it seems that we're not free to impose any mathematics
or any logic we want. Almost anyone would admit that at least you have to be consistent
and what's consistent and what isn't, isn't somehow something we can just make-up or
decide. When we try to stress conventionalist accounts, subjective accounts, we come up
against the objectivity of mathematics. When we try to stress the objectivity of mathematics
we come up against another set of problems. I think we can learn a lot more than we now
know about human knowledge & about scientific knowledge by going further into this area.
Talking of where we're going from where we are, sort of speak, I think the most interesting way
in which you could end this discussion Professor Putnam would by talking about what you
regard as the most interesting problems areas at the moment, and therefore, I take it, the most
likely growth areas for the immediate future in both of the subjects we've been discussing:
philosophy of science & philosophy of mathematics. Okay, I think that–if I'm allowed to confine
my prediction to the immediate future, because we know that long-run predictions are
always false. But in the immediate future, I would expect philosophy of mathematics to be a
growth area & philosophy of logic. I would expect philosophy of physics, I think, to decline
somewhat from its central place in philosophy of science. Although I think, part of it
touches philosophy of logic. The astounding suggestion has actually come forward,
in connection with quantum mechanics, that we may have to change our logic,
our view of what the true logical laws are, in order to really understand how the world can be
quantum mechanical. I think this side of philosophy of quantum mechanics that touches philosophy
of logic will be a hot discussion area. But more generally, I think, areas which we almost
don't think of as philosophy of science that become philosophy of language and philosophy
of mind, like these questions about computer models of the mind, computer models of language,
and these more general questions about theories of truth, the nature of truth, the nature of
verification, how science can be objective even though there's not a rigorous scientific
method. I think these questions will continue to be the staples of the field. One thing
that worries me about this whole area is its relationship to the educated layman, I mean, which
in a sense is the person our discussion has been for. After all, it's now over 70 years since
the 25 year old Einstein published the theory of relativity, and I'm sure you agree with
me that it's true to say now that the great majority of educated people with higher educations,
university degrees, and so on, still have scarcely any idea of what this is all
about. And it's done very little to actually influence their view of the world. Isn't there
a danger that now science and mathematics are simply racing ahead and the whole new
range or world of insight that that is giving us into the universe in which we live simply
isn't filtering through to the non-specialist, or not filtering through anything fast enough?
That is a danger, but it's one that something can be done about. There's now, for example, a
text of special relativity called "Spacetime Physics" which is designed for the first month of
the first Freshman college physics course. And the authors say at the beginning that
they look forward to the time when it will be taught in high schools. And do you think
that time will in fact come? Oh I'm sure of it. Yes. Well, I think you're right and indeed I hope you are.
Thank you very much Professor Putnam. Thank you.

Erik Verlinde Public Lecture: A New View on Gravity and the Dark Side of the Cosmos

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In his public lecture at Perimeter on October 4, 2017, Dr. Erik Verlinde explored the core ideas behind this research into emergent gravity, and examine the implications of this potential revolution in our understanding of the universe. Watch more Perimeter public lectures:

[Applause] thank welcome welcome to Perimeter Institute here in Waterloo Ontario Canada and welcome to perimeter Institute's public lecture series here live from the Mike Lazaridis theater of ideas my name is Greg dick come the director of educational outreach here at perimeter and it is a pleasure to welcome everyone here this evening both those of you here in the theater and those of you watching online the lecture will last approximately one hour and will be followed by a question-and-answer session so for those of you watching online dr. Kelly coil and a team of researchers are behind their keyboards ready to engage in conversation follow our Facebook or Twitter feed and use hashtag P I live and if you do have a question get it in early so can get all the way to my phone in time and now it is my pleasure to introduce tonight's very special guest speaker dr. ver Lind is a professor at the Institute for Theoretical Physics at the University of Amsterdam professor Burland is well known for his many contributions to science which include Burland algebra and the Burland formula he received his PhD from Huell trekked University in the Netherlands and completed his postdoctoral work at the Institute for Advanced Study at Princeton he was a staff member at the theory division of CERN and also completed professorships at both all tracked and Princeton universities in 2011 the Netherlands Organization for scientific research a water doctor awarded dr. Berlin the Spinoza prize the most prestigious prize a Dutch scientist can win dr. Berlin is also very familiar with perimeter as he was a member of our scientific advisory committee from 2010 to 2013 in 2010 dr. Berlin introduced a new approach to the idea of gravity that it's not a fundamental force but it's an emergent phenomena tonight dr. Berlin will explore the core ideas behind his research and examine the implications of this fast emerging revolution of our understanding of the universe ladies and gentlemen please join me in welcoming dr. Berlin to the stage thank you very much thank you thank you very much yeah it's a pleasure to be here and to be telling you this evening about what I think are exciting developments in theoretical physics in our understanding of gravity we are making progress and we're moving towards again a new theory a new view on gravity that differs from the old theory in the sense that it transcends it it sort of contains it but takes the next step and that's also because there I need important questions to be asked or answered about gravity which have to do with our universe in particular they're questions related to dark matter and dark energy which together I call the dark side of the cosmos I will be explaining that during the lecture it's also a timely lecture because yesterday the Nobel Prize in Physics was awarded for three researchers working on gravity and who together did very important work in making it possible to detect for the first time gravitational waves and also that I'll explain later more precisely what was being done in this experiment but this was a confirmation of the theory of Einstein so Einstein already 100 years ago predicted the existence of gravitational waves so now the theory is confirmed you might ask well why do we need a new theory and this has to do with theoretical advances because theory always develops further it has to do with observations things we don't understand about gravity and I'll explain that but also there's a bit of a philosophical point of view and I'm gonna start with that one because the way that science progresses has very much to do with the times that we live in and also with the technology that we use and normally we would say that science helps us to develop technology but there's also the other way that our current technology influences the way we think about science so we go back to the Middle Ages or a little later we have cannons and think about ballistic motion like cannonballs and these are objects where we don't even ask the question what they're made of they just move and this is how Newton sort of started of course in the in the 19th century people made steam engines and this is where we talk about gases that have pressures and temperature even then people didn't think so much about what is really made of but slowly one started developing the atom picture but the revolutions that happened in the 19th century were very much related to this existence of the steam engine the previous century we well we develop things like televisions and other things and a television if you think about what that is it's actually a particle accelerator because it accelerates electrons which are moved around with electric fields and and are projected on a screen and then we see photons coming out so the ideas of forces and particles is really the language of the 20th century and they're they're our understanding of nature was in terms of the most fundamental building blocks which are elementary particles and the fundamental forces so we built the vertical physics using that language today we are very far in the 21st century and again we are having a different type of technology we're having smartphones we have computers big data and most of what we're doing every day has to do with somehow with information and that's again a new language and this is again also influencing the way we think about science so I'm going to tell you that today is that the new view on gravity has to do with information and because it's basically the language that we're developing in our current century so we live in an Information Age and but what is information you might say well it's what I read in a newspaper because I'm interested in certain things but there's also an abstract way to think about information as the way it's stored in terms of bits and then we don't even look at what is really written somewhere we just count for instance how many bits we have how many bytes and so I I will think about information in this more abstract way so we're gonna even talk about information that we cannot really access but we still have a way of counting it by saying how many bits are used there's also another development going on namely we've got to make things smaller and smaller and then we're going to look at even sub-atomic skills or atomic skills where things become quantum mechanical and then information even as another meeting because in quantum mechanics you get something called qubits so not bits like zeros and ones but there's things that are so much in between so this is Mike Lazaridis who's indeed already one of the people who invested heavily in the idea of developing quantum computers and I think here he stands in front of something that has many qubits in it and qubits are funny objects because they can do things that are only possible in quantum mechanics they can namely not just be 0 and 1 beta can be something in the middle and furthermore they can do something called and being entangled in the sense that one qubit here is doing the same thing as somewhere else and this is a two qubits that are integrals where the zero is on one it's combined with a zero on the other or the one on the other is also combined with the one this is an example of entanglement so this language we're going to use even in our universe so we're going to think about the universe in terms of information and also in terms of this entangled quantum information so my new view on gravity has to do with a new view on the universe built out of information and we're gonna understand understand what then the forces in particular gravity then comes from from this new language so this is immediately related to an other concept again it's sort of a little bit of a philosophical one namely we used to think in the 20th century that everything can be reduced to the tiniest building blocks like we have elementary particles if we know what elementary particles tune and their forces we can derive everything else this is a reductionist point of view on nature we're living in an age where things are changing where we start realizing that when we build things that are larger and much more many things are involved that maybe this reductionist point of view doesn't give all the answers so let me tell you ask you what is this you probably don't recognize it it's just a set of pixels but to show what it is let me just zoom out a bit but it's the same same set of pixels but a little smaller and now it's picture where we suddenly see what it is of course this land mountains is a lake and trees and so on no it's a collection of pictures pixels and here we have suddenly giving meaning to a collection of objects where microscopically doesn't exist and this is the same in nature if we ask what things are made of then some of the terms that we use like maybe even matter or space and time may not exist and this is sort of the way we are going to and there's of course examples in in nature that are more down-to-earth actually already mentioned this but let me tell you then what the term is it's called emergence mainly we use concept and observe phenomena at Marcus Copic skills which are derived from the microscopic skill but have a priori no meaning in that language so the language that we use at macroscopic skills is different than the microscopic and we do use concepts and things that are not meaningful so we have to derive them we have to define them in terms of what's on the line so this is an example of emergency physics if we look at a roomful of gas and molecules that are moving around then we can describe it in terms of temperature and temperature is a property of all of the gas molecules together but an individual molecule doesn't have a temperature because actually the temperature is defined as the average energy per molecule so there we have to define quantities that we normally use like pressure and temperature sizing in thermodynamics from a more statistical perspective on the microscopic this is an example of emergence and an important role in this is played again by what's called the entropy which is namely if I look at all the gas molecules in here I don't want to know what they're exactly doing but I can count how many possibilities there are and that's the entropy that measures the number of possible states that these molecules can be in and it actually tells you the amount of information that's needed to describe all those things so here we already see a link with information and equality called entropy that link has been made precise by Shannon bits so these are coins can be zeros and ones but can be ups and I mean all kinds of ways you can make choices but here I have a coin which has four heads or tails so there are four possibilities if I have two coins so there are four possible States that's two to the N if n would be the number of coins and if you take a logarithm and here I take the log two logarithm then you count basically the number of these bits so entropy can be thought of as counting how many bits can I assign to well do I need and also entropy can usually be thought of as sort of a measure of chaos that's what most people think about it if there's a gas that does all kinds of funny things and there's chaos the chaotic then we have an entropy associated this state where the yellow star in one side in the blue on the other side here they're mixed clearly this has more entropy than debt because they're more possibilities here also if all the gas molecules are in part of this box and here they can move around in more locations I have more entropy here also because there's more information needed to describe it so the link between entropy and information is going to be important so if I talk about information later on and you wonder what I really mean it's counting the number of bits I'm going to introduce this idea of qubits later also because it's going to be also quantum mechanical points are important and I'm gonna end this talk by of this lecture actually by explaining you what this has to do with a new view on gravity and also the dark aspects of the universe and let me show you ready a picture that I'm gonna explain it's almost like this picture actually came from the poster of my lecture it's a galaxy according to Einstein's general relativity curved space-time but I'm gonna think about this in a different way where there's information around it having to do with the dark energy in the universe and I'm going to explain phenomena that we don't understand about galaxies based on this idea of gravity from information now I'm gonna start over again I gave you sort of a summary an idea of where this lecture is going to but now I'm gonna start at the beginning and really start from gravity through the the centuries and then get to the end again in this picture so this was more a philosophical introduction but now at least know the concepts where I'm talking about so I'm going to start again with Newton when Newton told us how to gravity works of course Newton explained that the moon and the Earth's are rotating around each other by the same force that makes the Apple fall and he did this with a thought experiment he had an insight I told you already about cannons and actually he did a thought experiment with a cannon he thought about a cannon on top of a hill which if you shoot the Cannonball it will fall down and head to earth but he imagines shooting it giving more speed more velocity so that it starts falling and eventually it starts missing the earth so while it's falling it starts going around so there's a trajectory actually it's not drawn here which is sort of a falling down on the earth but if you make hit it fast enough you can actually make it go around and eventually come back here it never goes further down because the energy is conserved and they always comes back to the same point if you shoot at harder it becomes a circle and if it then logic and is an ellipse and then there's a trajectory where it never comes back it's a parabola and then you have things that are even further out and they that's then you escape away and this idea that falling and going around the earth was the same thing that is how we got to the idea that basically the moon is falling continuously but is missing the earth all this is what it makes it move around this thought experiment gave him eventually are they also where all these shapes of the trajectories came from and this gives you also a force law and this is Newton's famous law of gravity so the law of gravity is well probably familiar it has tells you that the force is proportional to the size of the masses I have too big a big mass a small one I did the Earth or the moon and order the Sun and the earth then you multiply the two masses so it's proportional to the two masses but it's inversely proportional to the distance between them so it goes like 1 over R squared and that's actually the same way that the size of the sphere grows and actually want to say enemy if I go twice the distance so this is one distance to the earth to the Sun if I go twice a distance actually the force goes down by a factor of four and this is the same way that the area grows or there's some way in which this goes like one over the area and actually this area plays an important role in what I'm going to say because it's gonna link to something that has to do with information of course Newton's law has been tested very well and this is also why people had initially didn't doubt it to be right because I mean you can test it by making its predictions namely looking at the prediction here the velocity is actually calculated using Newton's law and you find that the velocity goes down as a function of the distance so these are the planets and you find that at larger distance the velocity is less and this has been measured and this is precisely what the measurement does it follows the prediction of Newton so this works very well but then if you go to the planet that's closest to the Sun which is mercury there's a tiny deviation the Newton would have predicted that the orbit of any planet has this ellipsoidal shape and that these two points always are staying at the same location this does not happen with mercury it actually rotates a little bit like that and it rotates with a few degree per century actually less than agreed but this has to be explained either by changing the law of gravity or by postulating some additional mass and this is sort of what people did people thought there might be some additional dark matter or some planet closer to the Sun that would explain this and they searched for it for half a century they didn't find it of course we now know that this is an indication that there's something wrong with Newton's theory not really wrong at least it can be improved and this is what I signed it he explained this phenomena by changing the gravitational law not by dark matter but having a different view on gravity so his view on gravity and that's the century ago was that gravity is a consequence of how space and time are curved this came out of his theory of relativity where he introduced well motion comparable to the speed of light or he at least made sure that the relativity postulates are consistent with the way that we think about gravity for instance that a signal cannot travel faster than light and then the only way that can be done is if you think about space itself as sort of a dynamical object that can curve and mass then influences the geometry of space-time and curse it in such a way that objects no longer move in straight line but start going in elliptical orbits at least approximately because this if you put do this for mercury it would actually explain exactly what mercury is doing and he calculated this and it's confront and say his theory got confirmed even very quickly afterwards for another prediction namely he also predicted that gravity would bend light so if space is curves then light is also affected by gravity and if there's a star here then the lights would travel if there's a mass between us not in a straight line but in a curved line like that and that has a consequence because then if we look at it we don't see the store at this location we see it actually slightly shifted because we always think that light goes straight and so we do see the image there so light gets banned at a bit and this is in a consequence of Einstein's formulation of gravity and it got confirmed by looking at the solar eclipse already like a century ago the other prediction in the image and it was I said was the lensing effect is related to it because this is where you think about a source here behind the the object you see light going towards the earth but it can go in two ways or even in many ways because it can go up or down and then you see the light from something behind and actually it makes a ring because it can curve around in all directions and this is called the Einstein ring it's a beautiful information again of the way that gravity works according to Einstein now let me now come to the confirmation that I introduced at the beginning namely his prediction of gravitational waves so we're gonna talk about black holes later but gravitational waves are waves in the space the shape of space-time itself actually it's ripples in space and time itself that propagates with the speed of light I already told you that that gravity cannot be transmitted instantaneously because then it would go faster than light so if something happens to gravity it has to travel out and travel towards us and one of the most spectacular events that can happen is if two black holes they are rotating in around each other and they start spiraling inward and eventually they merge together at that moment gravity waves are traveling outwards and the last bit is such a enormous amount of energy in being emitted that those waves gravity gravitational waves can reach us 1 billion years after it happened that's really spectacular for that they had to do measurements of distances because the shape of the space is being changed a little bit and they had to build a interferometer to measure these distances and then they found a signal on about I think it's 14th of August a little more than two years ago and they had two detectors one in in in Livingstone and the other one in Hanford and they both found the signal and that is a signal where suddenly they saw that the shape of space changes it's a signal that oscillates because of the rotation of the the black holes but very fast so the frequency is very high but at the last moment it goes up even further and it suddenly makes a high frequency bursts with high intensity it's called a chirp and now I'll show you actually I'll show you but also let's you'll hear it so this is the signal where it goes this is sort of without bill so see you see if the time goes this way and then suddenly it happens so now if I go the next it's called a chirp because the the frequency goes up like a bird I mean I like the way that the New Yorker sort of made the cartoon the next date says was that you I heard just now or was it two black holes colliding of course it was a joke if you only know that the signals go through the chirp and so this is where you have to know some physics so this is a reward at the Nobel Prize yesterday and I'm actually going to tell you so you about a quote that I read that Reiner Weiss gave one of the laureates on the television the telephone interview namely this signal is a very tiny I mean it's really a very tiny stretch is less than a millionth of the size of the nucleus of an atom quite incredible that they could measure and the reason is that it's very hard to change the shape of space so space is very stiff stiff and this has to do also with that this phenomena they looked at has this very short time scale where it goes very fast and very strong gravity black hole so all these phenomena and tests of gravity here I summarized them a little bit are describes and testing their testing the equations of Einstein I've written down is these equations here you don't need to be able to understand what I'm right on but this is what Einstein wrote down as his law of gravity and it describes black holes it describes the radiation from binary pulsars bending of light and and things in the solar system many ways we've tested this so why again do you need a new theory and for that I'm gonna do a little experiment we're going to show that indeed there may be things that we don't understand if we think about it too simplistically and I'm gonna do an experiment with snot with gravity but it's with elasticity namely elasticity is also about changing the shape of a material and it has a certain way of describing what's going on by simply saying if I apply a force I know exactly how the material changes its shape so I can even measure a force so this is a material that bounces like a bouncing ball does it again course the bounce is very short but I can measure also the mass because if I put it down then they're going to be a small dent in here if I know the elastic properties I can calculate from the size of the dent how heavy it is so I'm gonna test if there's some dark matter in here because under a calcul to test where I put it down and we're gonna wait what happens to that if I apply the theory of this elasticity nothing should happen because the force doesn't change but something is going to happen very slowly so suddenly you start seeing that the laws of physics depend on how you probe the system and on what timescale I'm gonna say that what happens in our dark universe is something that happens at a totally different time skill am I gonna need a new theory namely that's not a theory of elasticity there well the theory of elasticity of course is only a theory that we know works when we look at the whole object because inside there are molecules and I have to understand what really the stuff is made of to understand what the material is doing so you have to go to the microscopic sand derive the loss of elasticity and I'm gonna do the same thing with gravity I'm gonna go to think about what is space-time made of microscopically and then depending on its properties it can either if gravity like general relativity all the time or can do something else and this materials going to do something else because it actually going to flow watch it it's gonna actually make a dent deeper and deeper because it's made out of a polymer that's changing its shape because this polymers are moving around but they do is very slowly is silly putty by the way you can buy it in the dollar store actually I do it once in a while I go to the dollar store a couple to buy a couple of done and so I did last week there are actually tiny acts that there are a little bit in it but I put some together to make a bigger bowl so if you want to do this experiment at home just go to the Dollar Tree store and then you buy it and and it's fun stuff so this is where I am gonna go now to galaxies so thus gravity worked the same at galaxy scale s general ativy would say well say yes of course was Einstein his right there's no way that he can be wrong and therefore we apply Einstein's equations here and we're going to learn things but the other way you might say well let's test it usually the way you should do things let's test it there is a galaxy we're gonna see how they rotate and we see what the velocities are as a function of the distance now here you see you sort of make a model where you think that everything is going in a circle we look at the color of the light we know the redshifts you can calculate the velocities and then we see that the velocity start doing this we look at the amount of matter and most of the matters in the center and the same what we did with it with the solar system would have predicted that Newton's prediction would go like that it doesn't work the same way I've showed you gravity doesn't work the same way because added measurement this is not what people say people say nade works the same way there must be more gravity here because it's going much too fast and it made a fix not a tiny planet that explains deviation of mercury now a most amount of matter is going to be headed there and they call it dark matter for it is search for it and you don't find it maybe there's another explanation so here is again the same experiment we look at the distance we look at the way that the velocity goes and we see a deviation so this is Newtonian prediction athletes very much like the planets were doing going down and indeed because most of the matter here is in the center so you expect the velocity coordinate stays constant it really goes much faster and it would not stay together if there would not be an additional tractive force of course people say that's because there is more matter but what is really happening here is there more mass that we are missing or is there another explanation so this is the dark matter hypothesis is really that there's some collection of particles around our galaxy and other galaxies that explains this faster rotation and this is called the Dark Matter halo it's shown in blue that's not the actual color because you cannot see it but is an artist's impression but there might be another explanation but this is sort of a representation of the fact that there's more gravity needed to keep a galaxy together so I'm gonna need say that this is something to do with the fact that gravity is emergent and we have to understand what is made of more microscopically as offered other evidence that people point out I mean there's Lansing again at much larger scale it is it's Lansing of galaxy clusters where you see a cluster galaxy on the background being repeated many times if you see these these arcs that's sort of the image and you can calculate how much mass is then needed to explain this and you find that a much more mass than we see in terms of these galaxies so this is again seen as evidence for a stronger gravitational acceleration and therefore people say if we apply Newton's law here as well or general relativity you should conclude as dark matter and this is then the picture that people develop is that at large scales in our cosmos there must be a web of dark matter and this has to do with how structure how the galaxies in all these things form and it did you can do these measurements using lensing again this this is called a weak lensing map where you map out where is the gravity and where is the matter and you see that is even location whereas gravity where there's hardly any matter and this is useless evidence back if we look at larger skills what we do when we look from our planet out into the universe light has to travel towards us and takes an amount of time to get towards that means that we look at objects further away which are further in the past so this is you might say an image of distances circles that are bigger but actually it's also times that are earlier in the past and there are some farthest distance where we can see where we see the light coming from what is believed to be the Big Bang afterglow of the Big Bang it's called the Cosmic Microwave Background and this is after that we cannot look any further so with a largest distance we can look and this is the way that people built a current cosmological model and you can then estimate what is the amount of energy in our universe and the amount of matter and the result is kind of shocking that if we understand the matter that we are made of ourselves like protons neutrons and everything in the planets and the stars and we add it all up it's much less than what is actually needed to explain this universe so this is the budget for energy and mass together actually I put energy mass together because e equals MC squared and then you see that 95% of the energy in the universe is not understood it's called a sort of missing the ordinary matter is this 5% there's this Cosmic Microwave Background that's also a lot of particles actually this is this bit that Syrian less than a percent level one hundredth of a percent of all the energy so that energy in the photons is very little but most of the matter is dark that means we cannot see it it cannot be the kind of particles we are made of and this is the the matter that people are looking for and then there's dark energy which also is not known really what that is but it plays a role in explaining the expansion rate of the universe so the universe expands accelerated way and that can only be described in a by adding this additional energy to to our space now this is already telling me that something may be wrong because we are deriving our laws of physics only based on this part but what do we know about this and Einstein describes this by the way by adding just a constant to his equation and that that's sort of like 70% of the energy of the universe I mean that's available a waste that the other thing I already mentioned this is observational reasons to go beyond the Einstein theory in my opinion but the other one is theoretical I'm gonna make a now case that equations that Einstein wrote down can actually be indeed derived in a way similar to thermodynamics and this is where this story of emergence gravity and the link with information are is going to come from and for that I'm going to go back to the topic of black holes namely black holes give us the hints of why there is a connection between gravity and information so black hole is where all the matter is located is in this very tiny part of space so small that the matter collapses on itself and gravity becomes so strong that life cannot even escape so black holes have a whole rise in sort of a imaginary sphere around it that if you would go beyond that then there's no way to escape so they have a size and that depends on the mass that you put in a larger black hole a more massive one is also bigger by the way the black holes that collided in these gravity bases are like 60 times the mass of the Sun so there's really a lot of mass in those and they are big objects like tens of kilo mega kilometers or or maybe much more even and actually they are in the center of galaxies even much larger ones so black holes exist that's a prediction of Einstein but as theorists we like to think about it as objects where we can learn a lot about gravity because they're the most extreme and this horizon is going to play a very important role in understanding more about gravity so let me give you a little bit of a feel what is going on so I told you that it if I take the shape of the space-time when we have a mass sitting there you can actually compare this to a sheet of rubber where we put some mass locally and we get some dent in it actually here's some analogy with elasticity already happening the mass is really creating this deformation of the space-time but when the matter gets more concentrated this gets deeper and deeper and there's some limit where you just get a hole that's where the black hole appears and then there is some distance where light can no longer escape so I want to show you a little bit what it looks like to be close to a black hole black holes also curve light just like other objects it and and a bent light so if earth would be rotating around the black hole it looks like this you might get worried that Earth is being deformed here that's not what happening this is the image of what it looks like because earth when it comes back to the front it's just nicely round but the image of Earth gets projected around with the light where you can see the ring but that was the Einstein ring that I talked about it's just a light going around now I'm going to show you what it looks like if you fall into a black hole I took from the internet I should have acknowledged the person who did this but I forgot but anyway this is a simulation we're not going to do it for real so it's on where the equations and actually no one has fallen into a black hole so I cannot really verify that this is true we have had all of a kind of discussions really what happens when we fall into a black hole whether the horizon is really something can fall through we're gonna see that we're gonna be able to do it so we're using Einstein's equations and then see what happens so a number of things are gonna happen so there's a picture and we're gonna go around it the black hole there's a certain this is where you can simply make circles you don't have to do anything but when you get closer there's some moment when you get drawn into the black hole and you have to use an acceleration it's like a rocket engine to stay out then there's a distance when there's no hoping anymore you falling in and you eventually will cross the rice and then when you cross the rice and you continue but you will go to the center and hit a singularity but the horizon is a special occasion because life cannot be emitted from that anymore and also because clocks starts going differently the time stops basically at Horizon so we're gonna see a clock here that's gonna keep track and that's gonna go slowly so I'm going to show you what's happening so here we go actually the picture or maybe I should show this first elves first well we do wanna see it again the pictures actually was the galaxy and it's being deformed by as a lens so we have here the horizon appearing strangely enough the North in the South Pole are a little bit off and that's because again of the curvature the bending of light and we are they're still in a safe regime which is yellow but now we have to start using the engine and we static closer and closer eventually we're going to go through it and then in Bakke you see that we have no connection anymore with the outside and this is where there's no stopping us from following almost singularity and eventually time stops I'm gonna show this again because most people want that so there we go again so this indeed was a galaxy and this is an Einstein ring because it's the way that the light gets around and then we see the horizon appearing and so this is where light actually is going around and there's one particular distance which is called the photosphere where light just make circles we see a flesh when that happens because that's not the horizon itself the rising is here and this way need to North in the South Pole and they're not drawn what's inside basically because it's unknown so now we're inside and we can only look outward and we can still see a bit of the light coming in actually light can still go into a black hole but it cannot go out so you can still see where you came from but there's no way to communicate back to people outside so it's fun to think about black holes and this is also why the theorists do thought experiments near black holes and two famous people Stephen Hawking well well-known here of course and jacob bekenstein they both thought about black hole horizons and they wanted to know more properties like the thermodynamic properties if I throw in a box with ready it with gas particles in it it has an entropy is where the connection with information is going to come from because we want that the laws of thermodynamics are still true turns out that also the laws of quantum mechanics are going to play a role and indeed what that can stand Hawking showed that if he throw in some radiates some matter in a box from gas the ricin gets bigger but the entropy in the Box disappears but entropy always has to increase and they made the assumption that was actually back in stein that the horizon area has to do something with the amount of information that you throw in the entropy bekenstein did this calculation using quantum mechanics and he found a very surprising result in the black holes nothing can escape but it turns out quantum mechanically it emits radiation and actually gets smaller and the reason is is that in quantum mechanics you have the uncertainty principle that there is a possibility of creating pairs of particles in the vacuum and they are pair a pair particle and an antiparticle where one drops in the black hole and the other one escapes normally an empty space they would reunite again and they just annihilate each other but here one Dobson and the other one escapes and you get radiation coming out so this is the picture here it's also where these two particles near the horizon they won't escape someone falls in but if they are not on the horizon then they can combine again and this is going to be telling us something about the properties of this black hole may be that it has a temperature because its radiation is thermal radiation and if we have a temperature and we have a mass and therefore an energy we also have an entropy and that entropy is a formula that bekenstein already wrote down name it that it's proportional to the area so it has thermodynamic properties precisely the quantities that I introduced as being emergent the temperature and an entropy and entropy for a black hole is proportional to the area of its horizon this is was one of the more important discoveries actually already 40 years ago they've made this and I think it is the first crack in Einstein's theory nothing is perfect and actually that's one of my story lines is that every theory eventually gets replaced by better one and you have to look at the right clues of where to look and you find that the black hole entropy formula tells you something about what is the microscopic origin of gravity by the way I already said that Newton's law had something to do with areas this area of the black hole horizon is the same area actually you gonna talk about so there is a entropy formula that tells us how much information is contained in a black hole and we're gonna think about this information s bits I told you information for me is bits it's also can be measured by entropy because that tells us how many bits there are and this is why this formula tells us how many bits we can associate with a black hole not ordinary bits by the way it's going to be quantum qubits a little later so the information that is associated with black holes is not the information that we have classically on a computer it's going to be the next computer actually a black hole is the best computer you can have because you can store an enormous amount of information on it namely the density here is the Planck scale by building a chip like that this is where the limit is this is how much information you can store on on the surface and it's as I said not ordinary bits it's quantum information and now let me explain a little bit more about what that is I already said that bits are zeros and ones quantum bits they are also zeros and ones but you can also think about it as the spin of an electron for instance the spin of an electron can be either up or down but it can also be something in the middle and we call that a superposition so it has to decide still whether it's up or down before I do a measurement and this is why a qubit has many more possibilities so a bit has only two possibilities there is on one a qubit can be thought of as a sphere all points on this sphere is a different state of a qubit and this is why if you do calculation with qubits you're doing many calculations at the same time many more bits then we normally have in a classical computer it'll call them calculation you do all these things parallel all calculations are being done at the same time this is why quantum computers are much more powerful more importantly these qubits can be entangled already mentioned what that is namely that if I measure two qubits that the outcome is the same this was discovered let me do the calculation is like 80 years ago by again familiar name Einstein together with two colleagues actually you may wonder why I sent us something with quantum mechanics because he didn't like it well this was also motivated to show that or something very funny about quantum mechanics namely that if it measure an object and you measure the spin here it can determine the outcome of a measurement somewhere else instantaneously he called the spooky action at a distance is that this cannot be paper was not that important at the time but in recent times it's one of the most important papers because it's the first paper where they explained entanglement very clearly and this is what makes entangled qubits it makes it's the power of quantum mechanics it's the essence of quantum mechanics that we have entanglement and our universe is very entangled and so this is why this is the kind of information we're talking about so it's a property of the Quantum's it's an actually it's something that is already there before you start measuring it it tells you that if you do a measurement here that something else happens tomorrow so there's already the cubits that I showed before I mean this is where neatly of a zero in a zero if you do a measurement of this one it can be either zero or one so here and the other one here the automation outcome might be your one but the the outcome is always the same so if I measure this one is a zero then this one will be zero as well and if it's a one the other one is one but a Peoria's 50/50 probability when I do the measurement so this is called entanglement and I'm going to denote this by this picture of a sphere by connecting a little line between it so and think of it as like a connection between two of those Cupid's so I'm connecting qubits together and this is the way I'm gonna build space-time so this is going to be my microscopic picture of the molecules of space so this is what bekenstein and Hawking calculated they calculated that there was an entropy associated to horizons and this has to do precisely with this pair creation because here we are creating a pair of entangled particles and they describe the amount of information so the entangled qubits is really what's being counted by by this formula so this is the answer so what is this entropy counting it's entangled qubits and they are the building blocks of space-time and they are measured by the area but I'm gonna say it's the other way around actually the amount of cubits is going to determine the geometry and it's going to determine the area so the geometry of Einstein is going to be derived from this language so on disco as far as I want to go at least explaining the ideas this is a current state of the art kind of development going on in theoretical physics thinking about gravity in terms of quantum information and deriving its laws just the same way as we derive the laws of thermodynamics and that's called emergent gravity and this is where I want to connect now final slides to the dark universe so there's a slight summary space time and gravity are emergent and this is actually a lesson we learn not from just black hole physics I didn't tell you about string theory because I've only that many minutes talk but string theory itself also actually hints in the same direction a lot of what we're learning nowadays comes from studies in string theory where we also see that this emergence of gravity from quantum information is very natural this is all theoretical physics and you might say well why are we doing it are we learning anything new and in particular is there observational evidence I have to mention is that we have to read your eyes first the laws that we already know on this idea this can be done and I wrote a paper already about seven years ago a little more which was called on the origin of gravity and the loss of Newton because that's one of the laws you want to derive and what I showed here in this paper that indeed if you assume that the amount of information this entanglement is proportional to the area that's an assumption by the way then you can derive Newton's law just by using the same tricks that we use to derive thermodynamics so there is Newton's law and here is this picture of the information stored on a surface and we find indeed the one over R squared law because the area it grows like the area this by the way as I said as an assumption you may wonder whether this assumption is true and this is where the possibilities are maybe to explain what's going on here so now I'm going back to my original question is there some way that something strange or different happens in this galaxy already told you that the observations tell us at something distance happens but can we also explain this theoretically indeed I'm gonna say there are different laws acting here because the laws that we have currently derives Einstein's equations are derived from observations that we have done in the previous century colliding black holes lots of stuff but if you think about this question here how long have we been observing the universe if you think about the history of the earth actually saucer former from a flight actually from the internet I could have put it at the University the history of the universe if you would take that to be one year then humans only arrived one minute before midnight on the 31st of December and how long have we been doing sinus science fraction of a second it's like taking a snapshot of the history of the universe and then drawing conclusion about its entire history I showed you this experiment the snapshot was the bounce what happens to the universe is this and there's a lot of dark matter in here because it's created an enormous dent if I would applied my theory of elasticity to this I would have drawn the wrong conclusions so if the universe has this kind of slow dynamics happening at very large skills we can explain these phenomena and now let me go back to the picture here about what we don't know about the universe this is what we have used and let me ask you the question according to current theory where is all the information city in this picture any idea that little tiny yellow stuff it's the photons in the CMB that carries most of the information according to current through I think that's wrong information is contained there most of the information and then we have a totally different way of thinking about it we've missing most of the entropy this number is 10 to the 90 that's the number of bits you would need to describe the photons number I claim is 10 to the 120 because that's the size of the horizon of our universe if we would have only dark energy so it is going to be the conclusion I'm going to think about our universe as if we are living inside a giant black hole which has a horizon except we are not inside outside the black hole we're inside think about the universe as a black hole where the horizon is because of the following fact we know according to Hubble that things move away from us with faster velocity when we go for the distances the objects further away move further with higher velocity so this is Hubble's law the velocity is proportion to the constant the constant of Hubble times the distance so there is a distance when this would become the speed of light and things that are moving faster than the speed of light we cannot see so there's a farthest distance we can see and therefore we have a horizontal I while you take the velocity to be C and divide by H so this is the distance to the horizon if he would be in a universe which is constantly just expanding according to the Hubble law this is Delta then the size of the rice and the size of the universe and actually also the size of the number of bits I need namely it's gonna be the size of this horizon again measured in flanking units I'm gonna claim this is any information associated not to the horizon itself but to the dark energy that's an observational fact B I should tell you the picture first so I'm gonna explain what happens in galaxies rotation curves namely there's information contained in the dark net energy the matter actually pushes it away it's like elasticity pushing it away it creates a hole in it but entropy wants to move back it sort of wants to increase it pushes back I've done a calculation if you don't believe me I should take this aside because all the equations are on the blackboard these are the equations of a paper I wrote them about a year ago that does a calculation where at the end of it I'm going to explain the data that are here and let me already tell you a curious fact that should be is been a smoking gun for why this is the right explanation if you look at this curve here so this is what Newton would have predicted and this is what we observe turns out that the deviation always happens at a very particular gravitational acceleration independent of the size of the galaxy if you calculate or measure I should say that acceleration turns out it's related to the Hubble experimenter which is very mysterious because a galaxy is a very tiny object so what would that relation be I explain that in that paper and the formulas are like here so I use entropy the temperature and tango month eventually a formula comes out that describes this behavior and precisely the flattening of this rotation curves with this velocity of acceleration in there so these ideas are connected to observations and I think this is proof that quantum entanglement is the origin of gravity then you may ask what is it good for I get that question a lot I always show this one one of those questions I think we're gonna change I do think that this is a new view of gravity but also of the cosmos and we are interested always have been interested in the question where did it all come from that's a question that drives our curiosity and it takes us from science to technology and back again and it brought us from the period of the caveman to our current time and it's therefore the driving force of what we are doing curiosity about nature and then in the meantime developing technology as well so this is I think also for me done my motivation and maybe what we learn about understanding about quantum information and the universe will help us also apply it in some real things that is good for us all right thank you very much all right let's open the floor to questions that was terrific to the microphone for the theater audience is right there you can form a line and the online audience if Mike phone works well I'll get that updated too but if I get to go first I'm happy to go first all right no questions that must be there will be questions okay so let's start with this one so what what first inspired you to to become a physicist and then the Part B is what prepared you to ID a id8 something that goes so against the grain I a teenager actually I watched the documentary where Stephen Hawking was already edit explaining about black holes and my future a thesis advisor here that host was in it explaining about elementary particles it was in the mid seventies its program was called the key to the universe I was 14 years old and decided I wanted to do this so this is what I started doing and in particular the question about black holes and an entropy is something that here at often Stephen Hawking disgusts around for many decades then I joined in and I felt a number of things that the connection with thermodynamics already told me something about the emergence of gravity but I have to admit I always felt a certain unease with the way that people have extrapolated our current laws of gravity to describe the evolution of the universe and come with a very illogical thought namely that there was a moment that suddenly from nothing it exploded so I think that is a question that I want to eventually understand differently and I think this idea of emergence sort of grass I find this philosophically much more appealing than the way that that's been done so I feel there's something to be done and I have been making progress on black hole physics and other people have with string theory that I feel that we are on the onto something so I'm excited about it go to the in the theater right here going against standard model of cosmology you must come across all the objections do you address in any of papers the objections like the power spectrum of the CMB and bullet clusters and all those other secondary evidence yeah so the bullet cluster I I already addressed actually gave a talk this afternoon where I explained some of more of the details about this but also what I explained here so one thing that happens is if you think about how Einstein changed gravity from Newton he didn't take Newton's law and write down a new force law he had totally different concepts on where it came from and so what people are doing now is excluding the possibility that we take Einstein's equation and write some other equation the thing that really is changing is that's a totally new concept and it has to do with the slow dynamics that's taking place so there's no immediate connection between the location of the matter and whatever the gravitational field is that can have a delay in it and actually the collision like the bullet cluster can be explained in that way and I also feel like the reason why people try to exclude these possibilities I think is in part because they allow themselves only a limited class of possibilities if you want X so how should I say this if you think already what kind of modification that could be to gr many of them are probably not correct but there might be one and we have to think I do think we have to think out of the box because these problems are our large ones and we don't know yet where the answer is entirely but I think to make a business out of excluding other people's idea somehow I don't think that that's my way of doing things I like to construct things not destructed theater if energy can't be destroyed then what happens to the energy contained inside virtual particles when they disappear ah good question so there's a certain moment though there is uncertainty and that means the following if I look at a system very long I know that energy I can measure it but if I look at it very short I don't know really what the amount of energy is in there and that's what Heisenberg told us that there is a certain uncertainty in how short you look at this object and what the amount of energy is in there so for a short amount of time bass can borrow a little bit of energy as long as it gives a deck little later and that's sort of the the way that it happens and it's like you cheat with energy conservation as long as hottes don't notice it we'll go to an online question so would the discovery of dark matter invalidate your theory or would some parts of it survive so that it's a also a good question I mean I don't say that there are no other particles to be discovered the Dark Matter particle has to be a very special kind name it has a particle that does not decay it has to stay around and we have to explain why there is the amount that we observe and many people say it may not be one particle so they can add one or the other so what I will say is that we can discover new particles but it should not give us so much more matter in the form of particles that it starts changing the way that my equations work because then indeed these ideas are wrong it's true that there are still many steps to be taken so but I can indeed quite confidently say that I I really think there will be no particle found and if it happens I will have to go back to the drawing board thank you in theatres this may demonstrate my ignorance but if information the amount of information is directly proportional to area can we explain space-time in terms of 2d rather than 3d also a very good question I mean certainly things that we have been working on as a model what we call holography so a whole log Rafi is indeed a projection of the three-dimensional space on a two-dimensional plane and then you would say that all the information that is contained necessary to describe what's happening in that space can be recast on in terms of two dimensions so this is a theory that came also out of string theory there's a space which has not positive dark energy but negative cosmological constants called instead of the sitter's called anti-de sitter this is precisely a space where everything seems to live on the boundary and we're trying to reconstruct what's going on inside for ready two centuries SOI two centuries four to two decades and that is also taking a lot of difficulty and and I say that's not a space we live in not universe we live in so what I did here actually was show that not all the information is actually really living on the boundary but it's also filling up the volume it still satisfies this area law that if you add it all up gives you exactly the size of your horizon so I think I would hate if the laws of physics would be eventually so that I have to construct what's happening in this room from some two-dimensional surface the boundary of our universe that would be not a very practical way of doing things and as a feeling that this is also not going to be the final answer anyway so there's it's a little bit of a subtle issue because we're still in the middle of this development maybe a crew trollese next fight even because there's a bit of this picture this is the picture I mentioned which is where there's a theory on the boundary that's describing something happening in the bulk which has the volume which is has gravity inside but this is then the hologram that we're talking about and string theorists are doing this kind of stuff ladies and gentlemen dr. Eric Berlin's [Applause] you

The Riddle of AntiMatter

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Explore one of the deepest mysteries about the origin of our universe. According to standard theory, the early moments of the universe were marked by the explosive contact between subatomic particles of opposite charge. Featuring short interviews with Masaki Hori, Tokyo University and Jeffrey Hangst, Aarhus University.

Scientists are now focusing their most powerful technologies on an effort to figure out exactly what happened. Our understanding of cosmic history hangs on the question: how did matter as we know it survive? And what happened to its birth twin, its opposite, a mysterious substance known as antimatter?

A crew of astronauts is making its way to a launch pad at the Kennedy Space Center in Florida. Little noticed in the publicity surrounding the close of this storied program is the cargo bolted into Endeavor’s hold. It’s a science instrument that some hope will become one of the most important scientific contributions of human space flight.

It’s a kind of telescope, though it will not return dazzling images of cosmic realms long hidden from view, the distant corners of the universe, or the hidden structure of black holes and exploding stars.

Unlike the great observatories that were launched aboard the shuttle, it was not named for a famous astronomer, like Hubble, or the Chandra X-ray observatory.

The instrument, called the Alpha Magnetic Spectrometer, or AMS. The promise surrounding this device is that it will enable scientists to look at the universe in a completely new way.

Most telescopes are designed to capture photons, so-called neutral particles reflected or emitted by objects such as stars or galaxies. AMS will capture something different: exotic particles and atoms that are endowed with an electrical charge. The instrument is tuned to capture “cosmic rays” at high energy hurled out by supernova explosions or the turbulent regions surrounding black holes. And there are high hopes that it will capture particles of antimatter from a very early time that remains shrouded in mystery.

The chain of events that gave rise to the universe is described by what’s known as the Standard model. It’s a theory in the scientific sense, in that it combines a body of observations, experimental evidence, and mathematical models into a consistent overall picture. But this picture is not necessarily complete.

The universe began hot. After about a billionth of a second, it had cooled down enough for fundamental particles to emerge in pairs of opposite charge, known as quarks and antiquarks. After that came leptons and antileptons, such as electrons and positrons. These pairs began annihilating each other.

Most quark pairs were gone by the time the universe was a second old, with most leptons gone a few seconds later. When the dust settled, so to speak, a tiny amount of matter, about one particle in a billion, managed to survive the mass annihilation.

That tiny amount went on to form the universe we can know – all the light emitting gas, dust, stars, galaxies, and planets. To be sure, antimatter does exist in our universe today. The Fermi Gamma Ray Space Telescope spotted a giant plume of antimatter extending out from the center of our galaxy, most likely created by the acceleration of particles around a supermassive black hole.

The same telescope picked up signs of antimatter created by lightning strikes in giant thunderstorms in Earth’s atmosphere. Scientists have long known how to create antimatter artificially in physics labs – in the superhot environments created by crashing atoms together at nearly the speed of light.

Here is one of the biggest and most enduring mysteries in science: why do we live in a matter-dominated universe? What process caused matter to survive and antimatter to all but disappear? One possibility: that large amounts of antimatter have survived down the eons alongside matter.

In 1928, a young physicist, Paul Dirac, wrote equations that predicted the existence of antimatter. Dirac showed that every type of particle has a twin, exactly identical but of opposite charge. As Dirac saw it, the electron and the positron are mirror images of each other. With all the same properties, they would behave in exactly the same way whether in realms of matter or antimatter. It became clear, though, that ours is a matter universe. The Apollo astronauts went to the moon and back, never once getting annihilated. Solar cosmic rays proved to be matter, not antimatter.

It stands to reason that when the universe was more tightly packed, that it would have experienced an “annihilation catastrophe” that cleared the universe of large chunks of the stuff. Unless antimatter somehow became separated from its twin at birth and exists beyond our field of view, scientists are left to wonder: why do we live in a matter-dominated universe?

an international race is picking up speed to see our universe for what it really is and how it came to be according to the standard theory that describes the origins of the universe it's early moments were marked by the explosive contact between subatomic particles of opposite charge scientists are now focusing their most powerful technologies on an effort to figure out exactly what happened our understanding of cosmic history hangs on the question how did matter as we know it survived and what happened to its birth to him it's opposite a mysterious substance known as antimatter a crew of astronauts is making its way to a launch pad at the Kennedy Space Center in Florida they'll enter the space shuttle Endeavour for the 134th and second to the last flight of the space shuttle little noticed in the publicity surrounding the close of this storage program is the cargo bolted into endeavours hole it's a science instrument that some hope will become one of the most important scientific contributions of human spaceflight it's a kind of telescope though it will not return dazzling images of cosmic realms long hidden from view the distant corners of the universe or the hidden structure of black holes and exploding stars unlike the Great observatories that were launched aboard the shuttle it was not named for a famous astronomer like Hubble or the Chandra x-ray Observatory the instrument called the Alpha Magnetic Spectrometer or AMS is the brainchild of this man Samuel ting from Massachusetts Institute of Technology at the heart of the AMS is a large superconducting magnet and designed to operate in the pristine environment of space of which is the with its intensive power requirements the final version was attached to the International Space Station ation inside the cupola on the International Space Station being maneuvered into the promised surrounding this device II is that it will enable scientists to look at the universe in a completely new way you guys go as far as release never most telescopes are designed to capture photons so-called neutral particles reflected or emitted by objects such as stars or galaxies AMS will capture something different exotic particles and atoms that are endowed with an electrical charge among these are a theoretical Dark Matter particle called a neutrally no then there are the strangelets a type of quark that could amount to a whole new form of matter the instrument is tuned to capture cosmic rays at high energy hurled out by supernova explosions for the turbulent regions surrounding black holes and there are high hopes that it will capture particles of antimatter from a very early time that remains shrouded in mystery the chain of events that gave rise to the universe is described by what's known as the standard model it's a theory in the scientific sense in that it combines a body of observations experimental evidence and physical laws into a consistent overall picture but this picture is not necessarily complete the universe began hot after about a billionth of a second it had cooled down enough for fundamental particles to emerge in pairs of opposite charge known as quarks and antiquarks after that came leptons and anti leptons such as electrons and positrons these pairs began annihilating each other most pork pairs had annihilated by the time the universe was a second old with most leptons gone a few seconds later when the dust settled so to speak a tiny amount of matter about one particle in a billion managed to survive the mass annihilation that tiny amount went on to form the universe we know all the light emitting gas dust stars galaxies and planets to be sure antimatter does exist in our universe today the Fermi gamma-ray Space Telescope spotted a giant plume of antimatter extending out from the center of our galaxy most likely created by the acceleration of particles around a supermassive black hole the same telescope picked up signs of antimatter created by lightning strikes in giant thunderstorms in Earth's atmosphere a European cosmic ray satellite called pamela detected a huge store of anti protons in orbit around the earth created by high-energy particles striking the upper atmosphere then held there by magnetic fields that ringed the planet scientists have long known how to create antimatter artificially in physics labs in the superhot environments created by crashing atoms together at nearly the speed of light here is one of the biggest and most enduring mysteries in science why do we live in a matter-dominated universe what process caused matter to survive and antimatter to all but disappear one possibility that large amounts of antimatter have survived down the eons alongside matter that was the view of the german-born physicist Arthur Schuster who appears to have coined the term antimatter in 1898 he imagined that its opposite charge would allow it to act as a counter to gravity large tracts of space he wrote might thus be filled unknown to us with a substance in which gravity is practically non-existent until by some accidental cause such as a meteorite flying through it unstable equilibrium is established the matter collecting on one side the antimatter on the other until two worlds are formed separating from each other never to unite again the issue gathered dust until 1928 when a young physicist Paul Dirac wrote equations that predicted the existence of antimatter Dirac showed that every type of particle has a twin exactly identical but of opposite charge so for every proton there's an antiproton for every electron there's a positron for every neutron and antineutron within them are quarks and they're twins the anti quarks as Dirac saw it the electron and the positron are mirror images of each other with all the same properties they would behave in exactly the same way whether in realms of matter or antimatter in his Nobel Prize lecture in 1933 Dirac pondered a larger reality for antimatter if we accept he said the view of complete symmetry between positive and negative electric charge so far as concerns the fundamental laws of nature we must regard it rather as an accident that the earth and presumably the whole solar system contains a preponderance of negative electrons and positive protons it is quite possible that for some of the stars it is the other way about these stars being built up mainly of positrons and negative protons just the year before the physicist Karl Anderson had confirmed the existence of antimatter by shooting gamma rays at atoms creating electron positron pairs it became clear though that ours is a matter universe the Apollo astronauts went to the moon and back never once getting annihilated solar cosmic rays proved to be matter not antimatter traveling to every corner of the solar system our probes have not encountered any objects made of antimatter cosmic rays from the Milky Way are overwhelmingly matter if there are any large concentrations in nearby galaxies or galaxy clusters we should see gamma rays produced when particles and antiparticles find each other it stands to reason too that when the universe was more tightly packed that it would have experienced an annihilation catastrophe that cleared the universe of large chunks understand unless antimatter somehow became separated from its twin at birth and exists beyond our field of view scientists are left to wonder why do we live in a matter-dominated universe Dirac's symmetrical view of matter and antimatter which saw them as equivalent collapsed three decades later in 1964 the American physicists James Cronin and Val Fitch examined the decay of a particle called a k on to its antiparticle twin they found that the trance nation back to normal matter did not occur with the same probability that would suggest there must be small differences in the physical laws that govern matter and anti-matter to find out exactly what makes them different or asymmetrical would be a big step toward understanding how our universe took the shape that it did that's why physicists are hot on the trail of antimatter with new technologies designed to give them a closer look at this strange substance in nature and in the lab but if there is some antimatter out there escapees from the mass annihilation of the Big Bang still fleeing through the emptiness of space the crew of endeavor placed the AMS instrument on the International Space Station in May 2011 since then scientists have been combing the data for the signatures of antimatter particles striking its detector if they managed to detect heavier elements such as anti helium or anti carbon that would point to concentrations of antimatter in space large enough to a form stars where those elements are created and suggest that symmetry may not have been broken after all such heavier anti-atoms can exist at Brookhaven National Lab in New York scientists recently smashed gold atoms together at nearly the speed of light from about a billion individual collisions its detectors recorded the presence of 18 anti helium atoms atoms with two anti protons and two Aten neutrons the explosive potential of antimatter in this universe has long animated the voyages of science fiction it's the fuel of choice for getting beyond our solar system and out to the stars just to get into orbit the Space Shuttle had to be loaded up with some 15 times its weight in conventional rocket fuel the energy contained in antimatter is orders of magnitude greater in fact it would take just a coin sized portion to propel the shuttle into orbit because antimatter is so volatile with our matter filled universe the challenge for scientists is first to create it then to hold it for enough time to study it before it simply vanishes even as the shuttle Endeavour glided on to land for the last time AMS scientists were beginning to filter through the rush of charged particles in space meanwhile scientists on the ground were beginning their own intensive efforts to corral antimatter in their labs they are trying to do this at the giant European physics lab CERN in a little-known corner the antiproton deceleration lab a group of scientists is showing that you can actually trap and hold antimatter long enough to study the anti protons from the antiproton decelerator that's the machine that we need here at CERN come down this pipe right here and they come into our apparatus which is inside this large magnets this is a very strong magnetic field to help to confine the charged particles that make anti hydrogen we mix the anti protons with positrons inside this magnet trap and that's where we capture them inside the Alpha chamber the magnetic field holds the particles in place and isolates them from one another an electric field separates the electrons and positrons they are then carefully brought into contact when two positrons collide one falls into orbit around an antiproton forming anti hydrogen then the molecule is trapped by magnetic fields like a marble rolling around in a bathtub now remove the bathtub the magnetic fields the anti molecule smacks up against the wall of the detector and annihilates emitting a shower of particles so what we do is hold on to them for a thousand seconds and then release them to make sure they were there that's how you do this measurement that 1,000 seconds almost 17 minutes is a major accomplishment on the atomic life scale a thousand seconds is forever things on the atomic life scale are measured in nanoseconds or smaller perhaps so this is forever for an atom to be trapped the next step and that's what we're reporting now is to hold on to it see how long can we keep it around so that we can study it after all that's what we want to do we want to study the antimatter compare it to matter and see if they're the same and by study we mean interact with lasers or with microwave radiation to see what their structure is inside how do they behave do they behave exactly like hydrogen within the same lab the effort to pinpoint differences is already underway scientists working with the Asakusa detector are trying to measure the precise weight of an antiproton these oddball molecules contain one antiproton which would normally inhabit the atomic nucleus instead it orbits the nucleus in place of an electron it survives microseconds in the detector but that's enough for the scientists to hit it with a pair of lasers the molecule blows apart on impact and that enables them to calculate the weight of its components we've measured through a precision of nine digits and we found that the antimatter the antiproton mass is exactly the same as a proton mass 2 therefore our nine digits of precision if they find there is a difference it's bound to be subtle will it be enough to shed light on why matter survived and antimatter did not the differences may lie much deeper in the structure of matter that we've so far been able to go scientists are now preparing to throw a new generation of powerful technologies at the problem at the Large Hadron Collider at CERN they can send atoms whipping around a 27 kilometer tunnel and into ultra high-energy collisions looking at the zoo of particles that splatter onto the walls of the detectors they are hoping to find differences between quarks and their anti quark counterparts one recent computer calculation performed at Columbia University unveiled differences between quarks and antiquarks when it was assumed that these particles interact with dimensions beyond the four that define the universe we experience still its authors wondered whether the differences are enough to account for our matter filled universe understanding the asymmetry between matter and antimatter is one of the most important quests in modern cosmology because it would help expand or perhaps even challenge aspects of the standard model the clash of these opposite forms in the early universe parks back to William Blake's poem what's immortal hand or eye could frame thy fearful symmetry we now ask what in the chaotic birth of time and space could break nature's symmetry and set our universe in motion

15 Historical Photos You Believe But They’re Fakes

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There’s a reason old photos fascinate us — they let us see and understand that the life we’re used to now was once completely different and almost unimaginable for us today. Like a time machine, historical photographs transport us through the decades and plunge us into the atmosphere of bygone days. But are all of those photos real?

Today it’s rather difficult to tell a real photo from a fake one on the Internet. Mass media also usually misleads us. It happens since it’s really challenging to understand whether a picture has been Photoshopped or not. But these photo-editing gurus appeared even before Photoshop was invented and could change photos the way they wanted. In some cases, they didn’t even have to use any photo correction tools, they only had to start a rumor.

Einstein and a nuclear explosion 0:50
Baby Hitler 1:21
Queen Elizabeth and the Prime Minister of Canada 2:07
Women wearing shorts in public for the first time 2:39
David Bowie and Lemmy 3:18
Bob Marley and Jimi Hendrix playing soccer 3:58
A brave general 4:43
The first ambulance 5:13
Lincoln’s iconic photo 5:51
Niccolo Paganini’s daguerreotype 6:19
The Cottingley fairies 6:58
Fonda and Kerry at an anti-war rally 7:30
A banner of victory over the Reichstag 8:12
A levitating person 8:59
Marilyn Monroe and John Kennedy 9:48

#secretrevealed #historicalphotos #fake

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David Bowie and Lemmy: By onecolouredcalm/Imgur,

Lincoln’s iconic photo: By Library of Congress,

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Music by Epidemic Sound

– In one of the photos, the scientist is riding a bike near a house; in the other picture, there’s a series of 4 nuclear tests at the USA’s Nevada Test Site in 1962.
– Hitler saw the picture and denied being that terrifying-looking child. He ordered his real baby pictures to be published instead.
– The image was taken in 1937, and shorts weren’t common just then, but they were certainly around.
– As for the guy mistaken for Hendrix, he was a trumpet player called Glen Dacosta from the Jamaican band Zap Pow.
– The image claims to show General Ulysses S. Grant on horseback in front of his troops during the American Civil War. But this picture is a fake. It was made from 3 different images.
– The first ambulance as a specialized vehicle was designed by French doctor Dominique Jean Larrey. In 1792, he decided to reorganize the process of rescuing wounded soldiers.
– We all recognize this famous portrait of Abraham Lincoln standing near a table. But there’s only 1/8 of Lincoln in this image.
– This image was considered to be Paganini’s true daguerreotype. As it turned out years later, there are no actual daguerreotypes of the most celebrated violinist — none known to the general public, at least.
– The picture, credited to the Associated Press by mistake, went viral in 2004 during the presidential election campaign. But it was 2 images skillfully combined.
– In the photo, one of the soldiers had a wristwatch on each arm, indicating that he’d probably been looting. One watch was removed, and it could have saved the soldier’s life. Looters were punished with execution in Stalin’s times.
– All he did was jump from his chair into the air and pretend to have levitated. He explained that it was the spirits that had lifted him.
– Many people think that these pictures of Marilyn Monroe and John Kennedy’s affair are real. In fact, these are staged photos by Alison Jackson, who is famous for her bold pictures of celebrity doppelgangers.

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whoa fifteen historical photos you believe but they're fakes Photography is a great way of recording history and getting you a few hundred likes on social media but back to that history part rather often the image is altered and misleads us it turns out that photo editing gurus walked on earth before Photoshop was invented and could change photos any way they wanted so before we reveal some major photographic lies from the past get your unlimited access to a source you can absolutely trust join the Brightside family click the subscribe button and give that notification Bell a ring alright let's start off counting down from number 15 Einstein and a nuclear explosion on social media we often see a photo of Albert Einstein riding a bike with a pretty epic background an atomic explosion it's nothing like your average vacation shot right in fact this picture consists of two combined photos in one of them the scientist is riding a bike near a house in the other picture there's a series of four nuclear tests at the us's Nevada Test Site in 1962 number 14 baby Hitler now this picture of the then Chancellor of Germany appeared in many British and American newspapers in 1933 the captions mention the prophetic nature of the future evil leader who was born in 1889 however the picture was not real and had been altered quite a bit Adolf Hitler saw the picture and denied being that terrifying looking child he ordered his real baby pictures to be published instead however what gets into a newspaper or to make it worse multiple papers will never vanish completely five years later in 1938 Harriette downs from Ohio saw the picture in a magazine and recognized her son John May Warren who was two at the time the picture was taken number thirteen Queen Elizabeth and the Prime Minister of Canada well they say all is fair in love and war and politics you might disagree with this statement but whoever did the publicity for William Lyon Mackenzie King Canadian prime minister from 1935 to 1948 sure did they simply cut out King George the Six from the picture with Queen Elizabeth the Queen Mother to make the politician look more powerful in his election campaign hmm seems like the trick worked number 12 women wearing shorts in public for the first time this photo became famous thanks to a Reddit user who posted it with the caption women wearing shorts in public for the first time causes a car accident well it's not quite true this photo was staged and there were even more photos taken during that photo shoot by the way the image was taken in 1937 and shorts weren't common just that but they were certainly around if you take a closer look you'll see that the car doesn't have a single dent or scratch so whoever created this fake picture should have tried harder number 11 David Bowie and Lemmy many people believe that David Bowie and Lemmy the leader of Motorhead were posing for a photo the legendary musicians died just two weeks apart in December 2015 and January 2016 which is when this image went viral in fact it was nothing but a skillful combination of two images one of the pictures was actually of Lemmy with his girlfriend in 1972 the second one was reversed to fit in better and originally showed Bowie with singer and ex-girlfriend Claudia Lanier number 10 Bob Marley and Jimi Hendrix playing soccer this incredibly famous image of Bob Marley and Jimi Hendrix enjoying a game of soccer backstage has been around for years it was taken on November 27th 1979 at the San Diego sports arena any true Hendrix fan will say it's impossible since the star passed away in 1970 as it turns out the picture was taken during Marley's survival to it it all becomes obvious if you studied the uncropped image closely here pay attention to that shirt in the foreground as for the guide mistaken for Hendrix he was a trumpet player named Glenn DaCosta from the Jamaican bands a pal number nine a brave general the image claims to show general ulysses s grant on horseback in front of his troops during the American Civil War this photo was taken in a proud invincible atmosphere and was used to encourage soldiers but this picture is a fake it was made from three different images the body and the horse were taken from two different images of general Alexander McDowell McCook general Grant's soldiers were Confederate prisoners who had no connection to grant at all number eight the first ambulance you've probably seen a picture named first ambulance hope this title is in fact a lie in the photo you can see the u.s. ambulance used during the Civil War the first ambulance as a specialized vehicle was designed by French doctor Dominick Jean larae in 1792 he decided to reorganize the process of rescuing wounded soldiers as an independent institution the ambulance service was formed after the disastrous fire at the Vienna Ring Theatre in 1881 number seven Lincoln's iconic photo we all recognize this famous portrait of Abraham Lincoln standing near a table but there's only 1/8 of Lincoln in this image the photo was stitched together from two different pictures and the body actually belongs to a prominent politician named John Caldwell Calhoun the funny thing is that Lincoln was against slavery and Calhoun strongly defended this ideology number six niccolò paganini z' daguerreotype the daguerreotype process or degorio potti was the first publicly available photographic process introduced worldwide in 1839 and for nearly 20 years it was the one most commonly used this image was considered to be packing in EES true to gary o-type as it turns out years later there are no actual degorio types of the most celebrated violinist none known to the general public at least the person in the picture is Giuseppe Florina a violin maker he created this fake photo and had been misleading people for many years number five the Cottingley fairies cousins Elsie Wright and Frances Griffiths took several pictures that attracted the attention of Arthur Conan Doyle he was a spiritualist and believed that these young ladies had managed to take photos of tiny fairies he even used one of them to illustrate his book the girls later admitted that the photographs were fake and that they'd used cardboard cutouts of fairies copied from a popular children's book number four Fonda and Kari at an anti-war rally remember that I mentioned politicians using photography as a tool of propaganda well here's another good example of that this picture credited to the Associated Press by mistake went viral in 2004 during the presidential election campaign but it was two images skillfully combined one of them was taken on June 13th 1971 of John Kerry at an anti-war rally in Mineola New York the second was of Jane Fonda speaking at a Miami Beach rally in August 1972 can light the copyright owner of the original image of Kerry revealed the original negatives to prove the shot was a fake number three a banner of victory over the Reichstag did you know that this legendary photo was staged photographer yevgenii called 'i was choosing between three locations for the victory shot the Brandenburg Gate Tempelhof Airport and the Reichstag building which eventually won by the time the photographer Berlin Soviet soldiers had already raised their flag over the building this fact is universally known but not so many people know that the picture was retouched a little in the photo one of the soldiers had a wristwatch on each arm indicating that he probably had been looting one watch was removed and it could have saved the soldier's life looters were punished with execution in Stalin's times number two a levitating person technically this photo is real and it wasn't photo shot we also know the name of the person depicted in the photo but it's still a fraud the man is Colin Evans an early twentieth-century spiritualist medium now aren't these guys ever large know they're always medium anyway he was performing in complete darkness when the picture was taken all he did was jump from his chair into the air and pretend to have levitated he explained that it was the spirits that had lifted him a cord leading from a device in his hand indicated that it was Evans himself who triggered the flash photography finally it's time for the most provocative shot for today number one Marilyn Monroe and John Kennedy many people think that these pictures of Marilyn Monroe and John Kennedy's affair are real in fact these are staged photos by Alison Jackson who is famous for her bold pictures of celebrity doppelgangers the only known real photo of Marilyn and President John F Kennedy was taken the same day she performed her famous happy birthday mr. president at his 45th birthday party at Madison Square Garden on May 19 1962 so did you know that these images were fakes please share your thoughts in the comments below don't forget to give this video a like share it with your friends and click Subscribe stay on the bright side

Carl Sagan, Stephen Hawking and Arthur C. Clarke – God, The Universe and Everything Else (1988)

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Stephen Hawking, Arthur C. Clarke and Carl Sagan (via satellite) discuss the Big Bang theory, God, our existence as well as the possibility of extraterrestrial life.

Why can't you go faster than light?

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One of the most counterintuitive facts of our universe is that you can’t go faster than the speed of light. From this single observation arise all of the mind-bending behaviors of special relativity. But why is this so? In this in-depth video, Fermilab’s Dr. Don Lincoln explains the real reason that you can’t go faster than the speed of light. It will blow your mind.

over the past hundred years or so scientists have pushed our understanding of the universe into some extreme conditions for example the world of the very small the realm of very high speeds and under the frigid conditions of near absolute zero while each of us have developed an intuition about how the world works it's very important to remember that this intuition only applies to a very limited set of conditions for instance there's absolutely no reason to expect that matter will act the same in the center of the Sun as it does here on earth on a bright and sunny day however that last statement is hard for some people to accept and judging by my email INBOX the extreme realm that causes people the most difficulty is what happens when things are going super fast in 1905 Albert Einstein published his theory of special relativity it predicts all sorts of mind-blowing things for instance distance shorten and clocks slowed down I made another video about how clocks act at high speed it turns out that all of those seemingly crazy implications originate from a single cause or maybe two if we take it slow so first let me tell you what this video isn't it doesn't tell you about the postulates that Einstein used to build this intuition and it certainly doesn't derive as equations instead this video tries to tell you the key insights that make it easier to develop a relativistic intuition I hope to teach you why it is impossible to go faster than the speed of light if you're not a physics groupie hearing that there's a maximum speed in the universe might surprise you but it's true and if you are a groupie you've probably heard that the reason that you can't go faster than light is due to the fact that mass increases when you speed up it turns out that the explanation of mass changing as you go faster is a wrong one I know that statement is going to confuse some people including those with fairly sophisticated understandings of relativity but it's true however that then leaves an open question just why is it that you can't go faster than speed of light it turns out to be due to a combination of a deep and fundamental property of the universe and fairly simple geometry so let me explain how that all works the first two the two crucial insights is that Einstein taught us the space and time were not separate entities but rather they are two components of a bigger idea called space-time I'll give you a helpful visual way to think about this in a moment but for right now just trust me on this then we need to combine that insight with the observation that everybody sees the speed of light to be the same no matter how fast they're moving with respect to one another let's start with an analogy and then come back to relativity to understand the analogy you need to imagine a car driving on a huge flat surface further you need to imagine that the car can only move at one speed say 60 miles per hour or so the comments don't fill up with a metric snobbery hate-mail 100 kilometers per hour now let's put a couple of arrows on the screen to point out north and east well we know the overall speed the car is going we don't know how much of it is in the east direction and how much of it is in the north direction so let's take a closer look at that the car can move entirely in the eastward direction which means that it has no motion in the northward direction or the car can move entirely northward and not at all eastward or we can live dangerously and move towards the Northeast in this case we see that the car is moving in both the east and north directions with neither direction getting all of the motion so that's the core analogy and hopefully it's very clear now let's bring in relativity and relativity we don't have the east and north directions instead we have space-time let's imagine that the horizontal direction of space and the vertical direction is time so suppose that there is a single and fixed speed that we can travel through space-time this happens to be true so it's not a ridiculous supposition we can therefore mix these ideas with our earlier analogy an object can move vertically in that case there moving through space and they're moving entirely through time that's probably what you're doing right now you're sitting and watching this video so your position in space isn't changing however you are experiencing time you aren't moving through space but you're moving through time on the other hand what happens as you start moving through space that's a fancy way to say that you've gained some velocity well we see here that what starts to happen is that as you begin to move through space you move less through time and eventually when you move only through space you don't move through time at all and this is basically what relativity says as you move faster and faster your clocks slowed down and as you get very close to the speed of light your clocks very nearly stopped we've scientifically proven that this is what happens and I direct you to my video on time dilation so you can see one way that we've tested that so this brings us to our fundamental realization of relativity the reason that we can't move through space faster than the speed of light is because we're constantly moving through space time at a single speed the speed of light if we aren't moving through space we experience time in the fastest way and if we start moving through space we experience time slower and slower finally since we're moving through space time at a single speed that means when we're only moving through space there's no more speed to gain we move through space at the speed of light and that's it this observation wasn't made by Einstein it was made by his mentor Hermann Minkowski Minkowski was one of Einstein's mentors and he was a better mathematician two years after Einsteins a seminal 1905 paper Minkowski appreciated the geometrical underpinnings of special relativity and had determined this deep and fundamental explanation why we can't travel faster than light through space there are two final important points first while Minkowski showed why Lightspeed is the maximum speed through space what he didn't explain was why we move only at one speed through time to this day nobody really knows it seems to be a fundamental property of space-time maybe it will take another person as smart as Einstein to figure out that particular conundrum the second point is more technical and I mention it only for the real physics nerds in my analogy I connected space and time as being similar to east and north and there's a lot of merit in that morphing from motion through time to motion through space was like turning a car from moving north to moving east however this analogy is also technically inaccurate from a mathematical point of view it uses the geometry of circles well the proper geometry is that of hyperbolas I only bring this up because I want you to know my analogy is imperfect and you shouldn't push it too far otherwise you might come to a numerically incorrect conclusion and think that you've made a new discovery if you want to dig into this more deeply be sure to use the full and proper Minkowski mathematics still even with the limitations I mentioned the core point is valid the reason that you can't move faster through space than the speed of light is because every object moves through space-time at one and only one speed the speed of light once you've embraced that central idea and the fact that space and time are just like two directions of space-time then all of those seemingly weird observations of relativity just click into place and special relativity makes total sense so I don't know about you but I think this insight about relativity is just about the coolest thing ever if you liked this video be sure to LIKE subscribe and share let's get those numbers up and let me know what you think in the comments I'll see you next time and keep on physics

Lecture 1 | The Theoretical Minimum

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(January 9, 2012) Leonard Susskind provides an introduction to quantum mechanics.

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General Relativity & Curved Spacetime Explained! | Space Time | PBS Digital Studios

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The Final Installment of our General Relativity Series!!!

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We’ve been through the first few episodes of our crash course on general relativity, and came out alive! But it’s officially “time” for CURVED spacetime. Join Gabe on this week’s episode of PBS Space Time as he discusses Newton and Einstein’s dispute over inertial frames of reference. Is Einstein’s theory inconsistent? Is gravity even a force??? Check out the episode to find out!

Previous Installments of the General Relativity Series:

“Are Space And Time An Illusion?”:

“Is Gravity An Illusion?”

“Can A Circle Be A Straight Line?”

“Can You Trust Your Eyes In Spacetime?”:

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well we're finally here a synopsis of general relativity that builds on these previous four episodes if you haven't seen them then pause me now go watch them in order and meet me back here after the music to hear about curved space-time mutants and Einstein's dispute over gravity comes down to competing notions of what constitutes an inertial frame of reference Newton says that a frame on Earth's surface is inertial and relative to that frame a freely falling Apple accelerates down because it's pulled by a gravitational force but Einstein says nah it's the apples frame that behaves like a frame in deep space so the apples frame is inertial and the earth frame is actually accelerating upward you just get a false impression of a gravitational force downward for the same reason that a train car accelerating forward gives you a false impression that there's a backward force so who's right well between our gravity illusion episode and your comments we've seen that Einstein's position seems internally inconsistent remember that inertial frame in Zeke's face well the Apple accelerates relative to it so even Urschel frames define the standard of non acceleration how can both of those frames be inertial today we're finally going to show how curved space-time makes einstein's model of the world just a self-consistent as newton's step one is to express both Newtons and einstein's view points in geometric space-time terms since that's the only way to compare them in a reliably objective way remember humans experience the world and talk about the world dynamically as things moving through space over time but even in a world without gravity we already know that clocks rulers and our eyes can all mislead us so to be sure we're talking about real things as opposed to just artifacts of our perspective we have to translate dynamical statements into tense lists statements about static geometric objects in 4d space-time let's start with Newton he says that space-time is flat just think about it on the flat space-time diagrams of inertial observers the world lines of other inertial observers are straight indicating constant spatial velocity this captures Newton's idea that inertial observers shouldn't accelerate relative to other inertial observers Newtonian gravity would just be an additional force we introduced like any other that would cause some world lines to become curved II's facially accelerated this is a bit oversimplified but for today it'll do now for Einstein's position this is actually more subtle and it'll be easier to explain if I first set up an analogy using our old friend the 2-dimensional ant on the surface of the sphere a tiny patch at the equator looks like a plane and within that patch two great circles both look straight but suppose the ant believes that he lives on an actual plane and decides to draw an XY grid on a large patch of the sphere with its x-axis along the equator and the y axis along a longitude line relative to this grid the second grade circle looks bent so the ant concludes that it's not a geodesic but you see the ants mistake right his grid is distorted you can't put a big rectangular grid on a sphere without bunching it up try it with some graph paper and a basketball it doesn't work stated another way a sphere can accommodate local Euclidean grids and tiny patches but not global ones so the ant can use his axes as rulers and protractors within a patch but not between patches flat space definitions of straightness apply over small areas but not big ones okay Einstein's position is that Newton is making the same mistake as the ant inertial frames that means axes plus clocks are the spacetime equivalent of ants XY grid if space-time is curved then those frames are only valid over tiny space-time patches so when an observer in deep space says that the falling Apple is accelerating he's pushing his frames past the point of reliability just like the ant did in other words global inertial frames don't exist in space-time however global inertial observers do their observers that have no forces on them their world lines will be geodesics and their axes and clocks can serve as local inertial frames provided that we think of them as being reset in each successive space-time patch and by the way pictures like this are not intended to make literal visual sense on the contrary they're designed to break your excessive reliance on your eyes so that your brain becomes more free to accept what reality isn't remember no one can really see or draw space-time there is no spoon now the world line of a falling Apple turns out to be a geodesic it has no forces on it so there's no need to invent gravity okay but what about two apples in a falling box like at the end of our gravity illusion episode remember they get closer as the box fault now according to mutant that happens because the apples fall radially instead of down but according to Einstein it happens because the apples are on initially parallel geodesics that since space-time is curved can and do cross just like on the sphere in contrast the world line of a point on Earth's surface is not a geodesic it has a net force on it and it's really accelerated so does that mean that Earth's surface has to be expanding radially well be careful in order to compare distant parts of Earth you'd need a single frame that extends across space-time patches but that frame can't be inertial so any conclusions you base on it have to be interpreted with a heavy grain of salt okay so Einstein's gravity free curved space-time sounds like it's self consistent but then again so does Newton's flat space-time picture that has gravity injected as a kicker so once again which of them is right the answer is whoever agrees better with experiments and there's over a century of experiments to refer to now we haven't probably fleshed out all of general relativity yet but there's one experimental fact that I can use to show you that space-time must be curved just based on what we've seen in this series of episodes so far it's a cool argument originally presented over 50 years ago by physicist Alfred shild and it goes like this fire a laser pulse from the ground floor of a building up to a photon detector on the roof now wait five seconds and then do it again on a flat space-time diagram the world lines of those photons should be parallel and congruent without making any assumptions about how gravity affects light that would be true even if it turned out that gravity slowed photons down and bent their world lines since both photons would be affected identically now space-time is flat then clocks on the ground and on the roof should run at the same rate they're both stationary thus the vertical lines at the ends of the photon world lines should also be parallel and congruent but if you actually do this experiment you find that photons arrive on the roof slightly more than five seconds apart the excess time is less than a nanosecond but any discrepancy means that clocks are running at different rates in which case the opposite sides of this parallelogram aren't congruent and that's geometrically impossible if space-time is flat thus the very existence of gravitational time dilation regardless of its degree requires that space-time be curved and that means game over for Newton in fact to the extent that we can speak about space sometimes separately at all most of the everyday effects on earth the Newton would attribute to gravity are due to curvature in time the 3d space around earth is almost exactly Euclidean those pictures that you see of Earth deforming a grid the way a bowling ball deforms a rubber sheet or even the pictures we sometimes use on this show they all suggest spatial curvature only so they're somewhat misleading remember a frame consists of axes and clocks and around Earth space-time curvature manifests itself seam clocks much more than in rulers so even though it's hard to visualize it's curved time that makes the freefall orbits of satellites look spatially circular in frames of reference that cover too big a space time patch so why is space-time curved in the first place unfortunately the math gets heavier here and good analogies are harder to come by but here's the flow chart level answer consider a region of space-time and remember that means a collection of events not just locations its curvature and geodesics are determined by how much energy is present at those events via a set of rules called no surprise the Einstein equations so for example say you stick the energy distribution of the Sun into the Einstein equations and turn a crank what comes out is a map of the geodesics in the sun's space-time neighborhood now when you translate those geodesics into 3d spatial and temporal terms what you find is planetary orbits or spatially straight radially inward trajectories along which you would see spatial speed increase or pretty much anything else that you would otherwise attribute to a gravitational force it's pretty amazing I want to conclude with a question once asked by one of our viewers Evan Hughes if there's no gravity and gravity is not a force and why do we keep using that word well physicists are still human as far as I know most of us have no special ability to visualize or directly experience 40 space-time so we often think in Newtonian gravitational terms because it's easier and because the resulting errors are usually small we just remind ourselves that it's just a crutch that we have to use with caution but even when people are referring to relativity or string theory or whatever it's just a lot easier to say the word gravity than to say curvature or four-dimensional space-time you

What's Inside A Black Hole?

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What’s Inside A Black Hole?

Black holes are mysterious and bizarre objects in the universe that really have no explanation. In fact, we hardly know anything about what lies inside of a black hole. We know and understand what we see on the outside of a black hole, but we have no way of going inside one to take a look at what is really happening. Even if we sent a probe inside a black hole, it would not survive the journey, and there would be no way that the probe could transmit a signal outside once it had been sucked inside. This is because a black hole is the product of mass being squeezed together so densely, and so tightly, that it creates a gravitational pull that is so strong, that not even light can escape its grasp.

Supermassive black holes with masses millions to billions of times that of the sun are thought to lurk at the hearts of all galaxies in the universe. You may notice that when you see a photo of a spiral galaxy, such as the Milky Way, in the center of the galaxy is a giant mass of light, which many people would think looks like a massive sun.

But this is not light coming from the black hole itself. Remember, that light cannot escape the heavy gravitational pull. Instead, the light we see comes from the magnetic fields near a spinning black hole that propel electrons outward in a jet along the rotation axis. The electrons produce bright radio waves. Quasars are believed to produce their energy from massive black holes in the center of the galaxies in which the quasars are located. Because quasars are so bright, they drown out the light from all the other stars in the same galaxy.

You’re probably asking, ‘well, what’s a quasar?’ A Quasar is the short name for ‘quasi-stellar object’ and is a very highly energetic object surrounding an actively feeding Supermassive Black Hole. In more basic terms, the Supermassive Black Hole in the middle of a galaxy feeds intermittently. As it feeds, gas swirls around it at incredible speeds and forms an insanely bright hot orbiting disk. And if the black hole is swallowing a large amount of material, this feeding is accompanied by gigantic jets of gas. These are called Quasar. They are essentially fueled by the Black Holes they orbit.

What's inside a black hole Black holes are mysterious and bizarre objects in the universe that really have no explanation in fact We hardly know anything about what lies inside of a black? Hole we know and understand what we see on the outside of a black hole But we have no way of going inside one to take a look at what is really happening Even if we sent a probe inside a black hole It would not survive the journey And there would be no way that the probe could transmit a signal outside once it had been sucked inside This is because a black Hole is the product of mass being squeezed together, so densely and so tightly that it creates a gravitational pole That is so strong that not even light can escape its grasp Supermassive black holes with masses millions to billions of times that of the Sun are thought to lurk at the hearts of all galaxies in the universe You may notice that when you see a photo of a spiral galaxy Such as the Milky Way in the center of the galaxy is a giant mass of light? Which many people would think looks like a massive Sun, but this is not light coming from the black hole itself Remember that life cannot escape the heavy gravitational pull Instead the light we see comes from magnetic fields near a spinning black hole that propel electrons outward in a jet Along the rotation axis the electrons produce bright radio waves Quasars are believed to produce their energy from massive black holes in the center of the galaxies in which the quasars are located But quasars are so bright they drown out the light from all the other stars in the same galaxy. You're probably asking well What's a quasar a quasar is the short name for quasi stellar object and is a very highly energetic object? Surrounding an actively feeding supermassive black hole in more basic terms the supermassive black hole in the middle of a galaxy feeds intermittently as it feeds gas swirls around it at incredible speeds and Forms an insanely bright hot orbiting disc and if the black hole is swallowing a large amount of material this feeding is accomplished by gigantic Jets of gas these are called quasar They are essentially fueled by the black holes They orbit some supermassive black hole giants release an extraordinarily Large amount of light when they rip apart stars in devour matter and are likely the driving force behind these quasars When material gets too close to a black hole it forms that bright hot accretion disk around the black hole That accretion disk heats up to millions of degrees Blasting out an enormous amount of radiation The magnetic environment around the black hole forms twin Jets of material which flow out into space for millions of light years This becomes what is called an active galactic nucleus Or a GN the diet of known black holes consists mostly of gas and dust which fill the otherwise empty space throughout the universe black holes can also consume material torn from nearby stars in fact the most massive black holes can swallow stars whole Black holes can also grow by colliding and merging with other black holes This growth process is what can and usually does reveal the presence of a black hole? But supermassive black holes aren't always feeding if a black hole runs out of food the Jets run out of power and shut down Right up until something gets too close and the whole system starts up again the supermassive black hole at the center of our Milky Way Galaxy is all out of food or space material to consume It lies completely dormant for the time being a sleeping giant, so it doesn't have an active galactic nucleus And so there is no quasar emitting light however We are on a collision course with another galaxy and in 10 billion years or so when the Milky Way collides with the Andromeda galaxy Our supermassive black hole may roar back to life as a quasar as it begins to consume part of this new galaxy Now it might sound like black holes are dangerous and that anything that even remotely comes close to a black hole Would get sucked inside and be crushed and while it's true that if you manage to carefully drop an object into a black hole You'd never get that object back, but black holes are actually remarkably bad at pulling material close to them There are a couple of reasons for this one black holes aren't actually attractive to anything for any reason other than gravity Much like our solar system is in a stable orbits around the Sun the vast majority of a galaxy is in a stable orbit around the black hole with no real reason to go plunging towards the very center of The galaxy the second reason that black holes are bad at being astronomical vacuum cleaners is that they're really? Really inefficient at getting material close enough to them to cross the event horizon and add to the mass of the black hole Even small black holes which exist in great numbers in the galaxy are much better at tearing a companion star apart than they aren't actually Growing their own size by consuming the star hole so despite their reputation Black holes will not actually suck in objects from large distances a black hole can only capture objects that come very close to it They're more like venus flytraps than cosmic vacuum cleaners for example imagine replacing the Sun by a black hole of the same mass permanent darkness would fall on earth But the planets would continue to revolve around the black hole at the same distance and speed as they do now None of the planets would be sucked into the black hole our earth would be in danger Only if it came within some 10 miles of the black hole Much less than the actual distance of the Earth from the Sun which is a comforting 93 million miles away So after knowing all of this do we have any idea, what is inside of a black hole? Current theories predict that all the matter in a black Hole is piled up in a single point at the center But we do not understand how this central singularity works to properly understand the black hole center requires a fusion of the theory of gravity With the theory that describes the behavior of matter on the smallest scales called quantum mechanics This unifying theory has already been given a name quantum gravity, but how it works is still unknown This is one of the most important unsolved problems in physics Studies of black holes may one day provide the key to unlock this mystery Einstein's theory of general relativity allows unusual characteristics for black holes For example the central singularity might form a bridge to another universe. This is similar to a so-called wormhole Which is a mysterious solution of Einstein's equations that has no event horizon? Bridges and wormholes might allow travel to other universes or even time travel, but without observational and experimental data This is mostly speculation We do not know whether bridges or wormholes exist in the universe or could even have formed in principle By contrast black holes have been observed to exist and we understand how they form What is actually inside of a black Cole is still a mystery? So does a black hole live forever if there is nothing for a black hole to consume then no in Fact a very surprising thing happens you might have heard of Stephen Hawking He is a theoretical physicist in cosmologists, and is at the forefront on the study of black holes He came up with a theoretical prediction that black holes emit radiation this of course is now known as Hawking radiation Hawking radiation reduces the mass and energy of black holes and is therefore also known as black hole evaporation Because of this black holes that do not gain mass through other means are expected to shrink and ultimately vanish What it means is that if the black hole has nothing to eat it? Eventually evaporates the energy and mass that the black hole pulled inside of itself Evaporates back out into space in the form of radiation. It is almost as if a black Hole is a universe recycling machine Stephen Hawking proved this in 1974 by using the laws of quantum mechanics to study the region close to a black hole horizon The quantum theory describes the behavior of matter on the smallest scales it predicts that tiny particles and light are continuously created and destroyed on subatomic scales Some of the light thus created actually has a very small chance of escaping before it is destroyed to an outsider It is as though the event horizon glows the energy carried away by the glow decreases the black hole's mass until it is completely gone This surprising new insight show that there is still much to learn about black holes However, Hawking's glow is completely irrelevant for any of the black holes known to exist in the universe For them the temperature of the glow is almost zero and the energy loss is negligible The time needed for the black holes to lose much of their mass is unimaginably long however if much smaller black holes ever existed in the universe Then Hawking's findings would have been catastrophic a black hole as massive as a cruise ship would disappear in a bright flash in less than a second as You can see black holes are incredible and mysterious things perhaps one day We will know exactly what lies inside of a black Hole, maybe we will find out that they are gates to another dimension such as wormholes Or maybe we will never know and just come to accept their existence as they are

Mysteries of a Dark Universe

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Cosmology, the study of the universe as a whole, has been turned on its head by a stunning discovery that the universe is flying apart in all directions at an ever-increasing rate.

Is the universe bursting at the seams? Or is nature somehow fooling us?

The astronomers whose data revealed this accelerating universe have been awarded the Nobel Prize for Physics.

And yet, since 1998, when the discovery was first announced, scientists have struggled to come to grips with a mysterious presence that now appears to control the future of the cosmos: dark energy.

On remote mountaintops around the world, major astronomical centers hum along, with state of the art digital sensors, computers, air conditioning, infrastructure, and motors to turn the giant telescopes.

Deep in Chile’s Atacama desert, the Paranal Observatory is an astronomical Mecca.

This facility draws two megawatts of power, enough for around two thousand homes.

What astronomers get for all this is photons, tiny mass-less particles of light. They stream in from across time and space by the trillions from nearby sources, down to one or two per second from objects at the edge of the visible universe.

In this age of precision astronomy, observers have been studying the properties of these particles, to find clues to how stars live and die, how galaxies form, how black holes grow, and more.

But for all we’ve learned, we are finding out just how much still eludes our grasp, how short our efforts to understand the workings of the universe still fall.

A hundred years ago, most astronomers believed the universe consisted of a grand disk, the Milky Way. They saw stars, like our own sun, moving around it amid giant regions of dust and luminous gas.

The overall size and shape of this “island universe” appeared static and unchanging.

That view posed a challenge to Albert Einstein, who sought to explore the role that gravity, a dynamic force, plays in the universe as a whole.

There is a now legendary story in which Einstein tried to show why the gravity of all the stars and gas out there didn’t simply cause the universe to collapse into a heap.

He reasoned that there must be some repulsive force that countered gravity and held the Universe up.

He called this force the “cosmological constant.” Represented in his equations by the Greek letter Lambda, it’s often referred to as a fudge factor.

In 1916, the idea seemed reasonable. The Dutch physicist Willem de Sitter solved Einstein’s equations with a cosmological constant, lending support to the idea of a static universe.

Now enter the American astronomer, Vesto Slipher.

Working at the Lowell Observatory in Arizona, he examined a series of fuzzy patches in the sky called spiral nebulae, what we know as galaxies. He found that their light was slightly shifted in color.

It’s similar to the way a siren distorts, as an ambulance races past us.

If an object is moving toward Earth, the wavelength of its light is compressed, making it bluer. If it’s moving away, the light gets stretched out, making it redder.

12 of the 15 nebulae that Slipher examined were red-shifted, a sign they are racing away from us.

Edwin Hubble, a young astronomer, went in for a closer look. Using the giant new Hooker telescope in Southern California, he scoured the nebulae for a type of pulsating star, called a Cepheid. The rate at which their light rises and falls is an indicator of their intrinsic brightness.

By measuring their apparent brightness, Hubble could calculate the distance to their host galaxies.

Combining distances with redshifts, he found that the farther away these spirals are, the faster they are moving away from us. This relationship, called the Hubble Constant, showed that the universe is not static, but expanding.

Einstein acknowledged the breakthrough, and admitted that his famous fudge factor was the greatest blunder of his career.

cosmology the study of the universe as a whole has been turned on its head by a stunning discovery that the universe is flying apart in all directions at an ever-increasing rate is the universe bursting at the seams or is nature somehow fooling us the scientists whose data revealed this accelerating universe have been awarded the Nobel Prize for Physics and yet since 1998 when the discovery was first announced scientists have struggled to come to grips with the mysterious presence that now appears to control the future of the cosmos dark energy on remote mountaintops around the world major astronomical centers harm Allah with state-of-the-art digital sensors computers air-conditioning infrastructure and motors to turn the giant telescopes deep in Chile's Atacama Desert the Paranal Observatory is an astronomical Mecca this facility draws two megawatts of power enough for around 2,000 homes what astronomers get for all this is photons tiny massless particles of light they stream in from across time and space by the trillions from nearby sources down to one or two per second from objects at the edge of the visible universe in this age of precision astronomy observers have been studying the properties of these particles to find clues to how stars live and die our galaxies form how black holes grow but for all we've learned we are finding out just how much still eludes our grasp how short our efforts to understand the workings of the universe still for cosmology the study of the universe as a whole goes back to the ancient Greeks with no telescopes or other optical instruments to probe the Stars observers constructed models designed to make sense of what they saw their earliest theories stated that all matter in the universe is composed of some combination of four elements earth water fire and air each arises from opposing properties of heat and cold dry and wet acting upon more primitive forms of matter Aristotle took it a step further he held that the universe is divided into two parts the realm of earth in which everything is composed of the four substances and the realm of the stars and planets these bodies are made up of a fifth substance unchanging and incorruptible called ether or quintessence the Greek idea that the universe is a series of concentric circles with earth at the center yielded to a wealth of new discoveries about the universe that earth is a planet in a solar system located in a giant wheel of stars and gas a galaxy bound by gravity to a local group of 30 galaxies bound in turn to a cluster of over a thousand galaxies and to a super cluster with tens of thousands of galaxies this our cosmic region takes up a volume about 100 million light-years across set within a larger pattern of galaxies filaments super clusters and enormous empty vorlons earth is but a speck within a firmament so vast we can scarcely imagine for all we've learned from snatching photons the most basic nature of the universe has only grown more mysterious ironically modern models have recalled the mysterious Fifth Element conjured by the Greeks to explain a universe that appears to move in ways not easily explained to understand the predicament now faced by scientists let's see how they got there in the first place a hundred years ago most astronomers believe the universe consisted of a grand disk of stars and gas the Milky Way they saw stars like our own Sun moving around it amid giant regions of dust and luminous gas the overall size and shape of this island universe appeared static and unchanging that view posed a challenge to Albert Einstein who sought to explore the role that gravity a dynamic force plays in the universe as a whole there is an out legendary story in which Einstein tried to show why the gravity of all the stars and gas out there didn't simply cause the universe to collapse into a heap eery zijn that there must be some repulsive force that countered gravity and held the universe up he called this force the cosmological constant represented in his equations by the Greek letter lambda it's often referred to as a fudge factor in 1916 the idea seemed reasonable the Dutch physicist velum de sitter topped Einstein's equations with a cosmological constant lending support to the idea of a static universe now enter the American astronomer Vesto Slipher working at the Lowell Observatory in Arizona he examined a series of fuzzy patches in the sky called spiral nebulae what we know as galaxies he found that their light was slightly shifted in color you it's similar to the way a siren distorts as an ambulance races past us if an object is moving toward Earth the wavelength of its light is compressed making it blue if it's moving away the light gets stretched out making it redder 12 of the 15 nebulae that slifer examined were red shifted a sign they are racing away from us Edwin Hubble a young astronomer went in for a closer look using the giant new hooker telescope at the Mount Wilson Observatory in Southern California he scoured the nebulae for a type of pulsating star called a Cepheid the rate at which they're light rises and falls is an indicator of their intrinsic brightness by measuring their apparent brightness Hubble could calculate the distance to their host galaxies combining distances with redshifts he found that the farther away these spirals are the faster they are moving away from us this relationship called the Hubble constant showed that the universe is not static but expanding Einstein acknowledged the breakthrough and admitted that his famous fudge factor was the greatest blunder of his career the discovery revolutionized astronomy because it redefined the universe as a dynamic realm but if he were around today Einstein would be surprised to see his own failed idea return if the universe is expanding it must have emerged from a dense and hot primordial state a cosmic fireball we now call the Big Bang would have supplied the initial kick even as the universe expanded gravity began drawing matter together into a web-like structure that gave rise to galaxies and stars if there's enough matter out there we'll gravity one day reign in the Big Bang and cause the universe to collapse in on itself to find out astronomers renewed Hubble's quest to precisely measure the cosmic expansion rate working with the Hubble Space Telescope and giant new observatories on land they sought to measure distances far deeper than Hubble ever could people are talking about doing precision cosmology for the first time because it used to be cosmology well we have a rough idea how big the universe is maybe to a factor of two or three but now with these new measurements were really getting a handle on the overall density and structure of the universe and what they're telling us is not what we expected to hear roubles mileage markers were the Cepheid today astronomers look for stars like our Sun in their death throes they spend their lives gradually consuming the hydrogen gas that makes up their cores at the end of the line the dying star swells and sheds its outer layers leaving behind a tiny dense sphere the size of Earth it's so dense that if you could scoop out a teaspoonful of matter from its core it would weigh a thousand metric tons if this white dwarf happens to orbit another dying star it may begin to draw upon the companions expanding outer layers at a critical threshold it can grow no more and it explodes scientists at the University of Chicago and Argonne National Lab have been simulating the thermonuclear reaction that begins deep within the star a nuclear flame sends hot ash rising to the surface it breaks out then begins to wrap around the star a collision on the other side of the star triggers the explosion because type 1a supernovae are all thought to explode in the same way and because they are extremely bright they are ideal for measuring extreme distances it's like looking at cars with identical headlights approaching on a highway the dimmer they appear the farther away they are by documenting explosions through the depth of the universe two groups of astronomers had hoped to find out how quickly gravity has been raining in the cosmos capturing the trickle of photons from events six or eight billion years ago would test the sensitivity of even the most powerful modern telescopes when they spotted a type 1a supernova astronomers looked at how much its light was shifted to the red the larger the shift the more the universe had expanded since the explosion they combined this measurement with its distance based on the apparent brightness of the supernovae some explosions looked dinner than expected based on their redshift that meant their light had traveled over a greater distance to reach us that led the two teams to the same conclusion but the cosmic expansion rate had been slower in the deep past for the universe to reach its current size the expansion had to actually accelerate scientists have known since the 1930s that the universe is not necessarily the way it appears back then astronomer Fritz Zwicky measured the rotation rate of spiral galaxies and found that their gravitational pull was over 100 times greater than what he expected based on the amount of matter he could see there must be some gravitational presence Vickey surmised that you can't see with a telescope he dubbed it dark matter scientists today have successfully recreated the structure of the universe in computer simulations by incorporating dark matter in the gravitational sources that sculpted galaxy clusters and filaments apparently we now bind out there's another unseen presence at work in the universe called dark energy and it's whisper thin for comparison's sake water has a density of one gram per cubic centimeter dark energy is a mere ten to the minus twenty ninth grams per cubic centimeter that's a point followed by twenty eight zeros into one the equivalent of five hydrogen atoms in a cubic meter in their scan of the early universe using the W map satellite scientists concluded that matter and dark matter account for only about 26% of the content of the universe the remainder then is dark energy since 1998 something totally unexpected happened which is we discovered that not only our universe is expanding this expansion is accelerating you know this is a classical who ordered that type situation in seventy percent or so is dark energy in the universe you know about 70% of the surface of the earth is covered with water imagine we didn't have a clue what water was this is the situation we're in so what exactly is it the simplest answer takes us back to Einstein and his repulsive force the cosmological constant it's the idea that empty space is actually a seething stew of particles popping in and out of existence it's a type of energy that is constantly welling up from the vacuum this description is reminiscent of the sudden and violent outpouring of energy that many scientists believe launched our universe in the first place long after the Big Bang vacuum energy exerted enough pressure over extremely large scales to push the universe out and as the universe grew larger more and more of it came into existence causing the expansion to accelerate another explanation takes its name from Aristotle's quintessence while similar to vacuum energy in theory it can vary over time there are still other theories one unifies dark energy and dark matter into a single dark fluid that alters the action of gravity on large scales another digs deep into a warren of hidden physics to suggest that the push of dark energy may one day turn to a pull this theory predicts that in about ten billion years the universe will begin cascading back together in a Big Crunch destined to reduce all of creation to the size of a proton is there a way out of all this cosmic confusion some scientists suggest that the findings derived from type 1a supernovae might be based on an illusion that the measurements are due not to cosmic acceleration but to large-scale factors we have not yet detected since Nicholas Copernicus showed that the earth rotates around the Sun cosmologists have based their theories on the idea that we exist in no special place in that case our view of the universe is similar to any other vantage point in the universe that assumption has allowed us to extrapolate what we see to a vast scale we concluded for example that the universe has expanded in a uniform manner that explains the uniform temperature of light from the early universe within which we can see a pattern of variations and it explains the uniform distribution of galaxies within which we see a pattern of filaments and clusters is it possible that we are still only seeing part of a much grander cosmic map it's like looking at a desert and assuming the rest of the world is flat when in fact it's filled with potions and mountain ranges perhaps there are non-uniform cosmic structures larger than our field of view forming bulges or bubbles for argument's sake if we are located in the center of a giant bubble then supernovae out on the fringes might seem to be accelerating away or if we're in a region of higher density the universe might appear headed for collapse for now it looks like the discovery of the accelerating universe is holding up scientists using NASA's Galaxy Evolution Explorer telescope confirm the finding by using galaxies in the distant universe as another kind of mileage marker as another check they calculated the speed that galaxies should collapse into clusters based on their collective gravity but data showed that something is holding them back and breaking their fall into the clusters the discovery of dark energy is a major accomplishment in this age of precision cosmology ironically its effects may will be lost on our distant descendants right now we're in the outer suburbs of a great cosmic metropolis the Virgo supercluster in time gravity will drag the Milky Way and the rest of the local group into the city limits then stir us into the giant melting pot of a mecha galaxy I then if the wider universe is accelerating outward we'll see little evidence of where it all came from distant galaxies visible today will begin to pass beyond our vision at speeds exceeding that of life both distant generations will know less about the nature of time and space than we do today for now as the data trickles in one photon at a time our minds struggle to unravel the mysteries of a dark universe as they race ever faster beyond our dim horizons you

How Do You Observe a Black Hole?

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Black holes may hold the key to understanding the most fundamental truths of the universe, but how do you see something that’s, well, black? Astronomers think they have the answer. Thanks to a global array of radio telescopes that turn the Earth into a giant receiver, we’ve imaged one black hole (Messier 87) and may soon have the first picture of the event horizon of Sagittarius A*, the black hole at the center of the Milky Way galaxy.

PARTICIPANTS: Shep Doeleman, Andrea Ghez

MODERATOR: Brian Greene


This program is part of the BIG IDEAS SERIES, made possible with support from the JOHN TEMPLETON FOUNDATION.

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0:04 – Understanding escape velocity and black holes
9:25 – Panelist introductions
10:41 – Are black holes really out there?
12:06 – What resides in the center of our galaxy?
13:45 – Evidence of black holes
20:26 – Kek telescope experiment
24:43 – Event Horizon Telescope
32:21 – Simulating a black hole
34:27 – Will we find a deviation from Einstein’s theory?
36:24 – What’s the next phase of our understanding of gravity?


– Produced by John Plummer
– Associate Produced by Laura Dattaro
– Animation/Editing by Josh Zimmerman
– Music provided by APM
– Additional images and footage provided by: Getty Images, Shutterstock, Videoblocks

This program was recorded live at the 2018 World Science Festival and has been edited and condensed for YouTube.

Watch the full unedited program here:

the number of ways that you can think about black holes but one nice way in to the subject is to think about something that's much more familiar thinking about escape velocity let me describe what I mean through a couple of sequences here so imagine that you are on the surface of the earth so let's sort of zoom down right to our planet and we ask ourselves if we fire a projectile from the surface of the earth upward what will happen and we all pretty much know what will happen right so if we take a cannon and we fire a cannonball at a fairly modest speed it's going to go up it's going to come back down if we fire it with a somewhat larger speed it'll go up higher but still it'll come back down but finally if we launch it with the right speed it will go up and it will just barely escape the gravitational pull of the earth and it will go off into space and that speed required for that to happen is what we call escape velocity at the surface of the earth now what is the escape velocity at the surface of the earth yeah if someone actually said it was 11.2 km/s thank you Wow the gold star in the back there about 11 kilometers per second is what you need to surface the earth but here's the question if you were to look at a different planet well that's bigger than the earth what will happen well again you can pretty much picture what will happen if it's bigger it's more massive you're going to need a bigger cannon to fire that cannonball with higher speed because the escape velocity will go up it'll be larger than it is at the surface of the earth but of course if you have that big cannon you actually fire it the cannonball will go up and again if its speed is bigger than escape velocity it will be able to get away but now I want you to think about something a little bit less familiar imagine that this cannon is not firing cannon balls but it's firing balls of light photons now light goes really quickly right I mean light speed what does the speed of light above is everybody uses different units which is nice 671 million miles per hour 300 million comments per second right meters per second I should say so at that high speed of course light will easily be able to escape and be able to go off into space but here's the interesting thought experiment and this is a thought experiment that goes way back this was an experiment that this fella over here John Mitchell this is in the 1700s right long time ago he asked the following question he said look what if you were to imagine looking at say a star like the Sun now clearly the escape velocity at the surface of the Sun is much less than the speed of light so certainly all the light that the Sun emits easily gets away but just as the escape velocity of a planet goes up if you make it bigger more massive he asked well the same should happen for a star so let's imagine making the star bigger where the escape velocity goes up now if it's still less than the speed of light the light will get away but he asked what would happen if you made the star so big that the escape velocity at its surface would be bigger than the speed of light right in that case he imagined that if you made that gigantically massive star light could not get away the escape velocity would be bigger than the speed of light and if light doesn't get away the star would go dark a dark star now this is again in the 1700s right so he is thinking purely in a Newtonian framework that's the only description of gravity that we had back then so the natural question is is this musing of John Michell right to steal loads and this natural philosopher from the 18th century does this idea have relevance when you start to think about gravity in the manner that was given to us by this fellow over here Albert Einstein because I think as we all know in the early years of the 20th century Einstein rethought our understanding of gravity and he gave us the general theory of relativity in which gravity is now thought of in a completely new way not the Newtonian description gravity is thought of as warps and curves in the fabric of space and time so Einstein takes this idea this new way of thinking about gravity he writes his famous paper on the general theory of relativity this is in 1915 his paper becomes widely circulated and indeed about a year later 1916 on the Russian front there's a German astronomer mathematician named Karl Schwarzschild and he's out there in the trenches charged with calculating artillery trajectories and somehow just by coincidence what happens is Einsteins paper just kind of goes by he grabs a hold of it and he gets so captivated by Einsteins ideas that he forgets about artillery trajectories and starts to calculate with general relativity he finds that if you have a spherical body that you crush down to a very small size according to Einstein's math the warp in the fabric of space would be so extreme that nothing can pull away not even light can pull away so it's now a modern day version if you will of what John Michell had imagined an object that goes black because light cannot pull away from it so roughly speaking it would be as if you had a flashlight near the edge of one of these objects and when you turn on the light instead of a light going off into space like it's pulled down into the hole into the black hole this is the modern-day version of what a black hole would be now the term black hole it turned out this was coined on 112 Street and Broadway I'm not joking at the Goddard Institute of Space Studies on 112th and Broadway John Wheeler was given a talk and this way of describing these dark stars came up and wheeler pushed this idea he popularized to say he advanced our understanding of it but this is where the term black hole comes from now this of course is a sort of cartoon version that gets at the basic idea for those that want to see it a little bit more precisely here's really what goes on near the vicinity of a black hole and if you don't understand this it doesn't matter we can put down a spacetime diagram if you remember from high school this is where we have time on this vertical axis and you set off a beam of light that fills out a cone so-called light cone and what happens is the geometry of space and time is so distorted by a black hole that beyond what's called the event horizon the direction of time and space is so twisted that as light propagates it cannot get out of the edge it cannot go beyond the event horizon of the black hole and that's why no light can get out that's why the black hole is black now natural question is okay these are interesting ideas but how in the world would one of these objects come to be and people began to think about this idea for a long time 30s 40s 50s and let me give you one possible scenario by which the kind of object we're looking at a black hole would form and for that we can imagine that we have a large star like a red giant to support its incredible weight this star has nuclear processes taking place in the core that generate heat and light and pressure that props the star up but sooner or later the star uses up all of its nuclear fuel and at that point they can't support its own weight so it begins to implode and as it implodes it gets hotter and denser finally setting off an explosion that ripple through the star and when the explosion reaches the surface of the star it causes the outer layers to explode and what remains if the star was big enough to begin with is a tiny core a dense core that can no longer support its own weight at all and it will collapse all the way down into one of these objects these black holes that's the idea of how these objects could form and what we'd like to do here tonight is explore our current thinking about these objects are they real how would we actually see them and can we get any insight into what happens inside of these spectacular objects and to do that we are going to bring out some experts who spent their careers examining these very questions and let's get to them right now so our first guest is one of the world's leading experts in observational astrophysics who heads UCLA's galactic center group best known for a groundbreaking insights on the center of our galaxy this is the winner of among other things the Crawford Prize in astronomy from the Royal Swedish Academy of Science Anna MacArthur Fellow please welcome Andre agos all right also joining us is an astronomer at the harvard-smithsonian Center for Astrophysics who leads an international collaborative project called the event horizon telescope whose goal is to image the edge the event horizon of a black hole so please welcome Shep dollar mark for joining us here tonight let me just begin with sort of one general question so people have been thinking about this idea of black holes for a long time as I said all the way back in the 1700s and a lot of research has been done thousands of pages of calculations do you think that there are really black holes out there or our theorist imaginations overworked I think it's pretty clear that there are black holes out there of course I'm a little biased since you spend your life trying to observe them yes that's it the fact that there are two kinds of black holes yes black holes that you were just talking about the ones that come from the lifespan of stars and then the supermassive black holes that we think are at the center of the galaxy and those are the ones that you've actually been studying in some detail so that we're going to get to those in just a moment but Shep your general view is more or less the same or do you think there's a chance that it's a red herring that these black things are not really out there oh no it's a beyond a shadow of a doubt I really think they exist I mean there's all these lines of evidence and we see these terrifying engines that the Centers of galaxies that spew out these Jets on either side of them and the only thing that can power them are supermassive black holes so everything is pointing to the fact that these really do exist good so I'm glad you're saying that because had you both said no I don't know what we do with the rest of our time here today but that's great so so Andreea your work as I understand it has been focused on the center of the Milky Way galaxy so first of all just just give us some sense of what you think is residing in the center of our galaxy and then we'll try to look at the evidence that led you to come to that conclusion so we are pretty convinced that there's a supermassive black hole at the center of our galaxy and Oh Superman well when we say supermassive we mean a million – uh well in the case of our own galaxy 4 million times the mass of the Sun and in terms of these really big ones that are at the center of galaxies that's on the low end because we think about things that are a million to a billion times the mass of the Sun and and for a million solar mass black hole like how like for the Sun let's maybe start simple if the Sun was turned into a black hole how what would its radius be it would be about the size of college campus no it depends which college we're talking about good so so a couple kilometers across for the one in the center of the galaxy how big do we think it is it's about ten times the size of the Sun so about ten million ten million kilometers Wow so it's it's it's a big object but it still follows the same basic pattern that it has an edge and event horizon and all the standard lore would apply to it it's just on a bigger scale right it just scales simply with math yeah so so so what evidence do you have that it is a black hole can you sort of take us through that yeah so to prove that there's a black hole directly what you want to do is you want to you want to show that there's a lot of mass inside a small volume or inside a small region and particularly you'd like to show that it's confined within its short shield radius that you were just talking to the latest is is the radius for a given mass where if you can crush the mass within that radius it will naturally turn into a black hole right and so that's what we're the size that we're talking about because of course the black hole itself is infinitesimally small so this this isn't that the abstract size and so our job just clarify that so when you say that you're talking about when the black hole forms the matter crushes down to a small size yeah so the idea of the Schwarzschild radius or is that no light can escape it as we were just talking about but it's also true that once you get the mass to scale gravity will overcome all other known forces and there's nothing that can stop the collapse of the object so from a scientific point of view once you've shown that a mass is within its Schwarzschild radius you have come up with for the proof of a black hole so from the point of view of somebody who's hunting for black holes your job is to show that there's some amount of mass inside of a small volume so the way we've approached it at the center of the galaxy is to look for the stars that are at the heart of the galaxy and to develop techniques that allow us to not only see the stars that are that close but that allow us to observe how they go around the center so if you want to find the center of the galaxy you can look up in the night sky and find the constellation of Sagittarius it's the teapot and the teapot pours into the center of the galaxy all right that's your road so convenient and if you look up at the night sky not in of course New York but in a place that you can actually see the night sky you can see the Milky Way and the Milky Way is that band of white light that comes from the stars but there's also a lack of light which is from all the dust so you can't actually see the center of the galaxy at wavelengths at your eye detects so a key to the work that we've done is to use infrared technology so looking at light that is just long word of what your eye detects maybe we're a TV remote control works yep and that allows us to see the stars that are at the center of the galaxy and we'll have you found and we've found that they go one that we can see them which is rather amazing and that they go around the center of the galaxy quite fast so those my favorite star in the galaxy it's name is so2 goes around every same again so2 okay probably needs a better name yeah it's real catchy but you can use actually Newton's laws of physics to show that if you go around every 16 years and you measure the size of the orbit which is about the size of our solar system that shows that there's about four million times the mass of the Sun inside this incredibly small region and and to give you a sense of the change of our knowledge over our understanding of what resides at the center of the galaxy we've increased the density of dark matter by a factor of ten million compared to what was known before our work so in a sense we've we've advanced the case for the existence of supermassive black holes by that amount may think about anything in your life that you'd like more of and being able to get 10 million times more of right and that's what's happened at the center right so the basic argument as I understand it is you're tracking these stars and their motion can only be explained if there is a black hole of that mass residing in the center of the galaxy you're basically weighing this what's at the center there was this actual data this is the real thing so we've looked at two versions of it one is the flat version which was show uh was playing just a moment ago and and it showed my favorite star and this is actually a bigger view of the data that we that we've taken over the last and I can't believe I'm saying this 25 years have you been involved with it since the beginning this is my baby it is so in fact it's it's interesting to reflect back because when I first proposed this experiment when I first got my job at UCLA I thought I had a good idea it was actually turned down they said the technique wouldn't work and even if it did we wouldn't see stars and even if we saw stars we wouldn't see them move so it was a lot of no no no's right and in fact we were asking to do a project that was only three years long just to see that stars were moving fast no one anticipated that they were moving they would move so fast how fast is fast just to give it oh oh like three million miles an hour so they're they're hauling and it's and it's rather remarkable that we can measure something on a human time scale and so as this project has gone on and maybe we can talk a little later about you know what it takes the technology has changed so much that it's enabled us to do more and more sophisticated kinds of work so this three dimensional animation actually shows the kinds of stars that we see at the center of the galaxy and almost every single prediction for what we should see near the black hole is inconsistent with the observations what does that mean that means it's job security you're trying to figure it out yeah but but it's not inconsistent yet with say the general relativistic prediction no so there's both the physics side of this work where you're trying to ask physics questions like do supermassive black holes exist how does gravity work near a supermassive black hole so the where we are today is that we can definitive or at least in my opinion we can definitively say that the supermassive black hole exists and then the where we are actually we are so in the middle of this can we test Einstein's theory of general relativity and that is what your you're doing now if I understand like we're in actually a special time at this very moment right yes we're in such a special moment I can't believe I'm actually sitting here as opposed to being in Hawaii thank you for taking the time with but tell us tell us what's going on so the reason I'm so excited and we've been preparing for this for years so you know we've been doing wait there's no chance you're gonna miss like this special moment by officially I have grad students so we've been using the Keck telescopes which are pictured here for 25 years and watching the star that goes around every 16 years and if you want to test Einstein's theory of general relativity near supermassive black hole with these stars what you have to do is first make your first go around that gives you a baseline of what what part of space these stars are probing and that's 16 years right there that's 16 years right there my various moments in my life are at the star and then what you want to do is you want to catch it the next time it goes through closest approach and that next time was the year 2018 so I've been thinking 2018 or bust for a number of years so we're in it we're in this season and for us there really is a season because the earth goes around the Sun so and because we're looking at infrared light you're gonna hear from Shep there are different kinds of vices Shep doesn't care about this because the earth goes around the Sun there's only a part of the year that we can see the center of the galaxy at infrared wavelengths so for me we can see it from roughly March to roughly October so there was the beginning of the season and through these roughly six months this star is experiencing incredible accelerations and is experiencing the most extreme forms of gravity as it makes its closest approach so actually there are three key moments one that happened April 10th that happened roughly last week and one that's happening in September that are going to nail down this experiment so it is it's an exciting moment for us and to see the signal emerge from the data it's it's just a treat so if I understand correctly have a prediction based on the general theory of relativity what the trajectory should be well here we have to be a little bit careful because there's a series of kinds of experiments that you part me there's a series of tests of gravity one is how the the light from the star makes it from the star to us in other words how it escapes the curvature of space-time that's actually the first thing that we're getting at this summer the next thing is then how the object itself moves through space-time which is actually should emerge over the next few years so again and if you keep going and of course that's what we want to do you can actually measure the spin of the black hole so this experiment just keeps getting better right and and it's particularly interesting I gather because you know most people think that Einstein's general relativity has been confirmed but is that the right way of thinking about it well it's uh you know it's one of the fun gravity is one of the four fundamental forces but oddly enough it's the least tested of those forces so it's been tested in some regimes but it's never been tested near a supermassive black hole and in some sense a supermassive black hole or black holes in generals represent the breakdown of this theory so what you want to do is you want to get as close as possible to the Hat point where you actually know that theory is no longer holding up and I think we have to have today all sorts of pieces of evidence that says this theory is fraying at the edges so we just push that frontier forward by a large amount in a direction that hasn't been explored before so in principle you could find the first concrete evidence that we need to go beyond Einsteins ideas to really describe what's going on I mean the best of all worlds that would be the outcome of 16 plus years of observation well the outcome is actually just figuring out what's really happening you're the black hole whatever it is yeah yeah yeah spectacular so chef you you were also in the business of looking at black holes there's no business like black hole biz no business like back over there and so you're going about in a different way so we're hearing about infrared light as the probe being used to in andreas work you're using what radio yeah we're using radio waves it turns out that black holes in a paradox of their own gravity are some of the brightest things in the sky right and that's because of a very simple construct all the mat all the gas and dust is trying to get into a very small region so it heats up to hundreds of billions of degrees around Sagittarius a star the supermassive black hole in the center of our galaxy and it radiates in infrared that andraia looks at and also radio waves even little bit in x-rays so if you want to look at a black hole you can come at it from many many different angles no no critical to both of what you're saying is you're not really looking at the black hole you're looking at its effect on its environment right so you can't actually see it person exactly what happens in the black hole stays in the black yeah let's just get that out of the way right now but what we do is we tease around the edges right so in that cannonball analogy you had before light was leaving the black hole but it also orbits around the black hole just think about that for a minute light orbits something right and goes around in a circle and Einstein 100 years ago when he came up with this general theory of relativity those equations show that you should see the silhouette of light around the black hole and that's because of these light orbits around so we look at it and you see light moving around the black hole and it gets brighter on one side on the other side you see something that should be about five times the swirl radii across you know how how big it should be so the event horizon is here and you're looking at five times that distance yeah exactly so you never see inside the black hole you see outside and that shows us the geometry of space-time when you see something like this when you see this shadow feature you're really looking at the deepest puncture in space-time that we can imagine right and the question it's actual have you is this what you guys I mean can you share with us what you guys have seen this is the event horizon telescope I gather you're talking right so there so the question is if you wanted to zoom in by orders of many many thousands and see what was happening right the edge of a black hole you'd have to go way beyond where aundrea sees her stars and go much closer and those stars are about a thousand times farther out than this silhouette that you're seeing here right and if we could measure the size of the silhouette in the shape we test Einstein's theory of gravity right at the edge of the black hole right now how are you doing that yeah there is a handful of radio telescopes I gather yeah so to see something this small these are the smallest objects in the known universe right black holes are tiny and to see them you need magnifying power and as it is with all telescopes the bigger the telescope the more magnifying power you have now we can't make a one huge telescope that sees radio waves what we do is we install atomic clocks had multiple radio dishes around the world we record data and then we play it back at a central facility and we create a virtual telescope as big as the earth ourselves these are some of the people who who on these various places how many teams are there well we have eight geographic locations right now and we're going to nine and then ten the year after next and when you stitch together all of these telescopes you wind up getting a virtual dish that's the size of the earth that is exactly tuned it turns out to image the supermassive black hole in the center of our galaxy and we've just taken some of the first data from this event horizon telescope one year ago and we're crunching on the data now and what have you what have you found I can't tell you oh come on no it turns out that if you if you really want to make one of these images it takes a long time to calibrate the data it's all about the details a lot of people think that we just turn this telescope on and we'll see something immediately but it's you know we're nerds at heart and we just love to get to the telescopes and find all these details and it turns out that you really have to run down every single one of these possible sources of contamination the data before you can be sure that you've seen this kind of shadow silhouette yeah you know we were able to actually talk to a couple members of the of the team who slipped us actually some of the data I hope you don't mind if we if we show it here to show the chubbie this is actually I'm understanding this is the the most precise image ever of a black hole do we have that can we bring the lights down and show this is that is that doable yeah so so yeah all right there there there it is very good yeah so that's good enough for us thank you no oh um so uh you can look the real nervous there for a second yeah so so when will you be releasing I saw an article just a couple of days ago which is kind of a teaser it seemed like for a release of data that's coming up is that soon and it'll probably be in the first part of the 2019 2019 yeah because right now we're crunching the data you know we know that the event horizon telescope worked so what we did was we also looked at quasars supermassive black holes that are really far away where basically point sources and everything seems to have worked perfect technically on the telescope so so we know that all the systems are a go and then we turned all the telescope swivel to look at Sagittarius a star the supermassive black hole in the center of our galaxy and and we think everything is working fine there but we're still crunching on the data so and and the data I saw some article that had come from the South Pole and you had to wait for the the winter to clear to fly that was that the kind of yeah that's going on or well so that the whole point as Andrea said if you want to test Einstein's theory you've got to go to the most extreme points in the universe you've got to go to the ultimate proving ground which is the edge of a black hole and we have to go to some pretty extreme places ourselves right so we have teams that go down to the South Pole we go to the tops of extinct volcanoes where there are radio dishes that do the work that we want to do we go to Hawaii Mauna Kea high desert plains and Chile and you go up to these sites and it's really a bit of a labor of love because all these teams go there they work their hearts out they capture data in this technique that we use this event horizon telescope technique is really the ultimate and delayed gratification alright because here's what you do it so what when Andre goes to our telescope it's pretty straightforward from conceptually the light bounces off a paraboloid it goes to the focus that's it right you get what you want right there what happens with us is the light hits one of our dishes it's stored through high speed instrumentation that we've built over the last decade on hard disks the same kind of hard disk that you would get in your computer and they stay there until they're brought back on an airplane because nothing beats the bandwidth of a 747 filled with distress nothing okay even when I'm walking down the hallway with two of these disks you know I'm beating the fastest internet in the world okay and we bring them back together and the operation in this supercomputer that we use is equivalent to light bouncing off of a perfectly shaped parabola joining in coherence alright so we play it back together and we adjust it back and forth until we get it just right and that effectively turns the earth into a parabola if you think about that so all of this data has to come back and if it's at the South Pole it's in a deep freeze right so we've got to wait six months just to get that data back right all right so that's more of the delay that we've been faced not you now you have done some simulations of what you anticipate emerging from the data looking at the magnetic field and vicinity of a black hole can you take us through some of the things that you anticipate emerging from the study I think we have some things up sure so what you're seeing here is the best guess we have from your high speed simulations of what you would see if you had infinite resolution goggles right so you wind up seeing this this shadow feature the circular feature with some Jets leaving from the North and South Poles and that's because there are magnetic fields right around the boundary of the black hole there's relativistic particles they're orbiting in these magnetic fields and they're releasing something called synchrotron emission which is kind of a characteristic radio emission you get from these kinds of sources and it's so bright in that synchrotron emission that it shines out from the deepest part of the gravity well right so you so think about it everything has to go right it's a Goldilocks situation you have to be able to see through the Earth's atmosphere and radio waves can do that you've got to be able to see through the distance between the earth and the galactic center radio waves can summarize that just to give people a sense it so it's about 25,000 light-years away good right so it's you know this black hole is not threatening to us we observe it it's nice so these radio waves can go all the way to the you know from the black hole but then we're not done yet because it has to go through the hot gas swirling around the black hole right and then it has to go all the way down into the gravity well so it's a Goldilocks situation because we meet all those criterion with radio waves and it turns out that the earth happens to be just the right size so that when you look at radio waves with a wavelength of 1 millimeter they're perfectly tuned to take the picture of Sagittarius a star that's it with an earth-sized dish it was just resolution yeah so sometimes nature throws us all these curveballs you know we can't do this or this is hard this is one case where everything's falling into place and so we really think we have a good shot of taking a the first image of a black hole and and do you have a chance as well of finding a deviation from the general theory of relativity can this be viewed as another extreme testing ground well we're looking it's never a good idea to bet against Einstein okay I don't make it a point in my career to do it you know but it is a trust but verify situation okay I mean he's a he was a very smart guy let's put it that way but every theory needs to be tested well when you say he's a very smart guy that's true but he wasn't a great fan of this idea of black holes at all right I mean he kind of didn't think they were real well well this is how he was a little bit off on that one right okay so he had one bad moment but but this really speaks to this kind of golden age that Dandrea was talking about with the event horizon telescope where the observations are being made by the CAC we're really in this discovery space for black holes and we could be at the moment when we can start to answer these questions like do black holes exist was Einstein right at the very black hole boundary I mean you know you showed shorts child in the trenches in World War one yeah you know and he died later that year actually so this was his last big discovery and he wrote down the Schwarzschild metric and he gave what to take my space outside of black the shape of space outside the black hole and and now we're kind of engaging in this handshake across 100 years where we're kind of completing this circuit and we're saying you know you made these intense predictions and we're just at the point now where we might be able to test them right and that is extraordinary and and it speaks to the fact that science is not linear we don't go from point A to point B we don't say we're gonna march and test this it's very erratic and and that's why Einstein felt black holes might not exist it took a hundred years for them to become part of our lexicon right you're part of the reality of our everyday conversation now do you do do either of you or both of you as you're working on your observational projects do you have pet ideas or pet theories about what the next phase beyond Einstein might be or do you just basically just go forward into the data the observations and and that's the only thing that's really driving you or do have a an idea of what might be the next phase of this understanding of gravity well well let me just take this one second I'm a real I'm a realist I'm kind of a craftsman at heart like I like to go to the tops of mountains and make observations I like to see what's around the black hole right I can understand and wrap my brain around the light that's coming outside the event horizon what's inside the event horizon you know that's a question that is hard to even ask you know let alone just asked it I did it's harder to answer it I did it's easy to wonder at ya know but but but for example one thing we're looking at with the event horizon telescope is to see if that silhouette is not round ah what if it's distorted okay and if it's distorted then we have some framework of understanding how general relativity itself might be violated to give us those strange shapes so we're betting on Einstein we're betting it's gonna be circular but if it's not we have some ways of understanding what might make it non circular yep so we're winding down to the end of our section about Andre I wanted to ask you a question which is how do you proceed in an era when you might be going beyond Einstein when do you know that you're right when when do you know that things have coalesced to the point that you're willing to make a statement of that sort interesting and important question that we're really in the thick of because if you see things that don't make sense you you don't have a context you're you're kind of extend you're exposed and you have to convince yourself that what you're seeing is physics as opposed to experimental error right err err err so I I think there's a an interesting philosophical point here about how do you convince yourself you've got the right answer yeah I mean there was an interesting case with bicep2 oh yes a few years ago where some have said that they so knew what they were looking for that they were biased in assessing what the data was telling them it's a classic thing called confirmation bias so and this kind of work where we have such a respect for Einstein and his ideas that we go in with a premise that it must be correct so it is interesting in terms of how you actually design your team's work to avoid getting a result you believe to be true and allowing your team to really trust what the data is telling you so I think that's a that that's certainly my goal as a scientist to get to that point where you're really just listening or paying attention to the information that might be unexpected but to try to remove your your desire to have any particular answer be it Einstein right or be it Einstein wrong yep just to be open to whatever the answer truly is right yeah well I should say you know all of us revere Einstein but at the same time how thrilling would be if either or both you find evidence that we do need to go beyond the insights that he gave us a hundred years ago so we wish you well and we'll have you back a year or two maybe then you'll be able to give us some insight into what you guys have found so everybody please join me in thanking our great guys Jeff : oh thank you very much you

This Color Test Will Tell Your Mental Age!

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This color test will tell your mental age. This test is based on how different age groups perceive different colors.

There is a chance that your mental age might even match your real age! or probably it might be lesser or greater than your real age. Mental age is the age that you tend to behave like or try to act.

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What is a Black Hole? — Black Holes Explained

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BREAKING NEWS: First image of a Black Hole captured by the Event Horizon Telescope!
If you’re looking for a video to explain Black Holes to kids, we recommend this excellent video from Socratica Kids:

Black Holes are super dense regions of space. They have such immense gravity that anything close by is sucked in, never to escape. Even LIGHT! That’s why we call the BLACK HOLES.

Some black holes are small. Some are HUGE! There are stellar black holes, about the size of a dozen of our suns. Then there are SUPERMASSIVE black holes, that are the size of MILLIONS and MILLIONS of our suns! Scientists think there are supermassive black holes in the center of each galaxy. The supermassive black hole in the center of our Milky Way galaxy is called Sagittarius A. Recently, the Event Horizon Telescope was able to image the supermassive black hole in the center of the distant galaxy Messier 87. This black hole is known as M87, and was the first black hole ever to be imaged using the giant radio telescope EHT.

In this video, we talk about how Black Holes are formed and how we can detect them using various methods.
You can jump to chapters in our video here:

1:03 History of Black Holes
1:49 Theory of Relativity by Einstein – Spacetime
3:12 Are black holes real?
3:48 Finding black holes
4:13 Binary Stars
4:54 Schwarzschild Radius and the Event Horizon
5:24 Finding the mass of a black hole
5:56 Stellar and supermassive black holes
6:44 Angular momentum
7:37 The Ergosphere
8:09 Electric Charge of a black hole
8:42 No Hair Theorem
9:04 Inside a black hole
10:09 Current research topics

We highly recommend the Astronomy textbook “Universe” by Roger Freedman et al:
Universe 9th Edition
Universe 10th Edition

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#BlackHoles #Astronomy #EventHorizon

from faraway stars our tiny points of light but up close stars are massive seething fiery balls of burning gas this fierce display does not last forever eventually the nuclear fusion which powers the star will burn all its fuel gravity then collapses the remaining matter together for very large stars what happens next is a display of extremes first the star explodes in a supernova scattering much of its matter throughout the universe for a brief moment the dying star outshines its entire galaxy for once the light fades and darkness returns the remaining matter forms an object so dense that anything that gets too close will completely disappear from view this is a black hole the idea of a black hole originated hundreds of years ago in 1687 Isaac Newton published his landmark work known as the Principia here he detailed his laws of motion and the universal law of gravitation using a thought experiment involving a cannon place on a very tall mountain Newton derived the notion of escape velocity this is the launch speed required to break free from the pull of gravity in 1783 the English clergyman John Mitchell found that a star five hundred times larger than our Sun would have an escape velocity greater than the speed of light he called these giant objects dark stars because they could not emit starlight this idea lay dormant for more than a century then in the early 20th century Albert Einstein developed two theories of relativity that changed our view of space and time the special theory and the general theory the special theory is famous for the equation e equals MC squared the general theory painted a new and different picture of gravity according to the general theory of relativity matter and energy Bend space and time because of this objects which travel near large mass will appear to move along a curved path because of the bending in space-time we call this effect gravity one consequence of this idea is that light is also affected by gravity after all of space-time is curved then everything must follow along a curved path including light Einstein published his general theory of relativity in 1915 and while Newton's theory of gravity could be expressed using a simple formula Einstein's theory required a set of complex equations known as the field equations only a few months after Einstein's publication the German scientist Karl Schwarzschild found a surprising solution according to the field equations an extremely dense ball of matter creates a spherical region in space where nothing can escape not even light a curious result but did such things actually exist at first the idea of a black sphere in space from which nothing could escape was considered purely a mathematical result but one which would not really happen however as the decades passed our understanding of the life cycle of stars grew it was observed that some dying stars became pulsars another exotic object predicted by theory this suggested that dark stars could actually be real as well these strange spheres were named black holes and scientists began the hard work of finding them describing them and understanding how they are created but how do you find an object in space that is completely black luckily because black holes have a large mass they also have a large gravitational field so while we may not be able to see a black hole we can observe its gravity pulling on its neighbors with this in mind astronomers looked for a place where a visible star and the black hole were in close proximity to one another one such place is binary stars a binary star is a system of two stars orbiting one another we can spot them in several ways you can look for stars that change position back and forth ever so slightly alternatively if you observe a binary star from the side the brightness will change when one star passes behind the other so it's possible that somewhere in space there's a binary star consisting of a black hole and a visible star in fact such binary systems have been observed astronomers have found stars orbiting an invisible companion from the size of the visible star and its orbit astronomers calculated the mass of its invisible neighbor it fit the profile of a black hole since we can't see a black hole is there a way to find its size from Einsteins field equations we know that given the mass of a black hole we can determine the size of the sphere that separates the region of no escape from the rest of space the radius of the sphere is called the Schwarzschild radius in honor of Karl Schwarzschild the surface of the sphere is called the event horizon if anything crosses the event horizon it's gone forever hidden from the rest of the universe this means once you know the mass of a black hole you can compute its size using a simple formula and it's actually quite easy to measure the mass of a black hole just take a standard-issue space probe and shoot it into orbit around the black hole just like any other system of orbiting bodies like the earth orbiting the Sun or the moon orbiting the Earth the size and period of the orbit will tell you the mass of the black hole if you don't have a space rope handy then compute the mass and orbit of a companion star and use that to find the Schwarzschild radius black holes come in many sizes if it was made from a dying star then we call it a stellar mass black hole because its mass is in the same range as stars but we can go bigger much bigger and to do so we're going to visit the center of a galaxy galaxies can contain billions and billions of stars all orbiting a central point scientists now believe that in the center of most galaxies lives a black hole which we call a supermassive black hole because of its tremendous mass the size can vary from hundreds of thousands to even billions of solar masses for example at the center of our own Milky Way galaxy is a supermassive black hole with a mass 4 million times that of our Sun black holes have another property we can measure their spin just like the planets stars rotate and different stars spin at different speeds imagine we can adjust the size of the star but keep the mass constant if we increase the radius the spinning slows down if we decrease the size the spinning speeds up but while the rotational speed can vary the angular momentum never changes it remains constant even if the star were to collapse into a black hole it would still have angular momentum we could measure this by firing two probes into opposite orbits close to the black hole because of their angular momentum black holes create a spinning current and space-time the probe orbiting along with a current will travel faster than the one fighting it and by measuring the difference in their orbital periods we can compute the black hole's angular momentum this space-time current is so extreme it creates a region called the ergosphere where nothing including light can overcome it inside the Ergo sphere nothing can stand still everything inside this region is dragged along by the spinning space-time the event horizon fits inside the Ergo sphere and they touch at the poles so in one sense black holes are like whirlpools of space-time once inside the Ergo sphere you are caught by the current and after you cross the event horizon you disappear one final property of black holes we can measure is electric charge while most of the matter we encounter in our day-to-day lives is uncharged a black hole may have a net positive or negative charge this can easily be measured by seeing how hard the black hole pulls on a magnet what charged black holes are not expected to exist in nature this is because the universe is teeming with charged particles so a charged black hole would simply attract oppositely charged particles until the overall charge is neutralized there are three fundamental properties of a black hole we can measure mass angular momentum and electric charge it is believed that once you know these three values you can completely describe the black hole this result is humorously known as the no-hair theorem since other than these three properties black holes have no distinguishing characteristics it's not a blonde brunette or a redhead we now have a good idea of a black hole from the outside but what does it look like on the inside unfortunately we can't send a probe inside to take a look once any instrument crosses the event horizon it's gone but don't forget we have Einstein's field equations if these correctly describes space-time outside the black hole then we can use them to predict what's going on inside as well to solve the field equation scientists consider two separate cases rotating black holes and non rotating black holes non rotating black holes are simpler and were the first to be understood in this case all the matter inside the black hole collapses to a single point in the center called a singularity at this point space time is infinitely warped rotating black holes have a different interior in this case the mass inside of black hole will continue to collapse but because of the rotation it will coalesce into a circle not a point this circle has no thickness and is called a ring singularity black hole research continues to this day scientists are actively investigating the possibility that black holes appeared right after the Big Bang and the idea that black holes can create bridges called wormholes connecting distant points of our universe we know a great deal about black holes but there are still many mysteries to be solved it's a little-known fact that all YouTube videos are stored in the special fabric called play time when you watch a video it sends ripples of energy throughout play time and when you subscribe to a channel it creates a teeny tiny black hole so if you like black holes then you know what it is

Is the Universe Infinite?

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Explore the biggest question of all. How far do the stars stretch out into space? And what’s beyond them? In modern times, we built giant telescopes that have allowed us to cast our gaze deep into the universe. Astronomers have been able to look back to near the time of its birth. They’ve reconstructed the course of cosmic history in astonishing detail.

From intensive computer modeling, and myriad close observations, they’ve uncovered important clues to its ongoing evolution. Many now conclude that what we can see, the stars and galaxies that stretch out to the limits of our vision, represent only a small fraction of all there is.

Does the universe go on forever? Where do we fit within it? And how would the great thinkers have wrapped their brains around the far-out ideas on today’s cutting edge?

For those who find infinity hard to grasp, even troubling, you’re not alone. It’s a concept that has long tormented even the best minds.

Over two thousand years ago, the Greek mathematician Pythagoras and his followers saw numerical relationships as the key to understanding the world around them.

But in their investigation of geometric shapes, they discovered that some important ratios could not be expressed in simple numbers.

Take the circumference of a circle to its diameter, called Pi.

Computer scientists recently calculated Pi to 5 trillion digits, confirming what the Greeks learned: there are no repeating patterns and no ending in sight.

The discovery of the so-called irrational numbers like Pi was so disturbing, legend has it, that one member of the Pythagorian cult, Hippassus, was drowned at sea for divulging their existence.

A century later, the philosopher Zeno brought infinity into the open with a series of paradoxes: situations that are true, but strongly counter-intuitive.

In this modern update of one of Zeno’s paradoxes, say you have arrived at an intersection. But you are only allowed to cross the street in increments of half the distance to the other side. So to cross this finite distance, you must take an infinite number of steps.

In math today, it’s a given that you can subdivide any length an infinite number of times, or find an infinity of points along a line.

What made the idea of infinity so troubling to the Greeks is that it clashed with their goal of using numbers to explain the workings of the real world.

To the philosopher Aristotle, a century after Zeno, infinity evoked the formless chaos from which the world was thought to have emerged: a primordial state with no natural laws or limits, devoid of all form and content.

But if the universe is finite, what would happen if a warrior traveled to the edge and tossed a spear? Where would it go?

It would not fly off on an infinite journey, Aristotle said. Rather, it would join the motion of the stars in a crystalline sphere that encircled the Earth. To preserve the idea of a limited universe, Aristotle would craft an historic distinction.

On the one hand, Aristotle pointed to the irrational numbers such as Pi. Each new calculation results in an additional digit, but the final, final number in the string can never be specified. So Aristotle called it “potentially” infinite.

Then there’s the “actually infinite,” like the total number of points or subdivisions along a line. It’s literally uncountable. Aristotle reserved the status of “actually infinite” for the so-called “prime mover” that created the world and is beyond our capacity to understand. This became the basis for what’s called the Cosmological, or First Cause, argument for the existence of God.

since ancient times we've looked into the night skies and wondered how far to the stars stretch out into space and what's beyond them in modern times we built giant telescopes that have allowed us to cast our gaze deep into the universe astronomers have been able to look back to near the time of its birth they've reconstructed the course of cosmic history in astonishing detail from intensive computer modeling and myriad close observations they've uncovered important clues to its ongoing evolution many now conclude that what we can see the stars and galaxies that stretch out to the limits of our vision represent only a small fraction of all there is does the universe go on forever where do we fit within it and how would the great thinkers have wrapped their brains around the far-out ideas on today's cutting edge to begin to get a handle on infinity we are going to need some perspective on the numbers and scales that define our universe one place to start is a narrow side street in Charles Dickens London the Curiosity Shop fictional to be sure you you can find an unparalleled collection of staff old shrunken heads and your scripts newspapers books and rare examples of impressively large numbers from Zimbabwe comes a 100 trillion dollar note in late 2008 with that nation battered by hyperinflation it was worth about a dollar fifty u.s. go up two orders of magnitude to something decidedly more useful the fastest supercomputer in history will soon hum along at 20,000 trillion calculations per second a 20 followed by 15 serums you'll have to run it about a day and a half to equal the number of grains of sand on all the world's beaches that's around a sextillion a ten followed by 22 zeroes that's roughly the number of stars in the visible universe atoms in the visible universe that's upwards of 10 to the 78th power the 10 with 78 zeroes cubic centimeters a mere 10 to the 84th a septa vision Tilian to go up from there return to no less a source than the Guinness Book of World Records the largest named number in regular decimal notation the Buddha's time period Assam Kia is 10 to the 140th years or 100 Quinto Quadra Gentilly ins then there's the largest number ever used Graham's number is a calculation of angles in a type of hyper cube if you divided the visible universe into the smallest units known called black volumes the total of those units wouldn't get you anywhere close to Graham's number but it's still nowhere close to the ultimate sealing infinity for those who find infinity hard to grasp even troubling you're not alone it's a concept that has long tormented even the best minds over 2,000 years ago the Greek mathematician Pythagoras and his followers saw numerical relationships as the key to understanding the world around them but in their investigation of geometric shapes they discovered that some important ratios could not be expressed in simple numbers take the circumference of a circle to its diameter called pi computer scientists recently calculated PI to 5 trillion digits confirming what the Greeks learned there are no repeating patterns and no ending in sight the discovery of the so called irrational numbers like pi was so disturbing legend has it that one member of the Pythagorean code he passes was drowned at sea for divulging their existence a century later the philosopher Zeno brought infinity into the open with a series of paradoxes situations that are true but strongly counterintuitive in this modern update of one of Zeno's paradoxes say you have arrived at an intersection but you are only allowed to cross the street in increments of half the distance to the other side so to cross this finite distance you must take an infinite number of steps in math today it's a given that you can subdivide any length an infinite number of times or find an infinity of points along a line what made the idea of infinity so troubling to the Greeks is that it clashed with their goal of using numbers to explain the workings of the real world to the philosopher Aristotle a century after Zeno infinity evoked the formless chaos from which the world was thought to have emerged a primordial state with no natural laws or limits devoid of all form and content but if the universe is finite what would happen if a warrior traveled to the edge and tossed a spear where would it go it would not fly off on an infinite journey Aristotle said rather it would join the motion of the stars in a crystalline sphere that encircled the earth to preserve the idea of a limited universe Aristotle would craft an historic distinction on the one hand Aristotle pointed to the irrational numbers such as pi each new calculation results in an additional digit but the final final number in a string can never be specified so Aristotle called it potentially infinite then there's the actually infinite like the total number of points or subdivisions along a line it's literally uncountable Aristotle reserved the status of actually infinite for the so called prime mover that created the world and is beyond our capacity to understand this became the basis for what's called the cosmological or first cause argument for the existence of God another century later Archimedes incorporated actual infinity into measurements of curved lines and volumes his method boils down to a process of summation place a triangle inside a circle turn it into a square then a pentagon and so on as the number of sides increases to infinity their combined lengths equal the circumference of the circle by slicing and dicing curves into an infinite number of straight lines it was able to compare a variety of curves areas and volumes our committees anticipated techniques developed 2,000 years later and yet his ideas on infinity did not carry forward due to what the author David Foster Wallace described as a mathematical allergy that developed in response to Aristotle's potential infinity it was Aristotle's ideas that passed into the Christian era along with his cosmology with earth seated firmly at the center that view was not universal Islamic Hindu and even some Western thinkers posed alternate views that included infinite space in European circles the issue of infinity resurfaced during the Renaissance in 1543 the polish astronomer Nicolaus Copernicus argued that Earth orbits the Sun not the other way around the old Greek spheres began to fall by the wayside when a distant supernova then a comet were spotted by the astronomer Tycho Brahe these objects seem to behave independently of the other stars a monk named Giordano Bruno inflamed the issue by travelling Europe at the height of the Inquisition to proclaim an infinite universe in the year 1600 he was burned at the stake for this and other heresies just nine years later in 1609 Galileo Galilei used the first astronomical telescope to show that the universe is much larger than we thought in later writings he even sought to discredit the distinction between potential and actual infinity Galileo was forced to recant and the old Aristotelian view held sway any attempt to assign a value to infinity in numbers or in nature was doomed but that was the unique province of God finally at the end of the 19th century the mathematician Georg Cantor sought once and for all – divorce metaphysics from the abstract pursuit of math infinity he wrote had to be studied without arbitrariness and prejudice he became known for folding finite and infinite numbers into a unified theory of number sets considered a foundation of modern math one of his defenders used a paradox to show how infinite sets are subject to concrete comparisons say you've come to stay at this Grand Hotel you're in luck because here there is an infinite number of rooms oddly enough you learn there are no vacancies fortunately the manager says I can still check you in he assigns you to room number one and directs you down the corridor wonderful then he goes to work shifting the guest in room 1 to room to room 2 to 3 3 to 4 and so on so in this hotel there's a number set that includes an infinite number of guests and rooms then there's that same set plus you to infinite sets yet one is a subset of the other being able to use infinite sets of different sizes allowed mathematicians to design equations describing continuous motion and change over time echoing Aristotle a critic of the new set Theory suggested that the end of the corridor is still only a potential infinity with God representing the only actual infinity for those who pined for humble accommodations will recommend an alternative later on even as mathematicians embraced infinity astronomers in the early 20th century still saw a limited universe centered on the galaxies a flat disk of stars did the limits of our vision like the horizon at sea concealed and infinite universe beyond Albert Einstein for one believed that if that were true then the night sky would be filled with dense star light shining from every direction we'd reel from the effects of infinite gravity arguing for a finite universe he described a people living on the 2d surface of a sphere to them a beam of light moving through space would appear to go straight on an infinite journey in fact it follows a path determined by the overall gravity of the universe and curves back around like the old Greek spheres this view of a static and limited universe began to fall by the wayside in the 1920s Edwin Hubble and Milt Humason used the new 100-inch telescope on Mount Wilson in California to look at mysterious fuzzy patches of sky called nebulae they found that these patches were galaxies like our own and that some were very far away what's more they found that most are moving away from us the farther out they looked the faster the galaxies are moving this fact known as Hubble's law led to an inescapable conclusion that the universe is expanding furthermore if you run the clock back on this expansion it appears that it all began in one singular moment that moment has traditionally been described as an explosion a Big Bang how large the universe has gotten since then depends on how long it's been growing and how quickly using an array of modern telescopes astronomers have recently meld the beginning to 13.7 billion years ago taking into account the expansion of space ever since the radius of the visible universe the part we can see has expanded out to 46 billion light years these measurements have raised a new the ancient questions what's beyond our cosmic horizons is there an edge or does it somehow go on forever a new set of answers has emerged from a theory designed to address questions that arose from the original model of the Big Bang for one how did the universe get so large the Hubble Deep Field contains images of infant galaxies at less than 10% of the age of the universe near the edge of our cosmic horizons by the time one of those galaxies reached maturity it would have moved far far beyond our horizon and what of all the galaxies is visible at its horizons for another how did the universe get so smooth in every direction you look the density of galaxies is the same on large scales astronomers believe that whatever process fund the universe outward must have also blended it in its earliest moments the theory that addresses these questions was based on the discovery that energy is constantly welling up from the vacuum of space in the form of particles of opposite charge matter and antimatter the idea is that in primordial times an energy field embedded in this so-called quantum vacuum suddenly moved into a higher energy state causing space and time to literally inflate and our universe to burst forth if this theory is right then our universe is incomprehensibly large it's author the scientist Alan Guth wrote that the universe as a whole would have grown to at least 10 billion trillion times the size of our visible batch that's a 10 followed by 23 zeroes if you think that's big a variation on the theory describes the origin of our universe as a physical process that exists far beyond it out into the seemingly infinite void that had confounded Aristotle and other Greek thinkers in that case our universe would have inflated like a bubble and joined a stream of other bubble universes frothing up and expanding across an endless ocean of time and space a related idea theorizes a cosmic landscape unfolding in vast fractal patterns these new more expansive visions of the cosmos are not without their paradoxes logically speaking with infinite stars infinite planets infinite universes you will also have infinite possibilities the so called Infinite Monkey theorem has its roots in Aristotle's attempts to illustrate the perils of thinking about infinity ask a monkey to type or ask an infinite number of monkeys to type for an infinite amount of time you're sure to get a lot of random letters but there is a chance however small but somewhere somehow you'll get the full text of Shakespeare's Hamlet it's clearly absurd then again consider the increasingly strange nature of our universe as suggested by some new observations this is where we draw your attention from the famous Hotel infinity to a less well-appointed alternative you're sure to get a big welcome at the old Hall of Mirrors this ramshackle place would have thrown even the great thinkers for a loop it represents a kind of optical illusion that may be present in our view of deep space according to a new interpretation of data from one of the most important space satellites ever launched w map was sent out to make precision measurements of radiation left over from a period about 300,000 years after the Big Bang it revealed an intricate pattern of hot and cold spots now thought to represent the seeds of the galaxy filaments and walls seen on large scales the pattern was laid down by pressure waves that ricocheted through the expanding gas of the early universe one group of scientists looking at the sizes of these waves suggested that some are actually mirror images of themselves from this they argue that the universe could be much smaller than we think that's not the only strange new line of evidence tracking the movement of distant galaxies astronomers found huge clusters moving at about two million miles per hour in the direction of the constellation Centaurus with the results published in a top scientific journal the astronomers describe an immense gravitational presence that may loom beyond our visible horizon perhaps another universe that inflated near our own ideas like these may well have led to imprisonment or death in centuries past now they were part of a field of study that is bursting with data and ideas cosmology the study of the universe as a whole has long been infused with metaphysics and philosophy today it's steadily merging into the physical sciences so is the universe infinite scientists will continue to look for evidence of what lies beyond our horizons test theories on the nature of time and space but like the room at the end of an emphasis on Sur will always elude us

എന്തുകൊണ്ടാണ് ഈ ചിത്രത്തിന് ഇത്രയേറെ പ്രത്യേകത ? How to Understand the Image of a Black Hole ?

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How to Understand the Image of a Black Hole ? and What is Black Hole ? let us know …..

A black hole is a region of space time exhibiting such strong gravitational effects that nothing—not even particles and electromagnetic radiation such as light—can escape from inside it. The theory of general relativity predicts that a sufficiently compact mass can deform space time to form a black hole.

comment your feedback after watch the video …..


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Einstein's Theory Of Relativity Made Easy

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… Albert Einstein’s Theory of Relativity (Chapter 1): Introduction.

The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word “relativity” is sometimes used in reference to Galilean invariance.

The term “theory of relativity” was coined by Max Planck in 1908 to emphasize how special relativity (and later, general relativity) uses the principle of relativity.

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Special relativity is a theory of the structure of spacetime. It was introduced in Albert Einstein’s 1905 paper “On the Electrodynamics of Moving Bodies” (for the contributions of many other physicists see History of special relativity). Special relativity is based on two postulates which are contradictory in classical mechanics:

1. The laws of physics are the same for all observers in uniform motion relative to one another (principle of relativity),
2. The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the source of the light.

The resultant theory agrees with experiment better than classical mechanics, e.g. in the Michelson-Morley experiment that supports postulate 2, but also has many surprising consequences. Some of these are:

• Relativity of simultaneity: Two events, simultaneous for one observer, may not be simultaneous for another observer if the observers are in relative motion.
• Time dilation: Moving clocks are measured to tick more slowly than an observer’s “stationary” clock.
• Length contraction: Objects are measured to be shortened in the direction that they are moving with respect to the observer.
• Mass-energy equivalence: E = mc2, energy and mass are equivalent and transmutable.
• Maximum speed is finite: No physical object or message or field line can travel faster than light.

The defining feature of special relativity is the replacement of the Galilean transformations of classical mechanics by the Lorentz transformations. (See Maxwell’s equations of electromagnetism and introduction to special relativity).


General relativity is a theory of gravitation developed by Einstein in the years 1907–1915. The development of general relativity began with the equivalence principle, under which the states of accelerated motion and being at rest in a gravitational field (for example when standing on the surface of the Earth) are physically identical. The upshot of this is that free fall is inertial motion; an object in free fall is falling because that is how objects move when there is no force being exerted on them, instead of this being due to the force of gravity as is the case in classical mechanics.

This is incompatible with classical mechanics and special relativity because in those theories inertially moving objects cannot accelerate with respect to each other, but objects in free fall do so. To resolve this difficulty Einstein first proposed that spacetime is curved. In 1915, he devised the Einstein field equations which relate the curvature of spacetime with the mass, energy, and momentum within it.

Some of the consequences of general relativity are:

• Time goes slower in higher gravitational fields. This is called gravitational time dilation.
• Orbits precess in a way unexpected in Newton’s theory of gravity. (This has been observed in the orbit of Mercury and in binary pulsars).
• Rays of light bend in the presence of a gravitational field.
• Frame-dragging, in which a rotating mass “drags along” the space time around it.
• The Universe is expanding, and the far parts of it are moving away from us faster than the speed of light.

Technically, general relativity is a metric theory of gravitation whose defining feature is its use of the Einstein field equations. The solutions of the field equations are metric tensors which define the topology of the spacetime and how objects move inertially.

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relativity relativity is just a method for two people to agree on what they see if one of them is moving and since we all move about pretty regularly we can find many examples of how useful relativity is in everyday life even if we don't call it by name one miracle of modern life is the global positioning system or GPS it is pretty amazing that the GPS can pinpoint your location anywhere on earth to within a few yards and this magic depends entirely on the existence of the two dozen satellites 12,000 miles above the earth and a little relativity briefly here's how it works the GPS receiver gives a timing signal from several different high flying satellites and using Einstein's theory of relativity it calculates the distance from each satellite throw in a little triangulation and I'll come to your location simple and concept but to do this successfully the timing signals must be accurate to a few billions of a second so that the distance calculations can be accurate to a few yards but with all this motion going on time and distance must be reconciled carefully without an Stein's version of relativity the accuracy of the global positioning system would drift more than seven miles every day but of course relativity was not a new concept with Einstein the problem of how two people reconcile their observations about the world if one of them is moving has been addressed for centuries let's easier way into relativity with some common experiences if you are travelling in a car on a smooth straight stretch of highway there's no sensation of motion at all you mean I could read a book or a drink flip a coin and everything looks and feels the same as if the car we're sitting still that's because relative to the car view of the book the drink and the coin are not moving notice that this works only if the car is not changing direction or speed so if the car accelerates or turns pouring that drink becomes a real problem but constant motion feels just like sitting still and if you want to know what it feels like to move at a thousand miles per hour just look around because of the Earth's spin we zip along our time zone at a speedy 1,000 miles per hour and because of its motion around the Sun the earth carries us through space about 67,000 miles per hour and because of the motion of our solar system about the center of our galaxy we are moving at more than half a million miles an hour but it's not enough to ask how fast am i moving we must ask how fast am i moving relative to some other thing let's make up a simple rule that allows two observers to agree on how fast something is moving we begin at a moving walkway at the airport the walkway is moving at a brisk 3 miles per hour so if Susan simply stands on the walkway she is moving at 3 miles per hour relative to Sara who is standing still but not on the walkway if Susan walks on the walkway at 3 miles per hour she can accurately say she is walking at 3 miles per hour but Sara sees her moving at 6 miles per hour and if Susan walks against the walkway at 3 miles per hour Susan can still say she's walking at 3 miles per hour but now Sara sees her as standing still zero miles per hour so our first conclusion is that two observers can simply add or subtract their speed with respect to each other to any measurement of velocity they make this idea is the basis of classical relativity here's another scenario suppose there's a truck moving down the road at a constant speed of 50 miles per hour on the back or a baseball pitcher a catcher and their pitching coach armed with the speed gun as long as the truck doesn't speed up or slow down or hit any large bumps they can conduct pitching practice just the same as they would on the baseball field and when the pitcher throws a 100 mile-per-hour fastball the coaches speed gun will read 100 miles per hour the ball is indeed moving 100 miles per hour relative to the pitcher the catcher the coach and the truck but suppose an observer standing by the side of the road plucks the speed of that same baseball what speed would this observer measure for the ball well the ball would already be moving at 50 miles per hour when the pitcher was just holding it so this observer would measure a speed of a hundred and fifty miles per hour for the pitch the speed of the ball relative to the truck plus the speed of the truck relative to the observer the example of adding velocities in the bullet and plane example is classical relativity at its finest this classical version of relativity simply add in the velocities worked perfectly well for centuries for describing horse carts and ships or baseballs and trucks even airplanes and rockets and bullets but the relativity of classical physics is merely a very close approximation to reality at very very fast speeds classical relativity breaks down but this wouldn't be clear until scientists began flying Sopwith camels and examining the nature of the fastest known thing light

Brilliant Breakthroughs: Shep Doeleman Photographs a Black Hole

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A black hole is an object so dense that not even light can escape its gravitational pull. So how could you ever take a picture of one? It seemed impossible, but on April 10th, 2019, scientists from the Event Horizon Telescope, led by astronomer Shep Doeleman, announced that they’d done just that. Their image of the photons circling a supermassive black hole in the galaxy Messier 87 will revolutionize our understanding of the universe—and move the dial on what’s considered impossible.

– Produced by Brandon Royal and Mandi Gorenstein
– Edited by Josh Zimmerman
– Music by APM

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my name is Shepard Dolman I'm a researcher at the Smithsonian Astrophysical Observatory and I am trying to take the first picture of a black hole using radio astronomical techniques black holes are engines that redistribute matter and energy on galactic scales they are integral to the large-scale structure of the universe why we look in the sky and see what we do there's all these different lines of evidence that we think are very very solid the black holes exist that explain a lot of things in the universe when we think about observing a black hole we're really thinking about and a tightening the news like focusing in as deeply as we can on this exotic object the event horizon telescope project has a very simply stated goal to make the first image of a black hole of the event horizon and to really see what it looks like the magnifying power of a telescope is directly related to its size the bigger you can make the telescope the more magnifying power you have and if you want to take a picture of a black hole which is the smallest object we know of in the entire universe you need the ultimate in magnifying power so we do this by connecting telescopes that already exist around the world and we record data when this one's looking at the black hole record data when this one is looking the black hole and then we bring those recordings together and as the Earth rotates that we can reconstruct an image using a telescope that is just about the size of the earth so the event horizon telescope is designed to take the first image of light just outside the event horizon it hasn't yet been sucked in but it's illuminating this silhouette a hundred years ago Einstein came up with this entirely new theory of gravity fine Stein's equations told us what shape and size that silhouette should be we're really pushing these theories we're asking is there something else is there something we don't understand I really would like to feel that we did whatever we could to answer one of the deepest questions in the universe do black holes exist and what do they look like you

Time Is But a Stubborn Illusion – Sneak Peek | Genius

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Watch an exclusive sneak peek from the first episode of Genius, starring Geoffrey Rush as the older Einstein and Johnny Flynn as the younger.
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From Executive Producers Brian Grazer and Ron Howard, National Geographic’s first scripted anthology series, GENIUS, will focus on Nobel Prize-winning physicist Albert Einstein. The all-star cast includes Geoffrey Rush, Johnny Flynn, and Emily Watson.

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Time Is But a Stubborn Illusion – Sneak Peek | Genius

National Geographic

What is time? A deceptively simple
question, yet it is the key to understanding relativity. It is sort of the reason
my hair is going gray. [laughter] When we describe
motion, we do so as a function of time, 10 meters
per second, 100 miles per hour. But the mathematical
description of velocity is moot unless we
can define time. Is time universal? In other words, is there
an audible tick-tock throughout the galaxy, a
master clock, so to speak, forging ahead like
Mozart's metronome? The answer my friends is no. Time is not absolute. In fact, for us, the living
physicists, the distinction between the past,
present, and future is but a stubborn illusion. [music playing] A lot to consider, I know. I know. [laughter] But understanding time is
essential to understanding relativity. Now, I want you all
to close your eyes. Not to worry, I don't bite. But I am on the
lookout for a new pen. [laughter] Go on close your eyes. To truly grasp the idea of
time, we must take a step back and ask, what is light? So journey with me to the Sun. Light travels from the Sun to
the Earth through space, yes. When I was your age,
I wanted to know how can something, light,
travel through nothing, space? Let us isolate a light beam
and travel alongside it. But let us go faster. You're there with me. Faster. Faster! What is time? [thud] PROFESSOR WEBER: Herr,
Einstein, wake up! I wasn't sleeping, sir. I was thinking. Oh, really. About what exactly? The secrets of the
cosmos, I suppose. I suggest you think
about trigonometry instead, with your eyes open. And sit up! Laws of sines and cosines? c squared equals a squared
plus b squared, subtract 2 [inaudible] cosine b. PROFESSOR WEBER: The
area of a triangle? STUDENTS: The area equals
b squared times a times b over 2 times c. PROFESSOR WEBER: What is
the solution [inaudible] differential equation? Herr Einstein, are you
still too busy contemplating the secrets of the cosmos
to solve this equation? Oh, no sir. I've already solved it. PROFESSOR WEBER: Leave, now. On what offense? PROFESSOR WEBER: Your mere
presence spoils the respect of the class for me! That is not an
objective reason. Out! [music playing] The natural log of a
constant multiplied by x equals the natural log
of 1 plus v squared. And since v equals y
over x, that gives us the final function, x
squared plus y squared minus c x cubed equals 0. And speaking truthfully,
sir, your mere presence spoils my respect for the
future of Prussian mathematics. Out. [door slamming]

Quantum Computing – The Qubit Technology Revolution

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One of the strangest features of quantum mechanics is also potentially its most useful: entanglement. By harnessing the ability for two particles to be intimately intertwined across great distances, researchers are working to create technologies that even Einstein could not imagine, from quantum computers that can run millions of calculations in parallel, to new forms of cryptography that may be impossible to crack. Join us as we explore the coming age of quantum technology, which promises to bring with it a far deeper understanding of fundamental physics.

PARTICIPANTS: Jerry Chow, Julia Kempe, Seth Lloyd, Kathy-Anne Soderberg

MODERATOR: George Musser
Original program date: JUNE 3, 2017


This program is part of the Big Ideas Series, made possible with support from the John Templeton Foundation.

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Introduction of Participants 00:25

Program Begins: Quantum mechanics, weird or unfamiliar? 01:38

How much power is 20 Qubit’s? 10:28

What are the pros and cons of Superconducting quantum computing? 25:55

The factorization problem 40:01

Is there a relationship between quantum computing and machine learning? 48:31

Q & A 54:17

This program was filmed live at the 2017 World Science Festival and edited for YouTube.

So our plan today is to talk about what quantum
computers are. How people are building them. What they can do. What they can't do. They're not all powerful god like devices
so they do have limitations that we'll get into as well. OK. Without further ado let me introduce our esteemed
panelists. Our first panelist is a mathematician, computer
scientist, physicist, expert on quantum information theory. She was a professor at Tel Aviv University
and a researcher at the CNRS in Paris. Pease welcome Julia Kempe. Our next participant is the professor of quantum
mechanical engineering, that's a thing, at MIT. Director of the Keck center for extreme quantum
information theory and hopefully will explain why it's extreme to us. Please welcome Seth Lloyd. Next up, our next guest comes to us from the
Air Force Research Laboratory in Rome in upstate New York. She's a senior research scientist there and
the primary investigator for the Trapped-Ion Quantum Networking Group. Please welcome Kathy-Anne Soderbergh. And finally coming to us from IBM in Yorktown
Heights, just north of the city, is the Manager of the Experimental Quantum Computing Group,
distinguished research staff member. Please welcome Jerry Chow. So Seth, let me turn to you first. Quantum mechanics: weird or just unfamiliar? Definitely weird. It's, I prefer the word funky actually. OK you heard its. This is the official terminology. It's the James Brown of sciences. How so? I mean why and particularly in terms of computation
what is it? What's the special quality of quantum physics? So in quantum mechanics, things that we think
of being like particles, like basketballs or soccer balls, have waves that are attached
to them. And so you know I have a ball over here and
it's got a wave and then I have a ball over here and it's got a wave. But the funky thing about that is that the
waves can add up so I can have a ball that's both here and there at the same time. And if you map this to a bit in a quantum
computer, so this is zero, ball over here, and ball over there is one, then I can have
a quantum bit or qubit that is zero and one at the same time. So Julia, why would that be something you
would actually want? Why would this, I want to actually comment
on the weird first if I may. Funky please. Funky. Because I think it becomes a, it depends on
your point of view coming at it as a physicist with a lot of training in classical physics
it's indeed probably very weird, but if you look at it as a computer scientist it maybe
becomes less weird because we are not spoiled. Our intuition is still, that it's not, how
can I say, biased in any way. And I view it as something which is like probability
theory except the probabilities can be negative or they can be even complex that that is not
so essential. And so in that sense it's not very weird. It's just gets, requires a bit of getting
used to but it's pretty natural. And so for the qubit, why is it useful to
have qubits in being both zero and one at the same time? Cause if we have many of those, we can think
of having various states at the same time and we can think of computing all these possibilities
at the same time. So that leads us to this massive what's called
quantum parallelism. So Jerry, can you walk me through like just
a quick numeric example, you have a certain number of qubits, what that means in terms
of parallelism? Yeah. So I mean one of the, as has been mentioned
with regard to these qubits, you have these superpositions. And so you might have some number of bits
but instead of bits now you have qubits. Right. And in terms of this parallelism what you
can actually have is access to a much larger space of possibilities. So if you have n qubits you actually have,
using these principles of superposition and entanglement, you have access to a space of
up to two to the n possibilities. And so that type of, that type of exponential
space gets really, really large for rather modest numbers of qubits. In fact if you get to around n of three hundred
cubits you actually have some state-space that is greater than the total number of particles
in our universe. Kathy-Anne, walk me through an extremely simple
numerical example…suppose I, in fact we do have, but to take an example two of these
qubits. What does that mean in terms of the computational
space that we can work with? So if you have two qubits you have a four
qubit state space because you can have each one stored as a zero plus one and the other
stored as a zero plus one, so you get 00011011. Whereas classically you can only have zero
or one. You can't have anything in between. So the computer's in a sense an all possible
computational state space. Yes that's right. Now Seth, on the face of it that doesn't sound
like such a good idea because you want to get an answer from the computer and it's just
basically telling you everything. Yeah and indeed it's kind of dangerous. If I have a quantum bit that's zero and one
at the same time and I say yo are you zero or are you one? Well you know you could, OK, so the electron
is over here and I bring up a very sensitive electrometer that says, yo, are you here or
there? Well it's either going to show up here, say
with fifty percent probability or there were fifty percent probability. So it's just going to behave like something
that's generating a random number which is kind of useful but it's not, if you actually
want certainty for your answers that's not so great. So the kind of the way that these quantum
computations work is you set up all these waves and they're wiggling on top of each
other and they're, they're performing multiple computations simultaneously. So you can think of an individual wave, a
wave of say electron here and not there, that's kind of like a pure tone like ahh. An electron here and not there is like ahh. An electron here and there at the same time
is does somebody want to supply the other tone? It's a chord. So it's you, you get the computational power
from the interference from the kind of symphonic nature of this. So the idea of a quantum computation: you
set up all these waves, they make this beautiful music together in this symphonic way. But at the end of the day you actually want
to have an answer that says yes or no, or zero or one, and all the trickery and talent
goes into making that happen. So Julia, is that, any problem I care to pull
out of a hat or that my professors give me as a homework assignment. Can I turn it into a problem that's amenable
to this kind of chord pattern that then reduces to a single pure tone? That might depend on your artistry but in
general quantum computers are good at certain things and we would leave, you know, a lot
of other things to our normal classical computer. And of course you probably all heard of the
problem that a quantum computer can solve very well. And that's factoring numbers, large, very
large numbers into primes. And the way it's done, just like Seth was
saying and I was saying, you can think of these amplitudes of a quantum computer as
positive and negative numbers. We try to arrange these waves in a way that
all the bad answers cancel out because you can, you know ,you can have several ways to
arrive at the wrong answer. And what you'll try is have some with a positive
amplitude and some with a negative amplitude and they cancel out and then you arrive at
the right answer and you, voila you get a factor for a very big number. And that's one of the first and most remarkable
things that was discovered a quantum computer can do. And I can elaborate on why it's important. Most of you, all of you, I assume, are using
credit cards at the machine or over the Internet and you rely on the fact that they're encryption,
that they are encrypted. And it so happens that the modern day encryption
is based on assumptions of hardness of factoring or problems of that type. And it's these type of problems that a quantum
computer would be able to easily break. Interesting. Kathy, let me ask as you to drill down a little
bit more here. Sure So when I think of a computer I think of it
has, does arithmetic logical operations. How do you, I mean without going into details,
we'll get to some of the details later, but does the quantum computer also have those
same elements of it can add, it can subtract, it can do logical comparisons of things? Yes, yes you need all of the same similar
components to a classical computer to do quantum computing. But the way that you make the gates looks
very different than in a conventional computer. And that somewhat depends on the underlying
qubit technology. OK I'm going to definitely come back to the
details on that later. I just want to establish that it's a computer. Yes It has, you look at it and though it's configured
differently, does have the recognizable qualities of a computer. Yes You can program it in C or Java, and it has
one additional instruction which says take this quantum bit and put it here and there
at the same time, put it in the state of zero and one at the same time. So you supplemented ordinary computer language
with just one additional quantum instruction and you're good to go. If you can build the thing of course. Which we'll see in a little bit. Jerry, what are we up to just in general state
of the art about how many qubits we have and what does that mean in terms of vis a vis
a classical machine. Yeah. So there's many different physical implementations
of building a quantum computer. The underlying core of a quantum computer
we call a quantum processor. And what you basically need to build the quantum
processor is something that follows the laws of quantum mechanics and can have this quantum
mechanical zero and one. And in terms of where we are in experiments
we're looking at building universal based quantum computers of order of ten to twenty
qubits at the moment. And that's, that's kind of where the state
of the art is in the field. And just for reference sake, twenty bits doesn't
sound like a lot actually, but how does that what kind of power does that endow a machine
with? Well it's actually very interesting because
although you might have twenty qubits you can actually then have the state space up
to two to the twenty possibilities, right? But how much you're actually able to access
that then determines, is determined by your coherence time. So there's a metric known as coherence time
which says how good of a quantum state can you actually keep in your quantum processor. And different types of technologies varying
from superconducting to trapped-ions, like the kind Kathy-Anne works on, have different
amounts of coherence time. So overall this type of time times the number
of qubits, we try to we try to at least my colleagues that we've only started thinking
about a metric for this called quantum volume to kind of describe what is the power of a
quantum computer. So walk me through. What's a quantum volume? You can basically think of it as how many
steps of these logical operations, or these, these gate operations that you can do the
superposition or entanglement steps in the amount of time that before all the quantum
information is gone, becomes just classical. And so you have a certain number of steps
and then you have a certain amount of depth in terms of the total number of qubits that
are connected to one another. So Julia, let me ask this of you. If I just have a phone, a classical ordinary
computer and I store information in it, one hopes at least it will be able to retain that
for a long period of time. Is Jerry saying that actually it decays away? And why would it do that inside a quantum
computer? So the big challenge for a quantum computer
is indeed to maintain these coherences or these waves that are spread over, not just
you know one qubit but over a collection of, in this case, perhaps twenty qubits. And what we call entanglement these, these
correlations at a distance of these qubits. And it is true that this is what nature does
on a very small scale when we describe electrons and so on. But it's also true that we don't observe this
in our everyday life. I mean when you have a bit you have a big
it's either zero or one and the reason we don't observe it is that once we start interacting
with the environment, once this very fragile superposition is being subject to the surroundings,
it's being subjected to noise. And these very fragile superpositions will
start to what we call decohere, so just disappear. And the point is of course that we need to
be able to address this quantum computer. We need to be able to talk to it. We need to be able to manipulate it. So it has to be exposed to us, to our you
know to the world in that sense. And so we're living in this tradeoff situation
where on one hand we need to protect the state. So we would like to just put it in fridge
and never touch it. On the other hand we have to touch it in order
to manipulate it. And this is the big challenge that, you know,
these experimentalists are facing. To battle this decoherence invariably comes
along with the fact that we're exposed to the, you know, to the environment. Kathy-Anne, walking into your laboratory,
what would we see and then walk me through what that represents. Sure. So I'll talk about trapped-ion technology
which is what we work on and I believe Jerry will talk about superconducting qubits in
a few minutes. They're very different technologies but they're
both very advanced right now in the field. So for ions we track single atoms and we hold
them, they're they're charged so you can hold them using electric fields. So first we prepare a vacuum chamber, because
as you just heard these systems are very fragile, so you need to protect them from the environment. So these trapped-ions operate at room temperature
but we hold them in a vacuum chamber roughly ten to the minus twelve Torr – it's the same
vacuum as outer space. So the only thing in there is the atoms that
you want to manipulate. And you have a neutral atom source which is
just a piece of metal in a stainless steel oven that you heat up and then that creates
a beam of neutral atoms which you can put in your, what's called an ion trap, which
is just a collection of metal electrodes. Because as I said we trap these using electric
fields since they're charged. So you put an oscillating electric field on
that trap. What that looks like to the atom is a rotating
saddle. So then that looks like a bowl. And if you drop a marble in a bowl eventually
it'll come to rest at the bottom of the bowl. The trapped ions do the exact same thing and
these potentials. And so we shine the neutral atom beam near
the trap and then we have a laser that actually rips one of the electrons off the neutral
atom and that makes our ion. So that leaves it charged. And at the same time we have to shine a different
color of light in, because coming straight out of an oven the atoms are essentially screaming
hot and the trap potential just can't catch an atom it's going that fast. So you have to cool it down a little bit with
a laser, its laser cooling. And then that allows you to trap it in this
bowl like potential and then we shine yet another color of light on the atom and all
these different colors of light create different transitions within the atomic structure. So if you could look in the atom you would
see different energy levels inside and each color of light is resonant with a different
energy level. And so the detection light when we shine it
on. It hits a very strong transition in the atom,
which excites it from it its ground state, so the qubits themselves are held in the ground
states of these atoms. There's two ground states. And it sends it to an excited state. It's a very short lived state. And when it emits it emits a photon and it
does sense that this strong transition it does that hundreds of thousands of times and
then we collect those photons on a camera. The ion we're using is ytterbium so it emits
a UV. If it was a visible color you could actually
see it with your eye, it would be a tiny speck. Hang on. You can see atoms. You can see atoms. See atoms. What do they look like? Just like when you shine a flashlight on a
ball in a dark room, right, it scatters light and then your eyes can see it and you say
‘oh there's a ball sitting there’. The atoms do the same thing. They emit, they emit photons that if your
eye was visible through the UV you could see them. It would just be a tiny dot on a very dark
background. You can see a single atom fluorescing. The darkest, you know that the brightest star
on a very dark sky. Unfortunately we can't see in the UV with
our eyes so we have to use a camera. But if you were to walk into our lab you would
see large optical tables that are about six feet long by four feet wide filled with lasers. Because to do all the different operations
you need different frequencies of light. And then you'd see another vacuum chamber
that holds or another optical table excuse me the holds our vacuum chambers. OK. So let me just see if I follow. You load your system Yes With ytterbium ions? Yes. And to perform a computation just, for example,
how do you clear the memory? What would be the first step in your computation? Sure. So usually you start with some number let's
say between two and five ions is what you'd want. So you'd load two or five ions, let's say
two for this example. So we can turn the oven on for a set amount
of time then we shine the laser that takes that rips the electron off to create the ions
and we wait till we get two ions. And then we can see them on the camera. And so we initialize the system to a zero
state just like in conventional computing you have to initialize your computer to zero
state, and then if we wanted to put those two ions in a superposition we could shine
either a laser or a microwave at them and that would create a superposition. So you could think of a qubit on what's called
a block sphere, which is just a unit sphere where the up z axis could be your one qubit
state and then down z axis could be your zero qubit state. So you're prepared it in a zero, and then
we shine these microwaves or lasers on the atoms and it causes the population to rotate,
basically. And so you just stop when you get to the upstate
and you can look at that, it’s a trace on a scope. So for example I mean a standard operation,
simplest possible operation you might have in a computer system is a ‘not’. That's right. So how would you do a ‘not’? So you prepare, you would prepare your qubit
in the zero state then you would shine a microwave a laser beam on it for a set amount of time
and it would cause the population to evolve to the up state, and that's a ‘not’ gate
if it go from zero to one that's a ‘not’ gate. If you let that light or microwave interaction
on and it would go back down to the zero state and it would just keep rotating. So suppose I want to do something a bit more
sophisticated like an ‘and’ or something that actually combines two qubits. How would you how would you do that? So if you had two qubits in trapped-ions,
the nice thing is that because they're charged they want to repel each other, but because
there's a trapping potential on them they get pushed together so they find a happy medium
where they sit. But they have a shared motional mode due to
this interaction. So there are a lot like a Newton's cradle. If you pull a ball in a Newton's cradle you
see all the balls move together. That’s right. That’s right. And so the trapped ions do the same thing. If you start to shine a laser beam on one
and you excite some motion and actually excites motion in in both ions. And so then you have a databus that you can
get the ions to talk to each other. And if you had five ions you could actually
use this databus to get one in five to talk to each other directly. So you're not limited to your nearest neighbor
interactions in a trapped ion system. And you can use that to combine them. You can use that combined motional mode to
get the qubit states to talk to each other and create things like controlled ‘not’
gates, say. Great. So the Jerry, can you kind of repeat that
kind of virtuoso performance for your own lab? Yeah, I'll do my best there. But what's it like in there actually? So our lab looks a lot different from what
Kathy-Anne described. And that, that the reason for that is because
the underlying qubit is very different. One difference that, the main difference is
that instead of actually having physical, naturally occurring qubits, in this case ytterbium
ions, that you can you know that all of this work is based off of having a really, really
stable atomic clocks. What we're doing with superconducting qubits
is to actually engineer and build them on a chip. So it's a little more integrated. You're actually using lithographed techniques
that you know and love today with your silicon processors. And instead of the materials that are in your,
in your in your chipset or in your phone or your laptop we're using slightly different
materials to build superconducting circuits. So superconducting refers to materials that,
that when they're cold they have basically no resistance. And by using the right kind of superconductors
you can actually build quantum effects into circuit elements. So with Kathy-Anne, I have a good picture
for what the bit is. The ion is either pointing up, or you know
rotating that direction that corresponds up, or the other way so what's the corresponding? Yeah, so the way to think about it here is
that you're actually building an oscillator circuit. So if you if you go back to your electrical
engineering days think about the circuits that you might build with resistors or capacitors
or inductors, these are varied circuit elements. In the case of a superconducting circuit you
actually could use an element known as a Josephson junction. And a Josephson junction is basically a sandwich
of aluminum, aluminum oxide, aluminum. And what's phenomenal about this this element
is that you can combine it with it with a standard capacitor and you can make it oscillate
in the microwave regimes, so around five gigahertz and choosing the right parameters of the capacitance
in the Josephson injunction you can isolate it to build a qubit state, so zero and one,
that that resonates at around five gigahertz. So in your case can you walk through an example. You load your computer… Right. So in this case, in this case where we have
a silicon fabrication facility that builds these circuits, we, they come out in large
wafer form and then we have to cut them up into smaller chips. These chips are packaged into a printed circuit
board like what you might see in inside your phone. But this printed circuit board carries microwave
signals and so those the printed circuit board then needs to be cooled down to really, really
low temperatures to basically have the qubits function properly. So I said that we use the superconducting
materials. And so the materials are niobium and aluminum. And for them to superconduct and for there
to be so little noise that we can actually see these quantum mechanical effects at five
gigahertz, we need to cool down to fifteen millikelvin. So that's, since you already brought up the
space analogy, it's colder than outer space as well. And in fact you know with the microwave background
space is around it's a little under four kelvin there, but we're getting down to fifteen millikelvin. Wow And so the refrigeration systems that we built,
that we use they're commercially available but it is phenomenal that you can just turn
the turn hit a button turn a key and cool down to these these devices to such a low
temperature. So in the example of the trapped ions, if
you want to execute a ‘not’ operation you hit it with lasers or microwaves. What do you do in your case? Yes. In this case it's more electrically controlled. So you you're placing this chip inside this
printed circuit boards, it's inside of the refrigerator, but then you have all these
wires that come down through the refrigerator and those carry electrical signals. And so to do say, a ‘not ‘operation, what
we're doing is basically applying a shaped microwave pulse that's generated at room temperature,
so on the set of electronics that sits outside of the refrigerator, we generate a five gigahertz
signal for a certain amount of time say maybe twenty nanoseconds or thirty nanoseconds. That pulse gets sent down into the refrigerator,
applies just enough energy to flip your qubit state from zero to one. And then you could do. How would you do an ‘and’ or ‘nand.’ And then with regard to two qubit gates, so
our particular architecture connects qubits on the chip. So there's there's other microwave circuitry
that is used to, to define particularly interactions between qubits on a chip. But then those, those interactions are again
activated using microwaves so just the way that we do the not we might send it we might
send pulses at a slightly different frequency down into the refrigerator to induce a two
qubit operation such as a controlled ‘not’ gate. So everything you've described is acting on
the system. So how does this system act on us to return
its information and the result of the computation? Yeah, so in the case of Kathy-Anne they're
sending another laser beam to do the detection, and you can see it with the camera, but us
what we actually have to do is send a another microwave pulse which is resonant with a detection
cavity, so there's actually a resonator on the chip that oscillates at a slightly different
frequency depending on if the qubit is zero or if the qubit is one. And so we interrogate this cavity with a microwave
pulse and at a very low energy levels, so single photon energy levels at say six gigahertz,
and so that that signal goes down into the fridge, gets amplified through various stages
and then we basically have to digitize it to determine whether the qubit was a zero
or one. Cool. Seth, just to kind of bring some perspective
on the technical discussion here. What would be some pros and cons of the different
techniques? Why would you use trapped-ions in some cases,
superconducting qubits in others? Well so pretty much anything at the microscopic
level will compute if you shine light on it in the right way, via either lasers or microwaves. But some things compute better than others. So what's been happening over the last decade
and a half or so is that the technologies for instance superconducting quantum computing
have really advanced by a lot. I mean I was participating in the early experiments
to build I think the second superconducting qubit around 2000. It was a so-called ‘flux qubit’ these
super currents you have a little loop interrupted by Josephson junction. And so super current going around forever
that way you call it zero and super current going around forever that way, counter-clockwise,
sorry, clockwise for you then you call it one. And then you know super current going around
both ways simultaneously both clockwise and counterclockwise simultaneously, that's 0
and 1 at the same time. So that's how you get quantum bit in these
things. But you would let them sit for a little while
and then, you know, they'd get kind of completely randomized very, very rapidly. And so these originals superconducting qubits
were, well they sucked let's face it. That's the technical term like funky, right? So but then there was this great innovation
actually which Greg participated in, I think this was part of your PhD thesis, this was
developing – people thought oh the materials are bad, something's wrong with how we're
building these things. But it turned out that it was really much
more of a design issue and by being really sneaky about how you design these systems
you can make that much, much much, much more coherent so that they could you know you could
have, they could oscillate around or you could perform ten thousand logic operations before
these things got messed up. And so with superconducting systems I think
that what you did in your PhD thesis and afterwards was a really amazing innovation. And then which also allowed, because you building
them of these all these chips you can put many of them together, so there's a clear
path towards scalability. Similarly with ion traps, the first ion trap
experiments were done in the in the late 90s in the mid 1990s but they were you know two
qubit experiments, sometimes two qubits you can still do interesting things with two cubits,
right, you know. You can search your data space with four possibilities
and you can find is it here or here or here or here by only looking once. Like how can that be, classically? But quantum mechanically. We're about to find out actually in a little
while. Yeah. So, so what's happening is that there ,is
that there is a really there's been also with ion traps there have been all these advances
in integration and making ion traps larger and larger, integrating them with quantum
communication lines. So there's been a steady advance in constructing
more and more elaborate and complex quantum information processors. Ion traps and superconducting systems are
the two technologies that are furthest along the way. But there are a whole bunch of other technologies
like nitrogen vacancies and diamond topological systems and all kinds of crazy things because
again pretty much anything will compute. And even though as Jerry was saying that the
twenty qubits, OK that doesn't sound like a lot, but two to the twenty is about a million. Thirty cubits…two to the thirty is about
a billion. Forty cubits that's a trillion. Well you know now you're starting to try to
manipulate these, a trillion numbers, a billion or a trillion numbers and actually that becomes
very difficult classically. So the devices that are being built right
now are just at the threshold where we actually can't understand what's going on inside them
classically. Previously we were able to simulate what was
happening on a hugemungous classical computer and try to figure out what's going on. Now we're kind of on our own and sort of exploring
this quantum frontier and we, you know, we we are going to be able to try to figure out
what's going on. And then the hope is that when we build these
devices we can use them to build ever-larger devices and build quantum computers that have
a thousand qubits or a million qubits or a billion qubits. So Julia-Ann, the machines, and it's a great
moment to be in historically to be in, the machines are now crossing over and exceeding
the power of our most powerful classical computer. But then how do we know that they're working
properly if we can't even compare the result of the calculation of the quantum computer
to a classical computer any more? And working properly. I mean Because I don't know about you but my computer
crashes sometimes. I mean how can we ensure that they're working
properly is maybe a question I can answer because as you ask what, what architecture
will eventually you know win or be the best one and of course the question we need to
answer is which ones scales best for a large number of qubits? And in theory, I'm a theoretician so I you
know I mean I'm in a position where I write my papers saying let's assume we have a quantum
computer of ten thousand cubits and then but there is a lot of theory developed, a theory
of say quantum error correction for instance, where we face the fact that no matter how
well Kathy-Anne and Jerry perform their jobs, the elements out of which they build their
quantum computers will be faulty at some level. There will be a probability that they'll fail,
that they'll lose their coherence and so on. And there actually is a very beautiful theory
of quantum error correction that once we are above a certain threshold with the noise in
their system, so once the noise is small enough, then we can actually build in redundancy into
these qubits, in a way that the computation will flow flawlessly. And that's a very nice theory that will then
allow us to make the quantum computer work at a larger scale. So to fix the mistakes You can fix the mistakes. Yes. So I think this might be a good point to talk
about how they actually work. And Jerry I know you've got a demonstration
you'd like to present to us. Well first, the way that I want to actually
motivate this is based off of this search, a search algorithm and Seth already alluded
to this. But let's say you have four cards, right and
you play the game of monte or you might go to a street corner somewhere. Not that we're advocating you do that. Don’t do that. And so out of these four cards you've got
one of them which is different, one of them is the queen. And now, now we're going to flip them over
and when you play this game you're randomly going to try to find where that where that
queen is right. You're going to try once and you're going
to flip over a card and see whether or not it's the queen. And so on, on in playing this game you really
only have a one in four chance of getting it right on your on your first try. But now what's interesting about this type
of game is we can also ask well how would we how do we do this if we had a computer? What what what does a classic computer do
with this game and what does a quantum computer do with this game? OK. So in the case of a classical processor what
we're doing is when we when we flip over these cards you can think of this as as storing
a database. In this case we can also call it an oracle. So you store the database with the hidden
set of cards where the queen is properly located. With a classical computer what you're going
to do is in order to to find where it is you're going to look at all the possible arrangements. Right. So you're going to start with one particular
arrangement. Let's, let's start with placing the queen
in the first slot. And we're going to take that entry, use it
as an input, we're going to do some processing, in this case the green box where you're gonna
do some comparison with what's in the database and you're going to make a decision at the
end of it whether or not it correct or not. In this case it was not correct and you get
a zero. OK. And so now then you can try the next one. And again you're going to get to get a zero
and then the next one and this time you get it right. But of course classically you're going to
go through all four of them. And so after you go through all four you see
that on average you would have gotten this correct, basically you would get a correct
after querying this database about two and a quarter times. Right so this problem of search in this case
with a classical computer you can only kind of do this sequential, sequentially or by
choosing at random. But with a quantum processor, this is where
a lot of the ideas of quantum mechanics can come through. And so in the next slide here with the quantum
processor you have access to superposition. And so just like we talked about how you can
be in zero and one at the same time, what you can do with two qubit system is to make
a superposition of all four of the possibilities: 00, 01, 10, 11, to represent all four of the
possible arrangements of this hidden queen. And so we can take that superposition state,
use it as as basically as an input, call the database just once. Perform some processing step, in this case
the processing step involves entanglement and it involves this quantum interference
of adding adding together the waves. And it'll amplify the answer for exactly the
right answer. And so every time, no matter what you what
you place into the database, wherever you hid that card, you use only one call to the
database, you get the right answer using this algorithm. And this particular algorithm is known as
Grover's algorithm. It is a simple case that gives you the sense
for what is done differently in terms of processing information on a classic computer versus a
quantum computer. And so on the next slide what would you actually
would do when you want to program an actual quantum, quantum processor is to use this
language of quantum gates. And so what you see here is actually a quantum
circuit. And as Seth alluded to the idea of music,
we call this actually a score because it kind of looks like a musical score. And the concept of time really in time with
gates really has a strong analogy here because it's like you're playing different notes on
these different qubits. What you see here is really just, just two
of the qubits being populated with these different operations, which realizes Grover's algorithm. And to break it down a little bit further
in the next slide what you, what you see is that these various steps of superposition,
the stored database and the actual post-processing steps are all, are all encoded into these
various gate operations that you can apply. And in this case we can actually run it through
and get , get a result. And I can actually launch this live if you? Please by all means. While we are you switching over? Kathy-Anne, you were really one of the first
people to actually do this for real in your dissertation work. Can you describe what you accomplished? Yes sure. So we did it with trapped ions, we had two
trapped ions and as Jerry just showed you that'll give you the four element database. And what we did in practice was we had the
computer mark a state and then we would run the algorithm similar to the diagram that
Jerry just showed, it looks very similar and then at the end we would see what the probability
was that we recovered that marked state. And at the time the untangling gate that we
used we were just starting to learn to use it, it had just been demonstrated. And so we found the mark with a probability
of about sixty percent. But Jerry just told you it should be one percent
and that's because the fidelity, that's one way you can measure how good a quantum gate
is, the fidelity of our gate wasn't as high as we would have liked it to be, mostly due
to technical difficulties. This is a fundamental limit of trapped ions. They've since repeated this experiment with
three qubits recently, Chris Monroe's group at the University of Maryland, and they did
quite a bit better because the technology has progressed. Now at this point at these gates are at very
high fidelity near the fault tolerance level that Julia was saying earlier that you need
to run these computers. You were telling me earlier that these are
so delicate that you can so much as look at the laser wrong and it would it would give
you the, it wouldn't work. Yes so we used cadmium ions in my graduate
work and they, they need laser frequencies that are about two hundred fifty nanometers,
which is an incredibly difficult color of light to generate. You basically have to quadruple a laser to
get there. So you take a laser, you double it and then
you double it again. And doubling's hard and the efficiency is
low. And one of the people in our lab just had
the right acoustic sound to his voice that he would unlock are doubling cavities and
so sometimes when he came in the room he would start to talk and we were trying to run our
experiment and our laser would shut off. They're a very fragile system. So Jerry are you ready to go with thIs? Yeah. This is actually a live quantum computer. I wanted to start by just showing a little
bit about the interface of what we have. So this is the IBM ‘Q Experience’ and
what we actually have is a lot of content on there for anybody to get started with learning
how to program and actually use a quantum computer. So anybody can do this? Anybody can log in and sign up for an account. We have this library with various user guides
for beginners, if you're more familiar with some mathematics like linear algebra and even
another other guide which actually leads you to our Github developer repository. But through this, through this portal you
have access to learning about the basics of a qubit superposition, entanglement, simple
algorithms such as this Grover’s algorithm. And we also have a community board feature
where we have the ability for anyone to ask questions and to, and our IBM researchers
are more than happy to answer. Julia I wanted to go back to what you were
saying about the factorizing problem, that's in addition to the search algorithm the other
use that people we talk about with with quantum computers, so what's what's kind of state
of the art in that when you factor the number fifteen or, or get that high even? You can, I mean Jerry would probably be a
better person, but with twenty qubits you can imagine that you can factor perhaps with
some overhead I would guess you can maybe factor numbers up to a hundred? Which of course you can do in your head. So at this stage we are really at the level
where we demonstrate things when it comes to factoring. The cryptographic systems that I was talking
about that your credit cards rely on these usually have something maybe up to a thousand
bits? So I think once we get a quantum computer
to the order of perhaps one or several thousand qubits then you better stop using your credit
cards with the current encryption. So… One thing I would I would like to mention
though with regards to the Shor's algorithm though is that because of the error rates
that we end up having with the physical qubits, sure if you have a thousand perfect qubits
you might start thinking about Shor's algorithm for a thousand, thousand-digit numbers but
with, with needing quantum error-correction and a lot of the best known encodings you
have an overhead that significantly pushes that threshold further. So I think that in terms of Shor's algorithm
and a realistic Grover's search you're thinking about probably needing millions, of tens of
millions qubits. So it's it's a bit further off but it's still
there will come a day where There will come a day when you've got to worry
about your bank accounts but it's on, the horizon for that is a bit further beyond where
we are currently at. So millions of physical Millions of physical qubits, yeah so that's
only maybe around a few thousand logical qubits but the, the encoding that's what's going
to matter there. So Kathy-Anne you were describing also to
me earlier that on the one hand quantum computers take away our privacy by breaking these codes
but they might also restore. Can you describe some work, work you've done
for the restoration process? Yes so there's people working now on, in addition
to quantum, computing quantum networking and what you can do with quantum mechanics for
networking communication, the easiest example to explain, and it's been around for a while,
is called quantum key distribution, where you send a message between two parties say
Alice and Bob using single photons. And because the photons are encoded using
quantum mechanics you can actually make protocols that are ultra secure. And by that we mean they're tamper-proof,
meaning that even if an, an eavesdropper can't get between Alice and Bob to get the signal
because they don't have the corresponding information that was encoded in the quantum
mechanics. But even if an eavesdropper were to try and
grab the signal the protocols are tamper evident so Alice and Bob would see that immediately
when they started to talk about the results that they'd gotten and would abandon the protocol. So yes it can do things like break, break
encryption but it can also provide ultra secure protocols too. So what are you doing in your lab now to kind
of bring that into fruition? So we're working on quantum networking where
instead of sending key information, which that just sends information to generate a
key and then you would use the key for something else. We, and a lot of people in the field, are
moving towards quantum networking where you actually send quantum information directly
over some longer distance link. And so this allows you to do things like ultra
secure communication protocols or people are also looking at it for distributing computing. Where you don't just have one computer sitting
there with millions, let's say, of qubits but you distribute these qubits over a larger
space and you have smaller banks of qubits. Seth, you once told me, this is a couple of
years ago now, I don’t know if you remember the anecdote, the NSA funded some early quantum
computing work to show this wasn't possible because they didn't want to have unbreakable
codes. Can you walk through that? Oh yeah, so I was at the, so back in 1993
I wrote the first paper showing how you build a quantum computer using these methods of
zapping stuff with microwaves and lasers and things like that. And then we started to work with people to
build them. In 1994, I think the first U.S. government
meeting to fund, to discuss funding for quantum computing took place at DARPA in Arlington,
Virginia. And during this meeting there were a bunch
of people, including Peter Shor, they were there talking about stuff and a fellow named
stood up and he said I'm Keith Miller from the NSA and I am authorized to tell you that
the NSA is interested in quantum computing and then he sat down again. And everyone went, oh my God! Some people actually told us something. That's incredible! But it caused such a stir that he stood up
again and he said well I believe I'm also authorized to tell you this, of course the
NSA is interested in quantum computing because our primary mission is to protect the secrets
of the country, up to thirty years for top secrets. We have a whole bunch of information that's
out there that's already encrypted which if someone could build a quantum computer could
be decrypted. And that would be bad. So really what we would really prefer is that
it not be possible to build a quantum computer. By the way this is a good person to have funding
you, it's like they call up and they say how's it going? And we say oh it's terrible, the qubits aren't
working. Great great! That's wonderful. Here's your money. That didn't last very long. So then he said. But because of our secondary mission, if it
is possible, we want to have the first one, so. To bring this back down to more quotidian
kind of applications Jerry, you once described to me some of the molecular calculations you
were doing. Can you walk through what you're doing with
these molecules? Yeah. So, I think one of the more kind of near-term
areas that we'd like to look at application wise with quantum computers, actually is in
chemical simulation. So what's actually interesting is that it
dates back to Feynman around 1980s when he actually talked about, wouldn't it be great
to actually simulate nature using something that follows the same quantum mechanical principles
of nature. And there's been a lot of theoretical work
going into how would you actually map say problems in quantum chemistry, for example
electronic and molecular structure, onto physical quantum bits. And it's a really neat idea in the sense that
you can you can actually try and get an analog for a physical, a real physical system such
as the energy levels of say a hydrogen molecule, but actually run it on a on a on a chip right? Run that simulation on qubits that's inside
of one of our dilution refrigerators. And so we, our team has done various both
theoretical explorations and recently experimental demonstrations of how to do some rather simple
molecular calculations. So looking at the energy the ground state
energy of a simple molecule just like hydrogen so two H's and then lithium hydride, beryllium
hydride, but very small at this at this at this stage. But it shows the type of trajectory, if you
will, of our application in the near term because at some point with these different
molecular structures you get to a point where there's too many electrons in it that it's
impossible to again, simulate in on any classic computer. And it can be rather modest molecular sizes
that that already maxed out all those supercomputing resource in the world. And there's a lot of potential there for quantum
computing to really be a game changer in that in that field. Seth, I was wondering if you could fuse, merge
for me the two great computing tasks of our time; machine learning and quantum computing? Is there a relationship between the two? Yeah. For there is the only way to get information
right now is to, you know, sort of the only way get a grant right now is to apply to do
something with big data machine learning. And then in physics the only way to get a
grant is to do something with grapheme -the material is the future along with gallium
arsenide. So the real reason is to have something so
you can get a grant that's you know graphene based quantum random access memories for the
analysis of big data. It's a winner. I guarantee it. You heard it here. So it's interesting now that we are we actually
are about to have a simple quantum computers that have, you know, tens of qubits and fifty
qubits coming up. And I think that there's a reason reasonable
path to think of having up to a thousand physical qubits over the next five to ten years. I don't think that's unreasonable to expect. What will you do with these devices? Now because they are quantum mechanical and
they're very hard to simulate classically, As Jerry was saying, quantum mechanics you
know it's famously weird and funky and quantum systems exhibit funky and strange effects
like entanglement and Einstein Podolsky Rosen correlations, and Schrodinger's cat, and statistical
patterns in data that are very hard to capture classically. They're counterintuitive, it's hard for classical
computers to capture them. So if they can exhibit these, if quantum systems
can generate these funky patterns that you can't generate classically maybe they can
also recognize patterns that you can't recognize classically. Now machine learning is about taking patterns
of data and trying to tease them out and show that they're there, it's recognizing patterns
in data. Machine learning of course very trendy right
now, justifiably so not not really because actually I think you know it's about to supplant
human beings or anything like that but because actually it's gotten good. You know there's this there's this thing called
deep learning, which when I learned about it a three or four years ago I said wow! this
is fantastic, you know computers will tell us about love and truth and you know happiness
of all this deep stuff, but no such luck. It turns out that these are just neural electronic
analogs of neural circuitry that have many many many many levels in it so they're deep
in that sense. But they actually do do problems, they solve
problems that are hard to do. Now do you get inside of a machine learning
algorithm like say the Netflix algorithm where you know you say OK what should I watch today? And Netflix says, ‘’well I think that
you would like to see Dirty Harry’ but you, for some reason my students don't watch Clint
Eastwood any longer, I don't know what it is. You know what Netflix is doing is they're
actually looking at the preferences of everybody out there who's looking at Netflix, comparing
your preferences to theirs and then you know doing what's called a matrix completion algorithm
to recommend something to you. Now if you were to program that in a co-op
into a quantum computer it turns out that their algorithm which they only run, they
run it twice a day because it's so incredibly computationally intensive, that if you do
that on a quantum computer you could have a quantum computer that had say a hundred
quantum bits and you could do ten thousand operations and it would do the same set of
operations in a quantum mechanical fashion. So we decided hey this is great we'll call
this quantum Netflix algorithm, but then I googled quantum Netflix algorithm and it turns
out that Netflix calls their own algorithms "the quantum algorithm" even though it has
nothing whatsoever to do with quantum mechanics. So using you know quantum computers, quantum
systems in general exhibit strange and counterintuitive patterns. This gives you reason to hope that they can
recognize strange patterns and it turns out that the actual stuff that they're doing already
for things like factoring numbers is great for actually finding patterns and data. And actually this is a nice application that
people have been using to demonstrate, you know, simple versions of these algorithms
on small quantum computers Obviously the world as we know it would not
be the same without computers. They're just everywhere, they're ubiquitous. Will fifty years from now people say the same
thing about quantum computers? Will they be as transformative as classical
computers have been? That's an excellent question. I view, I think a quantum computer will remain,
it might be ubiquitous but it will remain a special purpose device for various things. I don't think it will replace the computers
as we know them in its entirety. So I view the future perhaps as you having
your laptop and then a little dongle with one of Jerry's or Kathy-Anne's contraptions. And then whenever you know whenever you need
to break into somebody else's credit card or whatever it is that you want to do you
make you know you make calls to that, you know, to that special device. I think that, that's more likely picture of
the future with a quantum computer in it then, yeah. So it's more like a GPU inside of an Xbox
type of thing. Yeah. I guess. That won't be literally a quantum iPhone. Although Apple may trademark that before Netflix
or Verizon I’m more optimistic, I think, you know,
they build it they will come. Right? So once we have quantum computers to play
around which we already do have thanks to IBM, I'm all over that and people will play
around, will come up with you know more quantum apps, quapps, quapps for all. Can you trademark that? I trademarked the cloud with a q. Questions. So the four card monte example I mean it's
it looks to me like something that could basically like backwards solve any kind of cryptographic
hash like as a black box or whatever the hash is. And yet I hear about these, these quantum-proof
cryptographic methods and because it seems like it doesn't matter what the actual hash
operations are, how does that, what is the general underlying principle for these quantum
proof hash hash hash functions? So a hash function in cryptography is a function
that just like scrambles everything up in a way where you can check to see if it's been
scrambled up in a proper fashion. And inverting these, so undoing this hashing
is supposed to be hard and that's the basis for a lot of cryptographic protocols. It's still hard on a quantum computer that
is this quantum searching will allow you to get a speed up to that will allow you to you
know solve some problems that you would be able to solve classically. But this kind of hashing problem is still
hard on a quantum computer. So one of the things that's going on right
now because exactly because quantum computers are getting more powerful, though let's face
it we're still you know we can basically compute our way out of a paper bag now where previously
we couldn't compute our way out of a paper bag. So but you know even the NSA has issued an
advisory saying you know if you're going to come up with an application that's good and
will still be secure twenty years down the line it's time for you to think of something
in addition because quantum computers might be there. So people are coming to trying to come up
with what's called post-quantum cryptography and I think that you're alluding to some of
these problems there. Now you make me wonder what post quantum cryptography
could possibly be? Can you just give a simple example? So based on a, so public key cryptography
is a way where you know I send, suppose so I buy green coffee beans over the Internet
and then roast them at home. Which you actually do. Yes I do actually. So yes it's so much so much fresher that way. It really is. I highly recommend it. So what I like to say try to send buy something
from Sweet Maria's in Berkeley, you know this 10 pounds of Costa Rican, then Sweet Maria’s
sends me a big number which is the product of two smaller numbers which are prime numbers. And this is called the public key, this big
number. I could use that number to encrypt my information
in a way such that only sweet Maria, who knows the two smaller numbers, can decrypt it and
that's the basis for public key cryptography. There's a public key, which is what they sent
out there. Anybody could encrypt but to decrypt you need
you know the private key, these two numbers. This is what quantum computers can do. If they can find the private key given the
public key which would be very disruptive thing because I frankly I like buying freshly
roasted green coffee and I would be pretty pissed off if I couldn't get it. So the idea is to you see this as a rather
specific protocol, so what people are trying to come up with are other protocols where
quantum computers can't break those protocols where there is a public key you can encrypt
using the public key but then it can only decrypt using the private key. But a quantum computer can't find the private
key. And so far there's been mixed success I would
say doing this. There's not nothing's ready for primetime. Yeah I should say. This is also important because even though
quantum computer is not there you might want to encode your information in a way that nobody
can decode it in the next one hundred years and one hundred years is a very long time,
right. And then we might assume the quantum computer
could be there, I mean a big one whatever. And the post refers to the fact that even
though you encrypted today maybe you don't want it to be decrypted you know in ninety
five years by one of the successors of Jerry's computers. And there are, there are methods nowadays
in fact that cryptographers have started to develop but they're extremely impractical
at this stage, that the public keys you would have to transmit are so long that it would
take you, you know hours basically to do that. But it's it it would be wrong to say that
there is no alternative but it's not a practical alternative. More questions. I saw a bunch. How does the observer effect claim to like
retrieving information? Can you elaborate? Well it seems like if you try to like observe
the information it would collapse, right, like it would just collapse back to two bits. So like how do you maintain like the four
bits or whatever? Observing it is essential to how we actually
make use of a quantum computer, right, because it has to be something tangible that we can
put in, has to be something tangible that we can take out. So the input will be classical bits the output
will be classical bits. In-between is where we make use of superposition,
entanglement and this two to the n exponential space, state space. And the key thing is is how do you tailor
your algorithm to make use of that so that when you perform that measurement you've learned
something that you otherwise wouldn't have wouldn't have been able to calculate. So it's all about how you define those interferences
of the waves through the operations you perform in between. You only observe at the end. Before that it's considered to be rude to
look at somebody's quantum computer while it's in operation. So, that's part of the difficulty in controlling
these very complex systems is because if you make a measurement or if the environment makes
a measurement without your knowledge the same thing happens. And so you have to control the system very
well so that you only look for, the environment only measures the system at the end of the
computation. So it sounds like a lot of the stuff that
you guys are working on is kind of like a straight analogy from a classical computer
to a quantum computer where like a bit is a qubit and you're working not gates, I was
wondering if you could talk about how quantum annealers like what D-Wave works on how well
you guys work on factors into that and if there are any sort of limitations using the
annealing paradigm. Cause I know that's usually better off for
like combinatorial optimization problems. But is there any other sort of limitation
on what an annealer can do versus what a quantum computer can do? Well I think that the first thing there an
annealer is a very it's a more restricted type of problem, right, so you get your hardware,
the way that you lay down these that these circuits in an annealer you defined all the
couplings between these these these these devices and you've defined a particular energy
landscape that you want to say optimize or find the ground state for. In the case with the systems that we were
building where you have full quantum control over any of the qubits, you really can drive
the system to any kind of quantum quantum problem that you want. And so it's it's reprogrammable in that sense
and you can define your optimization landscape in more generality. But maybe Seth you can also comment on the
D-wave. Yeah, I mean, also let me say that you keep
on letting all of the people who possess prior knowledge into this room will make our lives
harder. So what's that about? So quantum annealer as as Jerry was saying
it's a it's actually a very old idea and classically, there's a notion called simulated annealing
classically where you want to solve a hard problem. So you want to find the the minimum value
of some function, many problems are like this, like the traveling salesman problem, I want
to find the shortest path that will get me through all the cities of the United States
and back to where I started. That's a hard problem. And so what you do is you map this problem
into finding the lowest energy state of a physical system and then you try to find this
lowest energy state by cooling, annealing, that's why it's called, annealing to get down
to this lowest energy state. Now quantum annealing is a sneaky trick that
does this quantum mechanically. You construct a quantum system. I mean for instance D-Wave quantum annealer
is a tunable device with up to a couple thousand quantum bits, and they can tune all the couplings
between them And then you set it up so that the lowest energy state encodes the answer
to your problem.and then you try to find this lowest energy state by kind of oozing in a
funky quantum mechanical state of fashion from some known state to this unknown state. And either it works or it doesn't. Now it is an interesting situation because
actually nobody knows if this works is supposed to work even in theory. And so it's one of these things where if you
build it and then you see what happens. They find that some fraction of the time they
actually get the right answer. There's a lot of argument about whether this
is happening in an intrinsically quantum mechanical way or not. But I mean these are very interesting systems
so I mean D-Wave deserves great credit for building a large scale quantum system. It's got lots of entanglement in it. It's got, you know, it's it's has thousands
of quantum bits and it's actually a beautiful system just for doing experiments on. I'm going to a conference in Japan next week
or two weeks from now where basically people are going to report on all the experiments
that they're doing all these different D-Wave devices to try to figure out what the heck
is going on. Great. I'm afraid I'm going to have to cut off the
questions there Thanks to all of you for coming.