Views:653279|Rating:4.86|View Time:1:49:24Minutes|Likes:2611|Dislikes:73 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.
Complete Playlist for the Course:
Stanford Continuing Studies:
About Leonard Susskind:
Stanford University Channel on YouTube:
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
Views:989030|Rating:4.63|View Time:11:11Minutes|Likes:4958|Dislikes:396 Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! 🙂 !!
**DOH! There is a STUPID arithmetic mistake by me at the very end!** Sorry!
Linear Programming. I do a complete example!
For more free math videos, visit
okay in this video I'm going to do an example of what's called linear programming and the basic procedure for linear programming there's something you try to maximize or minimize usually subject to a couple of constraints or inequalities and what you'll do is you'll graph the inequalities you'll graph the region bounded by all the inequalities find the vertices which are basically just the corners of the region you'll basically plug those corner points into the function whatever the largest value is that you're maximum the smallest is your minimum so here's basically just a little example of what's going to happen you'll graph your region your inequalities you'll find some little region here it's in the green again you'll basically just find the vertices the corners plug those in and determine which one's a max and which one's a minimum okay so here's our actual problem that we'll do here so suppose you have 240 acres of land and you're going to make forty dollars per acre for the corn 30 dollars per acre of oats that you plant but it takes our to heart to harvest the stuff so suppose you have 320 hours available and it takes two hours of labor per acre for the corn and oats only take one hour of labor so how many acres of each should be planted to maximize profits okay so intuitively you know you'd probably like to plant a lot of well I don't know it's trade-off right if you plant corn you get you get more money but you know you can do two hours you can harvest two acres of oats for every one acre of corn but you actually double your money then so but then of course you're taking up extra space so alright so there's there's some issues here so let's see if we can't figure it out so I'm going to let X equal the number of acres of corn that we'll plant and then the same thing we'll let y equal the number of acres of oats that we plant ok the thing that we're trying to maximize here in this case we want to maximize our profit well what are what would our profit be well for every acre of corn you get basically $40 so we'll take 40 and multiply it by the number of acres of corn and this will represent the total income the total income from the corn and then we'll add to that 30 times y and that will represent simply the total income that'll be the total income from the oats if we plant why acres okay so we also have some other constraints here we only have 240 acres of land well so that's where we're going to get some of our constraints here okay so we've taken care of the profit okay so we only have 240 acres of land well certainly as well notice will have the inequalities X has to be greater than equal to zero Y has to be greater than or equal to zero because you can't you know you can either play 0 or some positive number of acres notice also one of our inequalities is that X plus y ok so we're planning X acres of corn Y a KERS of oats this is represents the total number of acres and we know that the total number of acres has to be under less than or equal to 240 likewise we only have 320 hours available man-hours to to accomplish our task so it takes 2 hours per acre of corn plus 1 hour per acre of ODEs and we know that that has to be less than or equal to 320 okay because that's how much time we have available so these are going to be our systems of inequalities here that we're going to have to graph here so let me erase this part okay so this is what we're trying to maximize again our profit equals 40 X plus 30 Y and now let me move these over to the side so X has to be greater than or equal to 0 Y has to be greater than or equal to 0 X plus y has to be less than or equal to 240 and then we have our other inequality 2x plus y has to be less than or equal to 320 so now all we're going to do is graph these regions find the points of intersection and basically plug them back into our profit equation ok so actually let me I'm going to redo this graph slightly we really don't even need anything except for the top right quadrant so there's X and there's Y right because if X has to be greater than or equal to 0 and Y has to be greater than or equal to 0 that only happens in the top right quadrant if we graph the inequality I'm going to write it well you could almost think the x and y-intercepts of this first inequality if you plug in x equals 0 we'll get y equals 240 if we let y equals 0 we'll get x equals 240 since it's less than or equal to we'll make it a solid line likewise we could graph so this will be the first region likewise we could graph the second region by finding X and y intercepts so if we let X equal 0 if we turn this into an equation we get 2 times 0 plus y equals 320 or equivalently just Y is 320 so we'll make that a little higher and then if we let y equals 0 we'll get 2x equals 320 divide both sides by 2 we'll get x equals 160 okay so not quite to scale so we'll graph so this is okay so this is the first line over here when we graph the second inequality it would look something like this and the region that satisfies both of these inequalities is going to be the area underneath so one part would say okay that would be the area or it's this the inequality the region we would shade underneath the first line if we look at the second line the region underneath would be that part and we're looking basically for the overlap so we're just going to keep the stuff in between so I'm even going to get rid of the other the other lines okay so now we have our little our region here all we have to do is basically figure out the corner points which really we already have done for the most part we know that this is going to be the point 160 comma 0 we know that the point up here is simply 0 comma 240 we've got the origin which is just 0 0 so the last thing we would have to do is figure out this other point and if we set the lines equal to each other so I'm going to solve for x and y here I'm basically going to turn my inequalities into equations so X plus y equals 240 2x plus y equals 320 and what I'm going to do is I'm going to actually rewrite the first one underneath so X plus y equals 240 and I'm going to use elimination by addition here to solve my system of inequalities or excuse me my system of equations now so multiply both sides of the first excuse me the second one by negative 1 we'll get 2x plus y equals 320 and the denominator you'll get negative x or not the denominator but the second equation negative X minus y equals negative 240 if we add these up the x's will get 1x the Y's will cancel 320 minus 240 is x equals 80 and once we know that x equals 80 we can plug that into either one of our equations to figure out the Y value so if we plug it into the first one or excuse me the second one we'll get 80 plus y equals 240 simply subtract 80 we'll get y equals 160 so x is 80 and Y is 160 okay now I have my 4 corner points okay so we've got the points 0 0 0 comma 2 40 80 comma 160 and last but not least we have 160 comma 0 okay so I'm just picking the corner points here and again all we have to do now is just simply plug those into our function C which is the biggest which is the smallest so let's see if we can't do this real quick so certainly if you plug in 0 your profits not going to be anything you'll get your profit of 0 so certainly that wouldn't make sense if we plug in 0 for x and 240 so we'll make it 244 why so okay so 40 times zero is certainly just equal to zero and then we'll have to add on 30 times 240 well 30 times 240 is going to give us 7200 or profit of seventy-two hundred dollars let's plug in our 80 and 160 so our profit will equal 40 times 80 plus 30 times 160 40 times 80 is thirty-two hundred thirty times 160 is going to be forty eight hundred if we add these together we get seven thousand and last but not least we can plug in our 160 value so it says our prophet will be 160 times 40 plus 30 times zero which is going to give us a profit of sixty-four hundred dollars so it looks like in this case it was actually certainly the smart thing to do kind of what we said was to plant all the oats because well you can basically for every acre of oats even though there's the time constraint you'll actually make twice as much money so so in case so in this problem our maximum the farmer if you're the farmer in this case should plant all oats and you'll make as much money as possible
Views:9715|Rating:0.00|View Time:1:29:43Minutes|Likes:|Dislikes: Thomas E. Woods, Jr., history professor at Suffolk Community College–and a prolific specialist in American Colonial history, the Progressive Era, and modern political history–presents this seminar covering the material in his books, and details and defends the Jeffersonian-Rothbardian perspective. Here is the cutting edge of libertarian history that completely rethinks the meaning and impact of the welfare-warfare state. Recorded at the Ludwig von Mises Institute in Auburn, Alabama; June 20-24, 2005.
Playlist for the complete ‘The Truth About American History’ seminar:
* * * * *
Dr. Thomas E. Woods, Jr. is senior fellow in American history at the Ludwig von Mises Institute and is the author of nine books, including the New York Times bestsellers Meltdown: A Free-Market Look at Why the Stock Market Collapsed, the Economy Tanked, and Government Bailouts Will Make Things Worse, and The Politically Incorrect Guide to American History. His latest, Nullification: How to Resist Federal Tyranny in the 21st Century was released in July 2010.
Thomas Woods’ official website:
* * * * *
DISCLAIMER: This media presentation is owned by the Ludwig von Mises Institute and is protected under Creative Commons license (CC BY-NC-ND 3.0).
This YouTube channel is in no way endorsed by or affiliated with the Mises Institute, any of its scholars or staff members.
all right good morning this morning I want to start talking about issues involving labor unions and labor history and in a way that the title is sort of misleading because you know there's much that can be said about labor markets that is not peculiarly Austrian but I didn't know how else to make it at least remotely provocative sounding so I put the word Austrian in the title again I want to start off by recommending a few books that are useful or at least a few authors you should look out for and the first one because I think it's been a relatively neglected book from about 1987 is a book by Howard Dickman named Indust called industrial democracy in America and you should make sure that if you look into this that you get the book by Howard Dickman because there's another book called industrial democracy in America by other authors which is not really as good his book it's subtitled ideological origins of national labor relations policy then of course you can hardly go wrong with wh Hut who's of course written a great deal on on labor economics and incidentally on matters of Labor history and then two of the great sort of free market labor economists out there would be of course Morgan Reynolds and Charles Baird now I've discussed this matter with one of those two gentlemen I've noted that it seems that this is an area in which there's tremendous work still to be done when there I know that I know what it's like being a young scholar and you're wondering where's my niche and what work still needs to be done and what can I do what's my role well here here's an area you might consider and that is the area of labor history because labor history is currently written is practically unreadable because it's written by people who frankly understand apparently almost nothing about the economics of how labor markets work it's it's based almost entirely on sentiment I mean it's it's it's like it's like Lisa Simpson is writing all these books you know she's she writes she is very Union sympathetic and but what we need are people who have a sound understanding of this and then can apply it to historical episodes in fact studying labor history oftentimes the best thing to do rather than trying to read labor historians who time after time sometimes distort what actually happened is to go back to the most primary source you can find for example in the late nineteenth century even the New York Times was actually relatively reliable in at least telling you the nuts and bolts of what happened in various strikes that would be a much better place to go actually than to go to many of the books that have been written so we net we definitely need sound work in labor history my father was a teamster for about 15 years okay and there is a Simpsons reference here of course that the Teamsters are doing some work at the Simpsons home and Homer Simpson walks outside and sees a few of the Teamsters just standing around he wants to see if he can out lazy the the Teamsters so they were all seeing who can stretch the loudest and you know be as obnoxious as possible now but but the fact is my father was a teamster so you know I I don't I don't want to just make cheap shots at these folks I want to be making sort of you know more you know deeper more significant points but the fact is that any Marxist worth his salt would think that I'm just the victim of false consciousness and if I come from a working-class family then for heaven's sake I should favor working-class interests well I do the back as I do favor working-class interest which is precisely why I hold the position as I do well practically everyone every every student over the course of his education hears the same kind of predictable story about the history of American labor labor unions and that is that American laborers were terribly exploited and their wages were reduced to practically subsistence level and then it was only due to favorable legislation or to the work of labor unions that the condition of Labor began to improve but had it not been for these it is simp taken for granted that you know the the vast bulk of us would still be working 80-hour weeks and our children would be working in mines a lot of my friends are working 80-hour weeks because they're lawyers or investment bankers yeah they make more money than I do but you know I like my 15 hour week and my leisure time very much much too much to give up for any other profession now Boombah Burke actually said on the issue of labor that he noted that a lot of times people form their judgments on this matter really of out of emotional factors really more than anything else and he says that this issue is quote on a field where the heart as well as the head is want to speak what people wish to believe they believe very readily well the standard tale of labor history is in fact almost entirely false and those parts of it that are true for example the low standard of living that people undoubtedly did enjoy in the 19th century are true for reasons other than those alleged by pro-union historians who see in them only confirmation of their prejudices against the market economy well as late as the 1920s labor law in America was based more or less on the following considerations first essential principles included freedom of contract and Association a labourer was perfectly free to reject any offer of compensation that an employer might make to him and conversely an employer was likewise entitled to reject any offer made by a laborer an employee was free to withhold his labor services if unsatisfied with his employers terms likewise a group of laborers jointly exercising this individual right were permitted to do so but no one was allowed to prevent individuals who wish to work from exercising their right to do that strikers like anyone else were forbidden to interfere with consumers right to shop where they liked strikes could not obstruct suppliers from making deliveries since to do so would again violate the rights of others and finally since the employers plant was private property the employer had the absolute right to decide who would be permitted to enter and complete strangers who wish to enter for the purpose of agitating his employees could be lawfully excluded altogether now incidentally the way I'm going to do this is start off with some historical background look at American labor law and then later try to address some of the myths of labor union ISM and try to explain what was the actual cause for the rising standard of living in in American history because again it's sort of carelessly assumed that because we had labor unions and then we had a rising standard of living that the unions caused the rising standard of living but of course that's a logical fallacy now this this outlook this posture whereby both sides in the labor relation were permitted to make offers voluntarily reject whatever offers they wished is is evident already in the early 19th century and it is not true as is often alleged by Pro Union historians that unions per se were being enjoined by the courts to cease and desist their activity it was not union activity per se that that the law sought to penalize it was if a group of workers wish to organize themselves and to engage in in peaceful activities a non-obstructive strike or various other to various social or other types of activities negotiating type activities the law did not stand in the way it was simply when you began to bash people's heads in because they wanted to work when you didn't or when you tried to obstruct deliveries to your employer or engaged in other kinds of property destruction or whatever that was what the law does something chose to forbid in 1806 for example there was a case in Philadelphia involving a group of journeyman who formed a union and then tried to get all local boot makers to hire only members of their Union and to fire and the existing employees anyone who was not a member of that Union well a judge found the Unionists guilty of risk of conspiracy and restraint of trade and levy defying upon them but he was levying the fine not because they organized themselves into a union but because they attempted to interfere with the peaceful labor relations of other people who just happened not to be union members other cases like this in the early 19th century in other states only solidified this principle so from the very beginning we see that the courts are acknowledging that people have a right to form unions to join them to partake in their activities but they do not have any rights to interfere with the lives of non-union workers and their employers now a very prominent case that is quoted a lot in in free-market type books typically isn't isn't ninth is an 1835 New York case called people versus Fisher this case involved unionists who are trying to prevent an independent boot maker from undercutting them in terms of wages apparently boots a very very competitive industry at the time the man who and this is what the court said court finding against what what the unionists were trying to do the court said the man who owns an article of trade or commerce is not obliged to sell it for any particular price nor is the mechanic obliged to labor for any particular price he may say that he will not make coarse boots for less than one dollar per pair but he has no right to say that no other mechanic shall make them for less if one individual does not possess such a right over the conduct of another no number of individuals can possess such a right all combinations therefore to effect such an object are injurious not only to the individual particularly oppressed but to the public at large it may be that Pennock who is the independent from greater industry or greater skill made more profit by making boots at seventy-five cents per pair than two then the defendants at a dollar he had a right to work for what he pleased his employer had a right to employ him for such a price as they could agree upon the interference of the defendants was unlawful its tendency is not only to individual oppression but to public inconvenience and embarrassment well even into the 1920s as I say this this understanding continued to prevail in the law and a case that professor Baird cites in a number of his works is that of the 1921 case of American steel foundries versus the tri-city central trades council now in this case this is this is a case that involves some actions that had occurred years earlier because sometimes obviously these cases take a long time to be heard but what basically took place is that in late 1913 American steel foundries closed its doors business conditions were unfavorable and they had to lay off about 1600 workers some of these workers were members of unions that were affiliated with the tri-city central trades council but the company had all haven't permitted people of whatever union or no union to be employed well a number of months later the company in fact reopened but on a limited basis and they rehired about 350 workers some of them union members but they rehired them on different pay scales there were there were pay cuts ranging from two cents to ten cents an hour compared to what the workers had been earning before the company had shut down in late 1913 well this tri-city trades council the vast majority of whom had never been employed by American steel foundries decided to declare a strike in protest of this wage cut although the lower pay scale paid to these 350 workers well out the 350 workers who had been rehired when the when steel foundries reopened only two of them joined this strike the other 348 wanted to keep working on the terms they'd been offered but the tri-city trades council which from the point of view of the firm is made up almost entirely of strangers decided that they were going to go ahead with this strike and they set up pickets substantial pickets made up basically of strangers at every single entrance to the firm and so for a period of about four weeks this in effects stranger picket engaged in repeated beatings and assaults against those workers who went in and tried to work we have reports of at least several employees who slept at the plant so they could continue working because they were afraid of facing the pickets well finally a federal court issued a restraining order and managed to put a stop to the violence well the union argued that the court had no authority to do that because they argue that the Clayton Act of 1914 had put restraints on the ability of the courts to intervene in that way but the Supreme Court in this 1921 case disagreed what the Supreme Court declared for one thing was first of all talked about what the Clayton Act said the Clayton Act had been called the magna carta of labor union ISM by Saved Samuel Gompers because the the the Clayton Act of 1914 had apparently at least exempted labor unions from prosecution under the Sherman Antitrust Act for conspiracies and restraint of trade but what the court found was that the Clayton Act protected unions only when they were carrying and they were lawfully carrying out their legitimate objectives and that the law protected only peaceable persuasion by employees so that the law does not protect of course people engaged in violence well interestingly in this tri-city trades council case of 1921 the Supreme Court went so far as to declare that even if you have a picket line that's peaceful let alone what was happening in this case where people are actually being beaten even when you have a picket line that's peaceful the Supreme Court declared that that is inherently intimidating and in effect tends to act as a barrier to entry to the struck firm and and in that way interferes with any firm's ability to carry on it's operations and so the court declared that a picket would would have to restrain itself to one one you could have one picket per entrance but you couldn't have you know flying squadrons of strangers showing up at every single entrance only only employees of the struck firm could actually serve as as picketers and although the picketers could talk to of course would speak to non striking employees they could only engage in non-threatening discussion if they in effect threatened people well then the court can enjoin that type of behavior because in effect this isn't this is inherently threatening behavior so that's a that's no needless to say labor historians hate this decision but this is that was it doesn't matter what the what their opinion is that was the state of the laws of 1921 things begin to change though in the 1930s first under Hoover and then under FDR so prior to the change in the law the the formation of unions per se was not considered legally actionable but simply the use of coercion to coerce others to deny employment to people who did not join the union well first we get in 1932 signed by Herbert Hoover the norris-laguardia act which had a number of important provisions but it will not be nearly as sweeping as what will come in the more distant future first this legislation made so-called yellow-dog contracts unenforceable in the courts these were contracts in which an employee could be required as a condition of employment to promise to restrain from union activity now again this is a this is a position that a lot of people to this day oppose that an employer should not be permitted as a contract as part of their contractual arrangement of their employees to be able to demand that employees not participate in union activity but of course in a system of free contract you know whatever terms people voluntarily agree on would would be considered acceptable and if and if of course if they can't attract enough employees by offering those terms they would under the pressure the free market be obligated to abandon them anyway Morgan Reynolds has actually an interesting article in the Journal of libertarian studies I think it's the only article he wrote for it so it's easy to track down if you go to mises.org and you look for Morgan Reynolds he has an article that among other things points out that yellow dog contracts in many cases were in fact initiated by employees themselves who had had experience with unions who found that oftentimes they were they were not they turned out not to be beneficial to the workers and they would rather not be bothered by a group of hostile strangers trying to interfere with their negotiations with their employers so oftentimes the this the the initiative for yellow dog contracts contrary to popular belief came from the employees themselves well according to this plank of a norris-laguardia act if you forbid yellow dog contracts you're saying that employers cannot boycott union labor they can't say that I'm going to hire you you have to promise not to engage in labor union agitation but on the other hand unions were not forbidden to boycott non-union labor they could of course carry on their their activities the Act exempted labor unions from prosecution under the Sherman Antitrust Act once and for all and in effect it's severely prohibited art private severely impaired the ability of the courts to issue injunctions in labor disputes in fact even when the even when the labor disputes had turned violent the the burden of proof to demonstrate that violence was in fact taking place was so high and unreasonable that in practical terms it made it impossible for courts to issue injunctions to stop this violent activity so in other words replacement workers could be being beaten and there was nothing that in effect a judge could do about it now the reason that that labor unions so disliked injunctions was that an injunction the purpose of an injunction was as fact laid by Morgan Reynolds I think explains that the best he says an injunction temporarily restrained union actions pending a trial and this explains the intense union campaign against its use in labor disputes because once violence ridden strikes were enjoined for a few days they were they were very difficult to revive reorganize and rekindle now it is one of the many myths by the way of American labor history that the courts just issued injunctions frequently and indiscriminately that it has issued injunctions even when labor unions were engaged in perfectly peaceful activities but this is why you should look at the work of a labor economist Sylvester Petro whose work the the labor policy of a free society was dedicated in part to ludwig von mises and he who wrote a great many scholarly articles on this subject and he actually did a study of work stoppages between the years 1880 and 1932 he found that injunctions were extremely rare he said federal injunctions were issued at not even 1% of all work stoppages while state injunctions were issued unless than 2% of all work stoppages and he says that even these very few injunctions were issued not to thwart labor union activity per se but instead to put a stop to violence against persons and property well now even this protection of the employers rights yes employers have rights to would henceforth be absent incidentally there was a book that was published in 1930 called the labor injunction that was written co-authored by Felix Frankfurter the justice and he in this book the thesis was that labor unions had been treated unfairly in the common law with excessive use of injunctions against peaceful activity and this revisionist work that's been carried on not only by Petro and others vigman has shown that in fact the the the frankfurter book is completely entirely dishonest I mean it's either grossly incompetent or just frankly dishonest now the New Deal of Franklin Roosevelt added to this the National Labor Relations Act of 1935 which tends to instead be called the Wagner Act because of Robert Wagner who introduced it now it used to be the case that a worker if you didn't want to join a union or pay the pay union dues then you just didn't you you just refrain from joining and you didn't pay the dues but the Wagner Act overturns this standard Liberty from the point from from when you begin with the Wagner Act and going forward if a majority of workers in a particular bargaining unit decide that they are going to unionize then that union represents all workers whether it was include the workers who decided to join the workers who did not want to join the workers who didn't vote one way or the other it represents them all and you know and this is this was argue it was argue that this was perfectly perfectly fair so from then on if a majority of workers choose to unionize all the workers must join and and pay union dues now the usual defense of this was to say that look the Wagner Act calls for a single certified bargaining agent to represent all workers in a given bargaining unit and so if you're going to have a single labor union to represent all workers which is called for by this act then it stands to reason that every worker who works in this unit should have to join that Union and pay dues because why should they get to freeride you know why should they enjoy at no cost of themselves all the benefits that come from the labor union negotiating on their behalf that was the that was the argument so therefore it makes sense to coerce and it's just to coerce all workers into paying union dues because all of them are enjoying the benefits of being represented by this single union well of course this overlooks the real problem which is the idea of having an exclusive union in the first place if the unions would just bargain on behalf of their own voluntary dues-paying members then there wouldn't be a problem of non-members getting union benefits for free if individuals were allowed to represent themselves or and to enter into contracts with employers on their own terms those who wish to remain non-union would not be free riding on the benefits bestowed by labor unions since the union would simply not bargain on their behalf but federal labor law no longer guarantees workers this freedom now it is true that in 1947 you get the taft-hartley Act which was passed at a time when much of the American population had grown extremely impatient with labor unions and and strike striking activity but the taft-hartley Act is quite mild effect in its provisions and it really doesn't overturn any of the major planks of the National Labor Relations Act which which again in summary had in effect taken the position of exclusive bargaining that once one union is decided Union represents every single worker and every single worker must pay union dues it doesn't overturn the idea that there has to be just one Union and that Union has exclusive representation but what it did do was to give the states in effect the right to pass right-to-work laws which at least at least said that that a union couldn't force union membership and and union dues on workers as the price for keeping their jobs but it doesn't say that you can have company unions or any such thing as that that's that's still forbidden but it at least means that you could in some states I don't know how many maybe 20 twenty-something states now have right-to-work laws which at least mean that you know you can you can exempt yourself and not but you not be in effect driven out or denied employment now it's interesting that just a year before the National Labor Relations Act was passed franklin roosevelt had opposed this idea of exclusive representation in 1934 the United Auto Workers had threatened to shut down the entire auto industry unless they were recognized as the exclusive bargaining agent for all Auto Workers to avoid that strike franklin roosevelt intervened and settled it on the basis of proportional representation he said that the United Auto Workers represents only its own members and people who want to belong to other unions or company unions or whatever would represent those people and people who wanted to have no union at all would represent themselves and Franklin Roosevelt said that in his opinion this was the only kind of union representation that was consistent with the American tradition of Liberty so he took the position at least in 1934 that we shouldn't have this position in which you have an exclusive bargaining agent and you can coerce people to be represented by it even if they don't want represent representation services from that Union now why why why the president changed his mind is a an interesting matter in itself but let's just continue on this visit this front now this this there's a term we need to introduce called Union security Union securities that is the is the sort of you know not so terrible sounding term that is used to refer to the practice whereby workers who don't even want the representation services of a union have them forced upon them and typically have to pay for them this was these these were the terms of the original 1935 legislation this is called unions union security because it is security for the Union and for the people who work for the Union because of course it guarantees them an income they're going to be collecting dues from everybody and that practice whereby people are coerced into paying these dues as a requirement for keeping their jobs which as I say was the original intent of the 1935 Act is obviously of great benefit to unions so so in effect what right-to-work laws do is they abolish Union security so that people don't have to join a union as a condition of employment but nevertheless it keeps this principle of exclusive representation intact for everybody else ok let's see yeah one of the things we want to do oh yeah know another thing that's been said in defense of this in defense of the idea that when a majority of workers vote to to choose a particular union to represent them that therefore it's legitimate for all workers to be in effect coerced into being represented by this one Union sometimes it's argued that this is just democracy and you know we recognize democracy in political affairs and there's no reason that democracy should not be extended into labor relations but the the traditional common law principle was that when I sell my labor services I am engaged in an action that is in the private the sphere of private human action not in the sphere of government action and that democracy in government you know involves you know if you're gonna have a government the idea of democracy is that we restrain it by having it at least be somewhat responsive to the popular will but we don't we don't arrange all of human affairs according to this principle I mean we don't decide our dinner based on what the state of Alabama wants us to eat you know we don't decide what our favorite color is based on what the consensus on this phone on our city block is we don't apply the democratic principle to private affairs because we would consider that to be a completely unjust interference on the part of a majority of people on the rights of the minority and likewise that had been that the view with regard to labor union ISM that the individual individuals retain the right either to represent themselves or to choose to be represented by a different organization now Labor Relations law has very often consisted of bizarre turns of phrase and Strauss strange almost Orwellian principles and the National Labor Relations Act is no exception because notice what notice what it says it says that it is an unfair labor practice for an employer by discriminant I description in regard to hire or tenure of employment to encourage or discourage membership in any labor organization so on the one hand it would be unfair for an employer to discriminate in hiring or in granting tenure to encourage or discourage membership in any labor organization hmm well that would seem to make Union security illegal a it would be unlawful for for an employer in effect to be hiring or not hiring on the basis of union activity because of course that's what the unions would in effect say you can't hire anybody unless they're going to be in our Union I mean once you hire them we're gonna force them into our Union says here it would be an unfair labor practice for an employer to encourage or discourage membership in any labor organization but it goes on to say provided that nothing in this act shall preclude an employer from making an agreement with a labor organization to require as a condition of employment membership therein well the translate that into normal English was that saying is that employers are forbidden from encouraging membership in a union but they can compel membership in a union like what you know this is this is how when you have laws on the you know that are based on special interest you get bizarre results such as this okay now once a union has been certified by a majority of workers I mean basically typically the way this goes is that once there's interest among the workers and in setting up a union establishing an Union certifying a union as their exclusive bargaining agent well what they first what they try to do is to get workers to sign cards that authorize the Union to act as their agent and once they get maybe a third of the workers assigning these authorization cards then the National Labor Relations Board will step in and conduct a certification election so in other words if a third of the of the of the workers have signed these cards that's sort of prima facie indication that there is an interest in organizing a union and so the National Labor Relations Board will oversee or will will though they'll be petitioned for a certification election then that election will be carried out by secret ballot which is at least an improvement over the old just raise your hand and if if the Union gets more than half 50% plus one of the workers then it gets representation privileges well we've already seen that that that privilege applies of permits the the Union to represent or claim to be the represent the Institute of institution of representation for all the workers regardless of their own feelings about unionization but what's significant is that there is no there is no routine decertification election like it's not like every two years they they go back and say well how do we feel now even if it's 20 years later and most of the workers have either died or retired or moved on to other jobs and the bulk of the remainder you know are either indifferent or not interested in the Union it is presumed to continue I mean there's no automatic desertification and you have to really jump through hoops to get a decertification election taking place now this principle of exclusive representation which once a union has been certified it is declared to represent everybody when it comes to democratic countries the United States is basically alone in organizing its Labor Relations in this way Canada also does it this way but basically they got the idea from the United States other democratic countries / meant a variety of representation within a particular firm including including things like company unions but also just a variety of different unions or no union at all this is considered to be a decision up to the individual worker and it's that you know in in other countries the assumption is the old traditional American assumption that people should not have to submit themselves to the will of the majority in cases involving the disposition of their own labor services now at front at least from 1935 to 1947 and then there were still some problems after 1947 there were limits on the free speech of the employer that were that were in place the National Labor Relations Act in fact said well actually let's just just point out that the the foot before going into that that an employer could not actually say to the workers hey you shouldn't vote in favor the Union like when he knew that a certification election was coming he shouldn't go around saying you shouldn't do that you should or shouldn't do this he had to be absolutely quiet so he had to permit total strangers to come onto his property and propagandize his workers and he in effect had to stay entirely out could not really speak in a way that would tend to influence the election well in 1947 with the taft-hartley amendments which is amending the National Labor Relations Act we get this statement that seems to give free speech rights to the employer it says the expressing of any views argument or opinion or the dissemination thereof shall not constitute or be evidence of an unfair labor practice on the under any of the provisions of this act if such expression contains no threat of reprisal or force or promise of benefit now there as I say there was that there was no free speech provision in the Wagner Act employers until 1947 were just required to sit there and they could they couldn't do it do anything but this provision that was inserted in 1947 it turns out has got a loophole you could drive a truck through because notice it says that an employer cannot be engaging in unfair labor practice just because he expresses a view just because he says something but if expressing that view contains a threat of reprisal or force or promise of benefit well then he can be hauled into court well the thing is almost anything that an employer might say with regard to labor union ISM could in some way be twisted as being a threat of reprisal or a promise of benefit I mean if the Union says hey you know I think this was really not in your interests and some day you may regret this well there you go that's a that's a threat isn't that some kind of a threat you may regret this well you better be more precise how will I regret this well you know things may things may turn bad for you that the the company may may go out of business because of the the wage demands or something can't say that so it turns out that yes you can speak against unionism but only in some weird way that no one really knows what you know exactly how to do it so for instance the Supreme Court in 1969 in a case that involved the National Labor Relations Board and the Gissel packing company made a unbelievable judgment it involved a company that in 1952 had had suffered a strike that had paralyzed it two of its plants were were shut down for three months and it did tremendous damage and eventually when they reopened they reopened on a non-union basis well years later the mid-sixties the Teamsters got the requisite number of signatures on those cards and they were going to hold a certification election well during that the campaign to try to get workers to go ahead and vote to certify the Teamsters the employer went around telling people you know did you not forget what happened in 1952 the the last time we had unions here we had this strike it was not in the best interest of anybody it paralyzed everybody people lost their jobs and that could happen to you again and if you became unemployed some of you would have especially because of your advanced age would be hard for you to find other jobs think about what you're doing well the Supreme Court declared that those were those statements were threats of reprisal and so even though the certification election went against the Union the court as as Baird points out set aside the election results and imposed a bargaining order on the employer so the employer was was ordered to recognize and bargain with the Union as exclusive bargaining agent without a second election so in effect although the employer as Baird points out may express general views about unions what he says cannot sound like a threat well in effect the employers now can't say anything that's sort of remotely anti-union because you could always twist that around to sound as if it were a threat of reprisal now the National Labor Relations Act also once also requires that once a single certified union is established employers are required to bargain in good faith with that organization now whether an employer has bargained in good faith is of course not an easy thing to determine what what exactly would constitute in good faith well don't worry the National Labor Relations Board will determine what constitutes in good faith so oftentimes what it means is that if if if a if a company just simply says look this is the package we're prepared to offer this is the only reasonable package the best package we have and they say that's final that's our final offer we can't possibly improve on it they would almost certainly be accused of not bargaining in good faith so what they have to start doing is they have to come out like it's a big game they have to come out with a terrible offer so that the union will say well that's terrible how about this one and then so in other words they have to in effect provoke kind of an argument back and forth they can't just come out and say we think this is the best thing take it or leave it you have to come out with a ridiculous plan the union has to start with a ridiculous plan and then they have to argue with each other employers under the Act are required to permit union organizers who were not employed in their firm to use their own property in order to persuade their employees to unionize with their with their union union workers can in fact block the employers access to replacements they can block deliveries coming in they can block customers not only is mass picketing now permitted which remember under the tri-city trades council case only you could have one picket per entrance but now you can have mass picketing you can have total strangers picketing and employers are now forced to rehire in many cases strikers even if they've been engaged in acts of violence they have to rehire them now a national there's a National Labor Relations Board ruling that actually said that obviously if a striker let's say killed somebody you wouldn't really be obligated to rehire him but the National Labor Relations Board said that the the employer can refuse to rehire a striker if his misconduct during the strike is so violent or of such serious character as to render him unfit for further service but on the other hand you have to rehire him if simply his behavior constitutes a trivial ruff incident that occurred quote in a moment of animal exuberance now the the the explanation was that certain kinds of impulsive behavior being quote normal outgrowths of the intense feelings developed on picket lines must have been in Congress's minds when they developed this law and and were defending the right the right to strike and so Charles Baird points out that excused instances of animal exuberance have included beatings stabbings bombings threatening of non-striker's families destruction of property blocking entrances to struck firms with broken glass and nails and hurling brickbats so an employer in other words in all of those cases has been required to hire back people who were guilty of such offenses it also meant under the the Wagner Act that the principle of vicarious responsibility did not hold so if the union organizer actually says to his his Union you know I have everybody I want you to go beat people over the head you know he bears and the Union as an organization bears no penalty for that would bear no penalty for that at all now there are two kinds of strikes that since the late 1930s have been recognized in American labor law and they've sometimes been called on the one hand economic strikes and on the other hand unfair labor practice or ULP strikes now an economic strike is what we sort of all tend to think of we think of a strike a strike that is undertaken in pursuit of higher wages better working conditions shorter hours perhaps and the like an unfair labor practice strike on the other hand is undertaken in response to a perception that the employer in the course of bargaining or perhaps in his very refusal to bargain has violated National Labor Relations Act rules so if he so in other words in the course of the bargaining or it has in some type of behavior or in trying to you know what whatever I mean if in any way he violates any of the standards that we've seen then that would the strike against him in that case would be an unfair labor practice strike so for example a lot of times when there's collective bargaining going on the union's bargaining the company's bargaining they're going back and forth but if they hit a brick wall in the bargaining well sometimes a union will strike and say the employer is not bargaining in good faith so it's an unfair labor practice strike now what's the difference who cares whether it's an economic strike or an unfair labor practice strike well the difference is that ever since about 1938 when the Supreme Court ruled on this employers are not allowed to hire permanent replacements in unfair labor practice strikes they can they can hire only temporary replacements when that strike is over they have to hire back any employee who wants to be rehired in that type of strike they have to hire them back immediately or otherwise they would have to start paying back pay to them so it's very significant what type of strike it is but with an economic strike employers do in fact have the right according to the Supreme Court to hire permanent replacement workers so strikers therefore have a right in the law to be immediately reinstated after every ULP strike is over and they have the right to be reinstated at the end of an economic strike when in cases where replacements have not been hired if there are still openings that have not been filled by replacements then the strikers in effect have a claim on those positions now this may seem like an artificial distinction and and of course in some ways it is the way that the court defended this distinction was to say that an employer who finds himself the subject of an economic strike whose workers are striking for higher wages or whatever has not necessarily done anything that violates the law he may simply just not have offered a package that was satisfactory to the workers and that's not if so facto legally actionable whereas in an unfair labor practice strike the presumption is that the employer has in fact broken the law because he's violated some principle of American labor law and so he should not in you know there's a sort of standard legal principle in it that if you break the law or you're doing something that's unlawful you shouldn't enjoy material benefits as a result of that so there should be a particular penalty in effect imposed obviously on a firm that is breaking the law whether we think that law should exist or not then one that the presumption is he's not breaking the law so in fact this is what the Supreme Court says although section 13 of the National Labor Relations Act provides that nothing in this act shall be construed so as to interfere with or impede or diminish in any way the right to strike it does not follow that an employer guilty of no act denounced by the statute has lost the right to protect and continue his business by supplying places left vacant by strikers and he is not bound discharge those hired filled those hot those hired to fill the places of strikers upon the election of the latter to resume their employment in order to create places for them okay so some some labor union sympathizers have argued that the Supreme Court here is not making rendering this decision in line with the original intent of the National Labor Relations Act that the Act did not in fact envision this but Robert Wagner himself said in 1939 that he was in favor of every step that the Supreme Court has taken toward clarifying the meaning and defining the scope of the Act now it may seem by the way because the although the law prohibits the the employer to just fire a striker typically with the exceptions there there are exceptions to that but that you can't just fire a striker you can hire permanent replacements as we've seen you can hire permanent replacements in the case of a of an economic strike and you can hire temporary replacements in the case of an unfair labor practice strike but what the heck is the difference between firing somebody for striking and on the other hand hiring a permanent replacement for that person permanent replacement for that person seems like the same thing and again unionists have long claimed that this is just a semantic difference and there is no there is no difference but there actually is there actually is a difference for one thing a permanent replacement has in other words of what I mean to say is a striker who's striking in an economic strike who has had a permanent replacement worker hired to replace him has indefinite preferential rehiring rights that is to say that in the future if an opening comes up at that firm the first people the employer is legally obligated to go to to ask do you want this position would be strikers who have had permanent replacements to replace them so that so in fact any time there's any job vacancy at all the employer cannot hire any new person until any eligible striker who is interested has been reinstated and there's no time limit on this could be years and years in the future he must go and give preferential hiring consideration to people who had been strikers and it's not even just that if the same job that the striker went on strike for reopens that I have to go to that person if any job in my firm comes open I have to go to that person even if it's a job that even if I'm a tire manufacturer and I start making bagels I have to go back to the original strikers and ask would you like a job making bagels so it is actually a fairly substantial difference between being fired in which case of course you would have no claim whatsoever on the employer whereas if you're if you have been permanently replaced nevertheless you are the first person to get any any opening not necessarily in fact it can it can even be it can be it can be for hire it can be for a more prestigious position in fact so it wouldn't even necessarily have to be at the same wage if the if the worker has found substantially equivalent employment elsewhere then this then this provision would would lapse now all of these legislative measures obviously make it much easier for labor unions to accomplish their goals and now in order to fulfill the purpose of a labor union which is to increase the state of purpose is to increase the wages of their members what labor unions have to do is to restrict an employer's access to alternative sources of labor so the idea is to artificially reduce the number of people in the labor force so to reduce the supply and therefore that would increase the price that would increase the wage that's the purpose of of the labor of the labor union so the labor unions typically are organized you know partly against their employer but they're primarily organized against other workers they're organized against people who want employment let's say with this firm and who are non-union they're not interested in that they want to restrict the supply so as to increase wages for their own work that's the point so non-union workers who wish to seek employment on the terms offered by an employer whose firm is unionized must be prevented from doing so so Edward Chamberlain of Harvard University once described the the legal status that labor unions have thereby been granted he said this if a is bargaining with B over the sale of his house and if a were given the privileges of a modern labor union he would be able one to conspire with all other owners of houses not to make any alternative offer to be using violence or the threat of violence if necessary to prevent them to to deprive to deprive B himself of access to any alternative offers three to surround the house of B and cut off all deliveries including food except by Parcel Post for to stop all movement from B's house so that if he were for instance a doctor he could not sell his services and make a living and five to institute a boycott of B's business all of these privileges if he were capable of carrying them out would no doubt strengthen A's position but they would not be regarded by anyone as part of quote bargaining unless a were a labor unit it's for this reason that Hayek once said I think it was in constitution of Liberty High have said we have now reached a state where unions have become uniquely privileged institutions to which the general rules of law do not apply now of course because there is such sympathy there's this kind of a mythos that surrounds labor unions that makes it an unthinkable offense that you would cross a picket line or continue working when a strike is going on or actually take a job at a plant at which you had not previously been important employee but take a job during a strike because you wish to work on the terms that are being offered I was wondered why it is that such people are considered to be the lowest of the Lummi don't they have families aren't they workers like why are they dehumanized but for example Jack London once wrote because of course we all know that those people are called scabs right you're a scab if you want to you know if you want to provide for your family in that situation you're just a scab Jack London said after God had finished the rattlesnake the toad the vampire he had some awful substance left with which he made a scab kind of kind of dehumanizing to think well any case what will often happen then was it would be that the police you know we need the public police to keep law and order well they'll just stand there like you know somebody's getting his head bashed in policemen will say hey I think I got to go give that guy a ticket over there he's going 43 miles an hour in a 40 mile zone so in other words they'll just stand there and let this type of behavior go on even in the face of intimidation violence often times this will just not happen there won't be any redress on the part of the by the public authorities so in effect coercion or the threat of coercion is at the heart of the labor union experience because how else are you going to keep other people from voluntarily entering into agreements with employers and thus apparently at least apparently driving down wages well you have to intimidate them into not doing this or use violence against them or build up this sort of again this mythos in people's minds that they wouldn't dream of doing it this is why Henry George once wrote in the 19th century those who tell you if trade unions bent on raising wages by moral suasion alone are like those who would tell you of tigers that live on oranges now there are a couple of examples of of incidents that occurred in the course of American labor history that I found particularly revealing and what they tell us about labor law for example there was a United Mine Workers strike in the early eighties in which and as Morgan Reynolds points Isis a non-union miners and mine owners armed themselves shut down their operations during for the duration of the strike truck convoys used lead trucks with five footlong magnets to sweep up nails and spikes on the road these were some of the tactics that were being used when UMW ambushes and gun battles broke out Kentucky governor John Y Brown adopted a policy of what he called strict neutrality declaring we're not going to camp on one side or the other a non-union line operator protested the concept of neutrality toward breaking the law is not found in any statute or practice in our society but in other words this you know violence could be used and then abide by unionists and the governor will say well you know Who am I to decide was right in this situation or there was an interesting arbitration ruling by the National Labor Relations Board in the mid-1970s that declared that was was speaking of a firm that had kept its plant open during a strike and the the ruling said this although the company had a legal right to keep the plant open its decision to do so gives it some share of responsibility for creating an environment conducive to violence so the company right the company kept its its its plant open and so it's it's really sort of their fault isn't it they should have just shut down now the the result of lit of union activity then is to reduce the number of jobs in an industry and to raise the money wages of union labor while at the same time and here's the thing that is not seen relegating many workers driven out of this line of work now by the decreased quantity of Labor demanded there two other lines of work whose money wages must decrease as a result of the greater supply of workers now forced to compete for them but it's not simply that labor union activity tends to displace people that well I'd like to get a job in this but I'm not in the Union and they don't want to let me in they want to restrict they want to restrict the number of workers so I'm sort of forced out of this industry I gotta go work for something else it's not just simply that well I would have worked here but now I work here and so it's just a wash the gains to certain workers are more than offset by the disabilities inflicted upon other workers I mean I mean quite apart from the the you know the subjective factor you know and mentally of being driven from your chosen field when union activity reduces the number of people who can be profitably employed in skilled trades it correspondingly increases the number of skilled laborers who are now forced to find work in fields that are well below their level of competence the outcome of this placement of skilled labor is no different from a situation in which laborers never possess these skills in the first place if Union privilege prevents some workers from putting their skills to proper use the effect is the same as if they had never gone to the trouble to acquire them at all thus society produces below its potential and wealth that would otherwise have been created never sees the light of day now of course the much of the reason that labor unions have the sympathy they do is that people have this sense that of course without unions how could workers be prosperous they don't have a strong negotiating position employers have a much stronger negotiating position and so therefore they have to have a counterbalance to that natural advantage that employers are alleged to enjoy and this is a this is a position that we we see an effect given voice even in Adam Smith's book The Wealth of Nations in speaking of workers and employers Smith said as follows he said it is not however difficult to foresee which of the two parties must upon all ordinary occasions have the advantage in the dispute and forced the other into a compliance with their terms the master is being fewer in number can combine much more easily and the law besides authorizes or at least does not prohibit their combinations while it prohibits those of the workmen well not in the u.s. certainly now we have no acts of parliament against combining to lower the price of work but many against combining to raise it in all such disputes and here's the key the masters can hold out much longer a landlord a farmer a master manufacturer or merchant though they did not employ a single workman could generally live a year or two upon the stocks which they have already acquired many workman could not subsist a week few could subsist a month and scarce any a year without employment in the long run the workman may be as necessary to his master as his master is to him but the necessity is not so immediate well I think that's a fairly standard understanding that most people have but yet I'm going to suggest that this is in fact not an accurate way of thinking about what actually happens in labor markets and that it doesn't correspond to either to sound theory or to in fact the experience that that various countries have had throughout recent history now if it's true first of all that that because the employer can allegedly can afford to wait longer because he's got bigger stocks of things he needs for subsistence whereas the worker is typically living very very close to subsistence and can't just sit around and wait if the employer can just sit there and say look this is my offer I'll just sit here and wait for you to crawl up to me and take it if that really is true then certain things should follow from that that don't in fact seem to follow from that I if labor is more easily exploited let's say than capital I mean you can't say to a you know pile of steel you know I'm only gonna I'm only gonna give you five bucks a pound so you just sit there and I'll just sit here and wait you know it wouldn't work with an inanimate object or the seller of an inanimate object also being an employer presumably has stocks to hold out so he can hold out so the the argument of labor exploitation would be that it's easier to exploit labor and hire it at a wage that its level of productivity you know doesn't just in other words when you hire labor the argument is that I can hire people for like nothing because they're gonna starve otherwise but with I use capital well pretty pretty much when I when I purchased some capital equipment you know I got to purchase it at the going rate I have to purchase it at a rate that is in some way commensurate with the benefits that will accrue to me from it because I'm buying it from after all another capitalist who himself has stocks of goods so I can't exploit capital in the way I can exploit a laborer well if that really were true then we would expect to find profits being much higher in labor intensive industries than in capital intensive industries but this does not seem to have empirical support there are also certain myths of labor union history that are incorrect that are based on this presumption that the labor is added at bargaining and negotiating disadvantage for example before there was anything remotely approaching substantial unionism in the United States there was already a very substantial upward trend in wages throughout the 19th century all through into the 20th right now labor unions account for I think there are nine percent of American labor is actually unionized it's it's basically always been a very in substantial figure relatively small it's gone up it went up in the 30s of course because the law was giving it a lot of advantages but it always been relatively small by the year 1900 it was about 3% 3% of the labor force is unionized and yet American workers into the 1920s we're continuing to have substantially higher wages than their much more heavily Union unionized counterparts in Europe they got the eight-hour day sooner and and and so on there's a standard view that says that large-scale employers the great big companies tend to exploit unorganized workers but in fact the empirical evidence is that the larger firms were in fact paying better than the smaller firms there's this claim that workers are in a disadvantage because they don't have as many as much in terms of savings where they can subsist on that while they're waiting for the employer to give in but in fact there does not seem to be any difference in the wage rates that workers with substantial savings received and workers without savings received now labor union ISM in fact impoverishes society in in a variety of ways that are not immediately apparent they're not intuitive I think first we have the distortions in the labor market that we've seen and in people being forced to go into fields for which they're over qualified because unionism has shut them out of the field for which they had they have trained but in fact the damage that unions have inflicted on the economy in recent American history is actually far greater than anybody might suppose and I cite in my book a study by by veteran Galloway that was published by the jointly by the National legal and Policy Center in the John M Olin Institute for employment practice and policy but that Galloway did this study in 2002 that is available online I think to this day and I think I could in fact if you just did a google search of all those names Vetter Galloway national legal and policy center John Mo Land Institute you'd probably find it but here's what they concluded and this sounds absolutely counterintuitive at the beginning they concluded that over the past half century alone labor unions have cost the American economy a whopping fifty trillion dollars that seems like they must have just they forgot to carry the one or they've got too many zeros or this can't possibly be be so but in fact this is not a misprint that was in fact that that was in fact their conclusion and they write this they say the dead weight economic losses that are brought on by labor union ISM are not one-shot impacts on the economy what our simulations reveal is the powerful effect of the compounding over more than half a century of what appears at first to be small annual effects now the study did find that Union labor does typically earn wages that are fifteen percent higher than those of their non-union counterparts but it also found that wages in general suffered dramatically as a result as a result of an economy that is thirty to forty percent smaller than it would have been in the absence of of labor union ISM now I I have a bunch of I think pretty overwhelming evidence on this about how unionism has in fact contributed to to not the well-being of workers but actually to the overall impoverishment of American labor but I think I'm going to save most of that for for next time and then I'm gonna look at a couple of historical episodes next time but I will just simply conclude with a thought experiment before taking any question the thought experiment is this as we know the usual argument is that in the absence of labor unions employers will pay unconscionably low wages but George Riesman has got a useful thought experiment to the contrary he says let's suppose you have a car in New York City which by the way is an unbelievable hassle where would you park it it costs a fortune it's a nightmare there's traffic all the time anyway and let's just say you decide that you just want to get rid of this car and you pretty much take anything that you can get for it in fact you take $1 for the car in fact let's say you would pay somebody to take this car off your hands now the question is does that mean that in practice you are in fact going to have to pay somebody to take that car away or you're gonna have to accept a bid of $1.00 well the fact is there are a lot of people in New York who want to buy cars and they're gonna outbid each other if a potential buyer offered you $1 you would turn them down even if even if it were true that in a state of complete despair you would have sold it at $1 that is not a relevant factor here what you would do in a desperate situation it's not relevant to what you would do in in a real-life situation you have in which you have many buyers so this person because of his low bid will miss out on the opportunity to own the car all together since his rivals will simply outbid him well in effect the same thing happens in the labor market I mean this is how Charles Baird explains it he says this idea that workers without unions will inherently have a disadvantage in bargaining power relative to employers is the basis for most individuals support of unionism and is picked up again in the Wagner Act in fact the Wagner Act expressly says in the act itself it actually includes a statement saying that because we all know that laborers are at a disadvantage in bargaining therefore we have to do this I mean they just state it as if it's it's obvious but that disadvantage is a hoary myth says beard a workers bargaining power depends on the workers alternatives if a worker either works for employer a or does not work that as if employer a is a monopsonist that is the only the only buyer effect in that case the worker has little bargaining power if the worker has several employment alternatives on the other hand he has strong bargaining power there may have been instances of monopsony or oligopoly in the 19th century but they were short-lived monopsony has not been a significant factor in the American labor market since the introduction and widespread use of the automobile and in fact Baird at another another occasion says that Henry Ford did more for the typical American worker than did Samuel Gompers the the who's the head of the American Federation of Labor for a long time because Henry Ford by making the automobile affordable now makes it possible for him for employees to to drive around and to get a variety of employment offers and then to be able to to choose between them the empirical evidence that simply does not bear out the conventional wisdom regarding unions if it were true that employers were really in a position to impose whatever wage rate they wished then why in the decades before large-scale labor union is and why wasn't why weren't wages heading toward zero in fact real wages were increasing dramatically at that time or why is it that skilled workers would earn more than unskilled workers they should all be earning subsistence according to the exploitation theory even you should be able to just because hey they can't wait that they're gonna starve they've got to take whatever offer you give them Why should there be any differentiation and the wages paid to skilled versus unskilled workers why not just pay them both both the same pittance well this has all been sort of a negative overview sort of Italy first laying out what the basic principles are of American labor law at this point and then looking at why it is that in fact labor unions do not are not responsible for the increased standard of living in fact why they help to depress it but although I do want to continue on that line a little bit next time I want to give a an alternative explanation alternative version of history that explains what in fact does account for the rising standard of living that American workers have enjoyed from the 19th century to the present so I think that'll be it for right now and we'll see what anybody if anybody thinks anything about this or has any comments or any any horror stories to share with us because my father sure had plenty of them because my father worked because he felt like it was the right thing to do and there'd be people he felt there are people who were taking advantage of the unionized situation who would hurt their thumb and they'd be out for 8 weeks and that drove him crazy he sort of felt like the honorable thing is to do your do your day's work and so you know we hope that my father being now nine years deceased that he has received his eternal ward for that yes well III guess let's see I'm trying to think of what what exactly are the things I went to I'm going to talk about things like the the homestead strike and the Haymarket incident and things like that but yeah it is interested that I think that actually is a valid point about the where the actual unionization is taking place is where wages are actually already quite strong to go to the next window and the first thing they did was and then at the end of each week they took all the social security and the federal and then this huge last thing they dumped it into this what is science and this is your money going to Washington and it was Garko every week you know this image is huge and so anyway but the first thing they knew they they couldn't do much for the taxes but they do one thing they could do have to take that union every every week and pay that so they stopped paying the unions oh that's like one of the best things I've ever heard of man to stop it yeah oh that's an outrage that's an outrage all right good yes yeah I know I know what I mean I I haven't I haven't done much study of government unions and people who are unionized who are under government employment because I sort of to me well it enters me is what are the effects of this stuff on the private sector and I sort of feel like if you know if you know government employment is all screwed up well you know all the better you know I feel like Bob they would say yeah means sometimes used violence that's very selective interpretation especially I think actually not not really because I think that that you know it like Bob Higgs for instance who is you know as small government or you know whatever a guy as you can find nevertheless he likes President Grover Cleveland in spite of what a lot of people criticize him for which is that he you know he sometimes did intervene in labor disputes or to or to try to to restore order the midst of strikes and that and that sort of thing and and and Higgs absolutely insisting that case after case he's totally justified in doing so that the violence that's taking place is typically on on the part of the on the part of the Union and that you know intervening or or having injunctions are exactly the we're exactly the right thing to do so in fact there's there's a reasonably good discussion of the Pullman Strike as I recall in crisis and Leviathan but but but I mean but yeah I mean I might my my reading of it is that you know is that is that I mean I guess well I guess well hold on on the gun question and we're gonna revisit the goon question like that they bring in their goons cuz I am going to talk later today about the what I just say that the the Homestead Strike because there you did have some people who are considered to be goons the the Pinkerton Detective Agency was was hired but typically that was done even though the Pinkertons were hated by people that they were typically hired because the public police weren't protecting the plant they had a history of not protecting the plant so if you know that the public authorities aren't going to protect the plant then you really have no choice other than to then to you know arm yourself with whatever private organization you can find not many people have spoken on behalf of the Pinkerton Detective Agency over the past hundred years but that's about the best I can do other LC yes Harry sir and as much as government that certain actions okay I haven't thought of it that way but hmm that's I never I never would have thought of that but that may be a legitimate Rothbard Ian's point where rothbard would say that when you're dealing with government enterprises or for example when you're dealing with the question of how do you discern Europe and how do you how do you assign property rights to you know government-owned firms and properties whatever and I recall reading as well that broth bars view often times which would also be his view of slaves working on a plantation would be that they they're the legitimate owners likewise people who are people in the in Eastern Europe the actual workers themselves would be the legitimate owners because there's no way that the the communist state could be a legitimate owner of anything and of course for Rothbart there's no way that any state could be a legitimate owner of anything because it doesn't acquire it through the normal process of voluntary consent that any normal civilized human being does so therefore if you want to look for who is the actual legitimate morally acceptable owner it may actually be the workers themselves with people who I mean perhaps there's something Lockean here the people who themselves are exerting their labor in this area they have a legitimate much more legitimate claim to be the owners so in this case in the case of government unions then I think it you may be able to have a point in saying that maybe the employees of these institutions are at least in some way perhaps more legitimately the owners and so they might be able in fact to engage in things like preventing people from coming onto the property because perhaps it is their property but at the same time there is the fact that that these institutions are taxpayer-funded and so you know I could just as well say that I'm at least a partial owner of that thing and so couldn't I in fact impose some kind of rule as to how it's going to go into function it's a complicated question and so it makes me more and more happy that I haven't done any work in government unions but but thanks I never thought that yeah dan the current immediate response of government employees in government sectors they which are is a hesitation towards privatization of like a special things like like police officer union in the sense that I think that the way in which these occupations develop in terms of their entrepreneurial incentives is kind of thrown out of whack being that all government operations are in a sense a subsidy and throw this allocation of resources in terms of in a very curtain area in the sense of who who capitalizes on a profit opportunity is the real entrepreneur and in the general production process of say like any consumer good like if you have been unionized labor force a car maker for these it's less thrown out of whack without a subsidy the labor the laborers recognize how the capitalist is making a killing off of our Labor's that we're going to collectively bargain so as to obstruct some of that profit to be entrepreneurial ourselves versus an entirely government subsidized industry like say police security is thrown out of whack right off the beginning from from the capitalist so the people who are or the employees like right yeah yeah that's right I know I mean and as I got to the end of my thinking that issue through I was not so certain at the end of my answer as I was at the beginning I think for at least some of those reasons Thanks okay yes sir and then I'll go here and then come back to you and I was engaged to come in it was Institute statistical process control to be able to guarantee quality as it came out and convinced General Motors that we now had quality product and they were they scheduled a visit to them to the plant there were three plants and writing on it was about a five million dollar contract with a company that did a gross 10 million so this this was a pretty big deal one of the employees was not happy with this whole idea of accountability and responsibilities one person and brothers and sisters and friends to cause a lot of violence on the day that GM was going to show up well you had people's jobs and everything else so they'd be bored the threats got really real we walked out and there were about 10 cars out in the parking lot and these were finally people they had not related to them and this is private property again so the I told me and this is a non union organization so I told the president my company as well what I would do is just fire them so he didn't fire it well the next thing make a long story short the NLRB found against us that we did not allow for Oregon organized labor to protest to be able to organize on our property – or there was no union there how could you how could you find against us the result was that the president of the company had to assemble the entire organization and the person right on the spot and the NLL in their finding insisted that the President had to publicly apologize in front of the entire organization that he fired her wrongly and that it was his heartfelt remorse it's unbelievable that the the National Labor Relations Board must be made up of just ideological zealots who take pleasure in hobbling you know a productive decent normal human being like this I mean I mean actually writing out what the guy has to say to humiliate himself I mean there's something too seriously twisted I know it because you make sure just ask you know who is John Galt you know you just okay yes yes let's see you know what let me check on that over the break and just to just to refresh my memory on it try to get to the bottom of that question okay and then certain then that'll be the last one got multiple paths and those patents were used widely commercially so he more than pays for his wages productivity cost of our agency from his patents the agriculture industry use them how when treat the US government entity getting packed and so those patents basically paying through the whole operations undertaken see we had a our agency was small spoon at Department a second small funding Bailey 16 points that was one question the other was I know for a fact the Guild's the Middle Ages it involved Jews to join Union their gills restricted in the United States well I mean there's certainly that mean that the Union sort of had a reputation for having for racial discrimination you know throughout I think that they had that reputation I mean even into the late 60s you could still see that yeah on the only the medieval guilds are sometimes pointed to as wonderful examples of what we need that because they had both the the workers and the employers in them and it was a it was mutually harmonious and everything but but I was just reading the other day that that the guilds were so anti-competitive that you were actually forbidden if you were a seller if you were actually you know you actually have our master producing some product you could not even sneeze in front of your store because that might draw undue attention to you you weren't supposed to try to outdo you know your your competition or undersell them or call special attention or advertise you know such as that was possible in those days but even sneezing might be your secret way of getting people to look over in your direction so you have to just stand there like an automaton waiting for people to come by I I happen to think that would not be a good model you know for the economy all right let's go eat thanks a lot