Einstein for the Masses

thank you for coming welcome second time around ready ale and you're right this is going to be videotaped but you shouldn't get your hopes up for breaking it a show business because they can only see the back of your head but you may have a very expressive back of your head in which case somebody may notice you and give you a call so this lecture on Einstein generally the best way to clear a room other than shouting fire is to say something about Einstein and then you have the place to yourself so I'm very glad that you were not intimidated by the title and my goal is called no LM left behind everyone you're all going to follow this and when you leave this room you will have a pretty good idea of what it's all about okay so maybe I should start by asking if you know how old the theory of relativity is any idea okay I heard I heard a century old turns out it is actually 300 years old so even though Einstein was the father of relativity that's a grandfather who is Galileo and that's a godfather who is Newton so they all came before and did a lot of things and Einstein actually came much later so that's what I want to tell you about so you get a picture of where Einstein belongs so the way we are going to do this is by the standard method for teaching the subject which is to begin with two infinitely long trains so I'm going to draw you a finite part of that train so here is one train and it's a parked in Union Station in New Haven this is train one this is train too so this is the top view of the train now you get into this train and all the blinds are drawn you cannot look outside it is the reason for that it's not because it's going through certain parts of New Jersey it's because we're going to do a scientific experiment that requires you not to look outside so here's let's say you're on this train there's another train before the shut the blinds you can look out and see the other train you can see it's also standing there then they close the blinds and you settle down and you explore the world around you you can do whatever you want maybe you will pour yourself a cup of water or you may be playing pool or if you're physicist you'll pull your mass and spring system from your pocket and you will you will attach immediately attach it to the wall and pull this mass and see it vibrate so we all have different ways of exploring universe this is what I do okay then you go to sleep and when you are asleep I tell you that I do one of two things one is I leave the train along the way this other is that when you're asleep I give it a speed of 100 miles per hour and you wake up and the question is can you tell whether you have acquired the speed or not that's the real question you have to figure it out using the laws of physics you cannot say I know it's not moving because it's there's Amtrak these arguments are sociological they're not they're not they're not part of science so the question is will you know and what Galileo noticed is that you cannot tell you cannot tell in a moving train that is moving as long as it's moving at a constant velocity that's very important if it's picking up speed and slowing down and so on you alone but if it's going at constant velocity nothing will betray that motion to you that's it that's the principle we have all experienced once in a while when the thing is very smooth our plane is going very smoothly you yourself realize that you're not aware of that motion so the principle of relativity is a statement that you cannot tell when it inside a train whether it's a quite a constant velocity or not so where is the relative in all of this I'm going to come to that so if you open the blind now and you look at the other train suppose you find the other train is going like that at 60 miles an hour will you know whether you're the one who's in motion or the other train now this has happened to us quite often when you're parked on the slope or you put your brakes and if car is in the slope you see the other car going forward you think you're slipping you press the brake harder you get the impression of movement so the whole thing is if you look out and you see this train going that way can you tell the answer is you can tell that is portion between the two of you that is the fact but you cannot really say for sure you are the one who has started off when you were sleeping and maybe you did nothing the other train got into motion in the opposite direction so velocity between two such people is relative in the sense that we can perceive it but we cannot be sure who is actually moving or whether there's any real sense in which one of us really is moving in fact if these two trains were in outer space you just wouldn't know now if you look at the other side let's say you open the window here and look you see a lot of cows and Street cows are running at 60 miles an hour now the question is what do you think is happening is it the cow service is the train so I know what you're going to say you're going to say it's got to be the cows but you realize theoretically Amtrak trains can move so that's the possibility you're not willing to admit that even though it's very remote so you keep thinking it's the cows but it could be it could be possible that's the cows are not moving it's the train so once again there is no way to resolve the difference so the summary of what I mentioned here is that constant velocity doesn't do anything that you can measure if you're inside you cannot figure out that's being given to you that's not true for non-uniform motion that's not true for accelerated motion for example if the engine driver slams the brake you know you're going to ram into the seat in front of you now if you if the blinds fly open you look at the other train it'll be decelerating the opposite direction can you say nothing is happening to me you're the one who's accelerating the other way well you cannot say that first of all you've lost all your teeth cannot say anything can you scribble a note and say I'm not moving you're moving well he will say if if that's the case how come you have no T because accelerated motion namely the slamming of the brake produces effects that you feel you cannot pass the buck to the other person and say you're moving the office away or if you're an astronaut and your rocket is taking off you are the one who feels all the g-forces you cannot argue that the rest of the planet is going the opposite way because they seem to be doing fine so here is the main thing if you're inside a closed strain and the Train axle rates at decelerates or goes on a curve you can tell if it's going at constant velocity you really cannot tell that's it that's what Galileo said that's called Galileo's principle of relativity and it's more than 300 years old so then the next person who comes in not much later is Newton so what did Newton do well Newton actually not only agreed with what Galileo said he actually explained why it is true so I'm going to tell you how in Newton's point of view you can actually understand what we all are aware of well Newton as you know wrote down three laws of physics I'm going to only talk about the first law the second law says something is equal to something else but I'm told in alumni reunions I should not write any equations but that every equation cost the development office $600,000 so no equations so I'll just take the first law okay the first law is a lot as a rambling sentence it's quite safe it says the following it's a law of inertia kwatak the law of inertia if there are no forces acting on a body it will either stay at rest if it started at rest or if it had an initial velocity will keep maintaining the initial velocity unless it's acted upon by a force that's the first law basically the first law says the velocity of an object will not change unless a force acts on it now we are all familiar with the first law I mean here it is I take this cup here and I put it there no force is acting on it it stays where it is so the law of inertia works for me if it works for me I'm called an inertial observer inertial observer is one for whom Newton's laws work so this works now the second part of the first law that if something has a constant velocity it will keep on doing it forever it's hard to visualize in daily life you give a push to something it goes a few feet and stops you don't it's hard to believe that it'll go on forever for free but we know that if you reduce the friction more and more or you went on ice and you give it a shop it keeps moving for a long time before it stops and an idealization is that if the ice is completely frictionless whatever you set in motion will move forever so that's harder to visualize in daily life but Galili have the imagination to realize that if you use the friction that would happen nowadays in outer space you can easily verify that if you throw something it will just keep going at that speed without anybody pushing it so that's the law of Newton and I want to just show you the following if Newton's law works for me when I'm in the platform let's say this is the station then it will continue to work even when the Train is set into motion in other words if newton's laws work before the Train moved it will continue to work even when the Train has a constant speed that's what I want to explain that will show you that Newton's laws are valid in the moving train as they are on the static train and when is when we say the world looks the same what we really mean is the laws of mechanics looks the same because lots of mechanics tell you everything that you can see in the mechanical world is explained by them so how do I know that the first law will work in a moving train that's what I want to explain to you so let me draw a side picture of the train here is a train there is a table here which is frictionless and that is a person sitting here okay my drawings a constant source of amusement for my class so this is a person sitting on a chair and this is a mug of beer on a which this inebriated person has put on a frictionless table now the train is moving at 60 miles per hour now I'm looking at the whole thing from the ground so I see the whole thing going by everything on the train is going at 60 miles an hour beer the person everything now what will the person in the train think I argue as follows the beer mug starts at 60 miles per hour there are no forces on it because there's no friction nothing so it'll keep going at 60 miles an hour the Train I've been assured is going at a constant speed of 60 therefore the mug and the person are all going at the same speed so the distance between them will not change that's what I predict he will see and indeed he will find the mug stays where it is that's how I can show that the law of inertia will work on the train because it works for me and I can translate what I see into what he will see now imagine that the person gives the the beer mug a shove so he starts going away from him at the speed of 10 miles per hour it starts out that way what will happen next I know what will happen next because I am still on the ground I am allowed to use Newton's laws and I say this mug is going at 70 miles per hour that's the 10 plus a 60 of the Train and this guy is still going at 60 so the difference in speed between them is 10 and that difference cannot change that means according to the person of the Train this mug will maintain its speed of 10 so I predict the person in the train will find the Newton's first law of inertia to be valid basically the idea is the person in the Train and I don't see everything the same way we disagree on where anything is I think the mug is going towards Boston he thinks the mug is in front of him I think the mug is are going at 60 miles per hour he thinks it's at rest but the differences are only with respect to velocity not with respect to acceleration the fact that the mug speed is not changing is true for me and it's true for him and that's all the first law of inertia say speed will not change without a good reason imagine now that suddenly the Train picks up speed so start going from sixty towards 70 miles per hour what will the person in the Train see well I don't have the person in the Train is allowed to use Newton's law or not but I'm still allowed to do it because I haven't done anything I am still on the platform so I argue as follows this mug is still going at 60 this person is starting to move at 70 I know what will happen the 70 will gain on the 60 and the two will soon meet how will it look like in the Train the person in the Train it would look like the mug is sliding backwards towards him that's what happens in a plane you didn't take off if you leave something on the tray in front of you it slides towards you towards the back in fact everything the plane that's not nailed down goes to the back of the plane during takeoff that's why all the physicists sit at the last row collecting of whatever stuff okay so okay you have any question you can ask me now any questions okay so everything on the train will accelerate to the back of the Train for no apparent reason that means the world will not look Newtonian to the person of the Train that's so when he wakes up he will know the train is accelerating because when you accelerate nothing stays where it is things go back you got to be very careful when you use the law you can say I went to Grand Central Station I left my ipod there and I came back it was gone what about the law of inertia well I guarantee you that the laws that were broken have nothing to do with Newton so some some unseen hand has come and taken the iPod that's always an explanation but in an accelerating train everything will accelerate backwards that's the reason why accelerated motion can have effects you can detect but uniform motion will leave no trace you will never know that's it that's all that is right up to the time of Newton so gallantly observed that if you want Newton explained that he said these are my loss of motion and my loss of motion are such that if they work for me on the ground they work for me on the train as long as the Train is going at constant velocity all right so I have not said anything about one of the key ingredients in this theory which has not entered the picture yet you know what I have in mind what do you think of anything of relativity what's the first thing that comes to your mind right okay our case you think about the velocity of light the velocity of light is not entered picture and now it's going to enter so the velocity of light is something that is occupied minds for many years alfred lee newman who you might know he said this much I know about the velocity of light it comes here too early in the morning after that every other quotation is going to be trivial but I'll tell you what other people had to say Galileo for one was very eager to find out if the velocity of light is finite or infinite namely does it take any time at all for the light signal to go from here to there or does it happen at once so he did that by taking one of his friends and he went on top of one mountain and his friend went on top of another mountain so this is Galileo is the friend and they both had these lanterns which can be covered so here's the deal he made with his friend he said I would suddenly open my cover to my lantern so emit a flash of light the minute you see it the light signal is going to you mean it you see it you open the thing in your Lantern I'll see that flash of light come here so I look at how long it takes for a round-trip then i'll divide the distance I'll divide by divide the distance by the time and I will get a speed that was Galilee as planned now we don't know what method he used to measure time one theories are used to water clock other words he used this pulse which is a reasonably good way to measure for example the pendulum the church very was spraying Galilee or notice that the period of the pendulum doesn't depend on how big it the oscillations are that he did with his pulse so I don't know how he measured it so he got a speed but you know that that was not the right speed because what he was really measuring is just the time it takes to react and how do you know that's what's happening how do you tell that you're just measuring your reaction time how will you know that's the case you think of how to realize your own mistake for me or yeah that's right that's very true you can sit on the same mountain or go to nearby mountain or a further away amount and you keep getting the same time you realize it's not the time of light travel you measuring but delay to respond so Galileo figured that it's very fast he gave some multiple of the speed of some and but he didn't say I don't remember what it was what he said is at least that fast the real breakthrough came and an astronomer called Romer found a way to find the velocity of light that's a very ingenious method so I'm going to give you a bare-bones version of it it's got you can put bells and whistles on it but the idea is still the same so here is the Sun and let's say here is the earth going on its orbit and here is Jupiter going on its orbit and this is Jupiter and at the time when I want to do this thing Jupiter is here Earth is here and there's a moon of Jupiter called IO which is going round and round let's say it goes around exactly every hour so every time the moon comes in front of Jupiter I see it and I make a notation I say I saw the Jupiter as a function of time I draw a blip then one hour later I should get a second blip and at two hours I should get a third blip and so on because all these motions are completely periodic is like a clock but what you find is that the second blip doesn't arrive on time but comes a little later third one comes even later and the reason is that the earth is moving away from Jupiter so the delay keeps on accumulating till six months later it's quite a bit several minutes compared to when the pulse is supposed to come 300 the pulse let us say comes ten minutes after it's supposed to come that 10 minutes is then the extra time it takes light to go across the orbit of the earth around the Sun and people have pretty good idea it's like hundred million miles and then you take the extra time and you divide it and you get a speed and he got a pretty good answer the answer he got was like two hundred thousand kilometers per second and the correct answer nowadays we know it's like three hundred thousand kilometers per second but it is a remarkable achievement and you need something of cosmological proportions before you can find the velocity of light you do anything in the laboratory things happen so quickly later on people found a way to measure it in the lab but this is the first astronomical measurement all right so light was then shown to have a finite velocity of propagation and the velocity was improved and by the time I come to the next part of the story people knew pretty much the answer is 300,000 kilometers per second all right so then there is a new development about light people don't know what light is they don't know what's going on they just know it travels at the speed then a person called young did an experiment which shows that light is actually a wave I should tell you what we mean by that statement what does it mean to say something is a wave waves a one very important property first of all we all know what waves are in water you can have waves the thing is going up and down up and down in relation to some undisturbed level of water waves have the property that they can interfere and that means the following imagine that this is your estate and there is a beach here and you park your yacht this is towed to give this to the Yale alumni your yacht is part I don't do this in the classroom because they don't know what I'm talking about but you guys you all have one right okay so you put your yard here and the waves are coming to block them you put a barricade so your yard is very tranquil suddenly there is a breach and these waves will come from this opening now radiate out and they will come to your board and the board will shake suppose you want to avoid that there are two solutions one is to find a way to block this but if all you have is say a sledgehammer you can still make progress because you can go and you can make a second breach here now that looks like bad news because now stuff is going to come from here too but you can arrange it so that when this guy and this guy meet they cancel each other because you see takes a little longer to go from here to there compared to that one so you got the crest and a trough and a crest and a trough you can arrange it so that when a crest from here comes a trough from there comes so one is telling the water go up are they selling the water to go down so it doesn't do anything little later this one says go down and that one says go up and doesn't do anything so you can find it you can arrange it so that you don't have any activity here that's called interference so two waves can cancel and if instead of water waves if this was light and you had a source of light here and a dark screen with two holes in it and you put another screen where behind you look at it you will find patterns of dark and bright and dark and bright dark were the two camps of cancel and bright where the two add up that's called interference and he showed that when you do it with light you get interference so it's a way but you don't know what it is that's waving see sound is a wave but I know exactly what's moving when I talk to you when my diaphragm pushes in and out it changes the air pressure and the add pressure propagates to you and it goes to your ear then the eardrum starts to move after that I don't know that's the biology department some wires come and pick it up and stop goes to your brain okay that's where we check out at the eardrum but I know that's how it travels so that's the propagation of sound in a violin string also when you pluck the string we know the deviation from horizontal that blip is what travels back and forth for light no one knew what it was you know it's a way we know it's got a wavelength that we can measure but what is it that's really shaking and what's the medium in which all this is happening that was not known so Maxwell this is the this last character before Einstein was studying electromagnetism is not interested in light studying electricity and magnetism electricity is quite familiar right it's when you rub your feet on the carpet and you touch the doorknob you get a spark this electricity magnetism has been known to people from ancient Greeks when parents noticed that kids were sticking stuff on the refrigerator using some little black rocks so from that time magnetism has been studied but we can say you have a magnetic field if the compass needle will do anything then there's a magnetic field there so what what max was studying is how this electric and magnetic fields travel in space and he found out they travel like waves and you calculated the speed of the waves and you put the numbers in and you get a speed which is universally oops I will not write anything I just write here 3 times 10 to the 8 meters per second so he got that speed that was a real shock that electromagnetic waves travel at exactly the speed as the speed of light so they said electromagnetism must be light now you got to be very careful just because you're traveling for example if I'm running next to a buffalo at the same speed doesn't mean I can conclude I'm a buffalo right we just have the same speed so the fact that electromagnetic waves are the same speed as light doesn't mean it's like well they said that's what it is and they were right but later on we know the gravity waves also travel at the speed of light but they are not light but at that time they were quite right so light was in fact electromagnetic waves and the question is these waves moving in they said let's give it a name we'll call it the ether there's something called ether and ethers everywhere it's even between here and the distant stars we know it's there because we can see the Stars if there is no ether between us and the Stars the light cannot travel without the medium so ethers everywhere okay then the speed of light is calculated to be this number is always in the medium in which it travels for example the speed of sound is 700 and something-something miles per hour with respect to the air if I travel now with respect to that air in the direction of the sound the speed will change for me the speed of sound will be reduced in fact you can you mention will go even faster than some if you could fly in the Concord that's what it does it goes even faster than some so the speed of sound is the number that's given with respect to the air in which it is traveling the speed of light must be the speed with respect the medium in which light is traveling this mysterious ether so if I go and measure the speed of sound today in my lab I would generally not expect to get that number because in all probability my lab is moving relative to this mysterious eat there are some speed that difference must show up in the speed of light but when you measure it you get exactly the answer as if you were at rest respect the medium then you say okay you know what maybe today my lab at this instant is at rest but wait 12 hours a few more hours since the earth is spinning one instant you're moving like this twenty twelve hours later you're moving like that you cannot be addressed the whole time also you're going around the Sun you cannot be addressed the whole time and yet no matter when you measure the speed of light you get the same answer daytime nighttime anytime of the year moving whichever way you like you get the same answer and one simple explanation was maybe the earth is carrying the either with it for example the atmosphere we are breathing we don't leave it behind us the earth moves we carry the atmosphere with us or when you go in a plane if you talk to somebody across the other end of the plane you don't have to worry about the fact the whole thing is moving because the air is being carried by the plane you don't have to worry about it so they said maybe that's what's happening maybe the ether is carried by the earth but one can show from celestial experiments looking at stars that you cannot take it with you cannot take the ether with you then you have a real problem here is this thing travelling in some mysterious medium no matter who is looking at it it has the same speed you realize that's very strange how can something have the same speed for everybody someone standing someone moving someone moving the opposite way they all get the same speed so people didn't know what to make of it till Einstein came and said I know what's going on I know why light is behaving this way forget about ether there is no medium collie that we don't need it I'm just going to postulate that the speed of light is same for everybody no matter how they're moving now you might think this guy is famous for saying that I mean he doesn't explain anything he just says it's the way it is because it's the way it is I'm going to postulate it so that's if that's all he had done it would not be the whole story he explained why the speed of light is the way this he said if I go to the strain that Galileo talked about and I wake up I do all experiments with water and masses and springs and they all look exactly the same as before but suppose I sink the center light pulse and measured its speed if the speed of light dependent on the speed of the train I will get a different answer when I wake up and from that difference I can deduce the fact that I'm moving that means the loss of mechanics conspired to hide my motion but not the loss of light loss of optics he said I don't buy that I don't believe that some laws of nature remain the same in a moving train and other laws vary so the speed of light behaves the way it does because it's part of a big conspiracy to hide your velocity as long as it's uniform that's why light behaves the way it does it have to if it had behaved any other way person on a moving train can detect her speed without looking outside that means there's at least one thing that is different in the moving train maybe mechanics it's the same optics is different he said I don't buy that everything is got to be the same it was an act of faith really even though it's not a very religious person most scientists may be religious may not be religious but they all physicists certainly have a belief in the order of natural phenomena we believe you are playing against a reasonable opponent that the puzzles have reasonable and clever answers and whoever designed the system certainly will make sure that the laws of science behave uniformly that everything is same on the train not just mechanics not the first 10 chapters of my book but the whole book so he said that now you can say is that all he did no because in saying the speed of light is a constant he then set himself up for a lot of consequences which are very bizarre and that's what I'm going to talk about now because you should think about what it means to say the speed of something is a constant so imagine you're standing on the ground and there is a car and it's speeding by at some 60 mph you clock it is going at 60 now suppose you get into another car and you travel in the same direction at 40 mph you expect the speed of this to be 20 everybody agrees you got to subtract your 40 from that 60 that's how velocity is hand if you had a velocity of 60 from the ground and you go at 40 to the right you subtract your 40 and you get 20 but what I'm telling you is if this had not been a car but a light pulse you know signal of light this traveling if it had a speed C on the ground it has the same speed C even seen by a moving car moving in the same direction in fact even if this car is going at half the speed of light it would still appear to travel at the full speed to that person that is what Einstein says is happening but you realize that means big trouble right it's not the way things behave so let me make it very very clear here is a light signal going at speed C as seen by the ground I am going at a speed 3/4 of C what do I what does he think I should get he thinks I should get 1/4 C as the measures be but I get C so that the velocity I get is much bigger than what he expects so what how do you explain that so you say look I thought you will get 1/4 of C but you're getting C so something is wrong with the way you're doing your measurement how do you measure it speed you see how far it goes by putting some meter sticks one against each other then you see how long it takes with your clock you divide distance over time and in that calculation some of you are getting four times the answer now there are two ways in which it can happen one way is that your clocks are not running at the same rate as before when we were both standing relative to each other at rest the minute you went on the strain some of your clocks have slowed down suppose they're running at 1/4 the normal speed and that means when light has gone for 4 seconds you think it's gone for only 1 second so you divide by 1 instead of 4 that's why you got this 4 times the answer another option is the meter sticks which we bought from the same store which used to agree before you got on your train your meter sticks of shrunk they're shrunk to 1/4 their size so that when light is gone only 4 yard do you think is gone 16 yards so you knew you either inflate the numerator or reduce the denominator in the velocity calculation to get this or maybe you're doing both maybe both things are happening but something has to happen so you have to abandon your notion that meter sticks and clocks run at the same rate in a moving train as in a static train and then he went on and calculated the amount by which these two things happen that's a calculation I won't perform but I do want to tell you some of the interesting consequences then I will stop talking then we we can explore the consequences the first consequence is that events which are simultaneous for me may not be simultaneous for you so here's an example you can give so imagine a pair of twins okay one is born in LA one is born in New York did you listen to what I said this one is so when I when I mention this to my class they pointed out that no ordinary mother could've given this is a mother from the yo mama jokes she is so big she can give birth to kids coast-to-coast alright so anyway let's forget the kids let's say there is some other event that takes place simultaneously according to me then the claim is that if you go on a rocket ship or any other state of motion you will think they're not simultaneous that is really interesting right because we have a notion that when things two things happen at the same time say in LA in New York that's the real meaning in which they happen at the same time we're not fooled by the fact the time difference of three hours we know there is a sense in which there really did happen at the same time we think that's an absolute statement but the point is that if the whole events are seen by a moving observer there will not be at the same time and this is how Einstein explained it so he said let me take this train we just at rest and I want to make two things happen are the two ends of the train at the same time maybe two explosions so what I'm going to do is I'm going to take two mirrors placed like that at some angle I'm going to send a light signal from here it'll split one will go to the left and one will go to the right and since it I'm right in the middle of the train they will go and hit the two ends and let's say the trigger two explosions those explosions happen at the same time I couldn't have done it more carefully but now imagine that the train that I am in is actually moving related with the platform and you are seeing it from the platform to you this is what's happening let's see what you will say is happening the light signal left here this signal is going to the right at the speed C the speed of light is the same but this end of the train is moving away from their signal where at this side of the train is rushing to meet the signal it's very clear this end will hit first and a little later the light will hit that end so you will agree that to the person on the ground the two events would not be simultaneous now here is where people sometimes ask why do you use this light signal why not send two pigeons produce two pigeons and see what they do I'll just shout hey do that and the two guys the two into the train do what you said the reason you don't do any of those is we don't know anything about the behavior of sound in this new relativistic physics we don't know about you can send to Federal Express guys will they get that at the same time we don't know because we don't how they behave but one thing we do know is by postulate the velocity of light is a constant regardless of the source regardless of the observer that's why I can say with confidence that even though the signal is emitted in the train the right signal and left signal both travel at the same speed c1 towards it and that's running away from it one - at the end that's rushing to meet it consequently they won't be simultaneous now it turns out that this lack of simultaneity is really there and you just cannot say who is right and who is wrong you just can say I made it as simultaneous as I could the best of my ability but you don't have to agree it's a very interesting case what people really can disagree on what the simultaneous and what's not it depends on the observer so that's the immediate consequence you can see where it came from you got to do more work if you want to know how much is the time difference for that you got to do calculation but the fact that they won't occur at the same time you can see immediately now this also means that two events with a simultaneous for one person can occur in different sequences even a can occur before B and I can find a guy for whom B occurred before a now if your Einsteins you should again get worried in fact the greatest thing but I understand which you admire once you start practicing any kind of Sciences not only that he was very clever but he was very gutsy because once you invent something new and the mathematics takes you in all kinds of directions you have no choice you're wedded to that formalism and you got to defend all the consequences of your theory so here's the consequence a and B are two events which are simultaneous for me but not simultaneous for you you can also show that if a occurred after B for me then B cannot occur after a for someone else that can lead to a lot of paradoxes so event a is my father is born even B is I am born okay now there's another observer for whom I am born but my father is not born yet you realize that causes a lot of problems right the nurse says what shall we name this kid I don't know his father is not born yet no you don't want that to happen so there are certain events where one event is causally connected to a second event but a is the cause of B in this case my father is the reason I am here the theory should not I love the order of those events to be exchanged that other events where it could not have been the cause of B that's defined in relativity as such that there is no time for a light signal to go from event a to even B then no way a can influence be in the in that case you can find another person for whom the ordered is reversed so the order of events is not it in some sense is absolute if a is the cause of B or could have been the concept B theory doesn't allow me to exchange their order but if they are not causally connected you can find people who completely disagree on when something happened okay so that's the second thing involving time and here's another thing involving time that's very interesting remember I said maybe a moving clock slows down let's see how that can happen now if you take the clock that I am wearing there's no way we can show that because I have no idea what's in it open it nothing is moving nowadays we don't have clocks work and Einstein didn't know how clocks work either but he devised or at least to teach it we devised a very simple clock where we can all understand why a moving clock slows down this clock is simplicity itself you got two mirrors and you have a source of light that emits a blip it goes to the top mirror and bounces back and goes back and forth and every time it makes a round-trip it hits a detector and it goes click okay that's my clock the round trip is L plus another L view / speed of light you get the time that's the time period of my clock so I have a clock like that and you have a clock like that and your clock and mine are identical we bought them at the same store but now you go on your train you hold your clock and I look at your clock here is what I find your clock is doing this because you are moving according to me so when the light was emitted at the bottom you were here a little later you were there when they'd hit the top then you were here and then you were there in other words an up-and-down motion in the train looks like a zigzag motion from the ground we can all understand that but it's the exact path we all know is longer than straight up and down it's a very simple calculation to see how much longer and that this involves Pythagoras theorem namely comparing the hypotenuse to the vertical side and you can get the time difference so I can tell you how much you will be slow but here is the paradox paradoxes you are entitled to say you are not moving at all because the loss of mechanics that everything is same for you as for me in fact according to you my clock is going that way is exactly opposite way so you understand how if you and I have two clocks my clock is up and down your zigzag for me and according to you the picture is just reversed so each person is able to argue the other person's clock is running slow because it's not taking the shortest path so going on a zigzag but this leads to a paradox what if these two guys meet when they meet one day whose clock will really be behind because each seems to have a solid case so that is the twin paradox the twin paradox is the following you have this same twins one is now in Houston or in Florida the other gets into rocket goes on an orbit around the Earth 500 times and they come back now the person in the ground says hey you've been moving and therefore your clock is slow therefore when I compared your clock to my clock your clock should have take to er seconds then but what if the person the rocket says the same thing you can say I'm not moving you're moving so you should be in fact forget clocks the human body is a clock I am a clock if you watch me patiently in a few years the rest of my head will fall down my teeth will fall down you can measure time in decades by watching human beings if you cannot wait you can watch the cells how they grow and die in the replicate the human body is a clock therefore the human body's aging should also slow down in a moving plane so the twin paradox is more dramatically illustrated by saying the following suppose the twin on the earth waited 10 years for the journey to end and the twin on the rocket by the time is aged only five years so when they meet the rocket wind should be younger than the one who didn't go on the trip but what if the rocket Quinn says I never went anywhere you went somewhere you should be younger the person is when they meet who will be right you have to answer that if you're I understand you have to provide a definite answer because when you do the experiment you can get only one answer so the answer that Einstein gave is that the person who went on the rocket will be younger now why is that why is it that they both cannot make the same claim the answer is that I am on the earth I never went anywhere Newton lost valid for me the whole time you got into this rocket when for a brief period you were accelerating you knew that Newton's laws didn't work in your frame if you accelerate it too much you are going to die not me then your accelerated picked up speed then you can go to uniform speed then you slowed down turned around picked up speed and came back slowed down and stopped so you have done a lot of acceleration therefore you are the person who cannot ever claim to be equal to me so the answer to the twin paradoxes is not really paradox the twins are not equal in the claim one had accelerated motion in the other dude so these two clocks which are going in opposite direction can never be compared unless one of them stops moving and goes to the other one whoever stops and turns around and goes back that clock is moved that clock would be behind the other clock so this is the manner in which the twin paradox which is and people now find that even though human beings cannot be kept alive much longer by traveling elementary particles can be lot of particles produced in Geneva for example they're not supposed to live very long but if they go at very high velocities their internal clock slows down and they live much much longer than you expect so that is the behavior of time in this theory the behavior of length is more complicated so I don't want to explain that but the claim is that whenever a broad starts moving relative to you you would think it's shorter than it is everything that's moving will appear short to you and according to that person everything you have will appear short to that person you got to make sure there are no paradoxes there these are other things one can study if one wants to but I didn't want to do all of that so let me just say the point I want you to carry is that I'm going to stop so you're at least 10 minutes to question me the point was the principle of relativity says that when you get into a train which is going at a constant speed there is nothing that will betray that constant speed to you it makes no difference it was true for mechanics and in the end is also true for light but if it's true for light it led to a very strange requirement that the speed of light be the same for all observers and that is very contradictory to popular intuition by the speed of something depends on how fast you're moving so Einstein said well I will not let light change its speed I will let our measurement of time and space change suitably to accommodate the constant velocity of light that's what led to the change in the notion of simultaneity how long it takes for a clock to tick how long is any object it all depends on how you measure it so space and time got revolutionized so that in the end the speed of light comes out to be the same that's the first part of relativity equal MC square is not anywhere near this in fact it's not a central result in this theory it is great phenomenological consequence but you can see there is no reference to that right now and it's not that easy to explain as to what I was able to explain to you so it's really a footnote where not for the great consequences it has as a logical structure that comes somewhere else what I mentioned to you is the heart of the special theory a few years after that Einstein generalized his theory to the general theory of relativity in which he said I don't even like the fact that an accelerated person has to admit he is accelerating I want him to also talk his way out of acceleration you can see how can that be when you are an accelerated train all kinds of stuff starts rushing to the back of your train how can you talk your way out of it and here is how you can do that here is my train and if I'm accelerating you agree nothing anything that's not nailed down goes to the back of the Train falls Edison drape to the back of the Train here is what I can say is happening my train is not moving at all but when I was sleeping you went and put a huge fat planet behind my train which is pulling everything I leave here towards that so you cannot tell if you are in the gravitational field of a planet or whether you are accelerating the opposite way so that's how gravity enters the theory so Einstein's general theory is really a theory of gravitation see gravity has a remarkable fact that everything falls at the same rate that's a remarkable property of gravitation whatever you drop falls at the same rate therefore you can imagine being in outer space no gravity but your lab is accelerating upwards at 9.8 meters per second there also everything you drop will go to the floor at 9.8 basically the objects are not going the floor is rushing to meet them but you cannot tell the difference so that's how the gravitation theory was deduced by Einstein a few years later that is viewed by one and all as the most imaginative leap made by pure thought because that was done not because of any experiment but by sense of dissatisfaction with the special theory that it made people in uniform motion equal but he wanted to make everybody equal and then in the quest for that he found this great theory all right so I will stop now and answer questions thank you okay see a hand in the back yes remember 10 miles an hour is the speed you give it a speed of 10 miles an hour and if you are going that means from the ground the the beer will be going at 70 you will be going at 60 if you pick up speed that's acceleration if you go from 60 to 70 if you gain speed then you know you will catch up with the mug but from the train point if you look like the mug came back to meet you okay yes the in the general theory there is no paradox at all so you can also solve it but in other words you can say this involves accelerated motion so we won't answer it if you want you can use a general theory to actually show very clearly why one person will be slower than the other one yes yes but it won't be simultaneous for a guy on the train yes you can arrange it so that the person on the ground is satisfied to their simultaneous what you won't be in the Train so if you do it so simultaneous for you it would not be simultaneous on the ground but you're quite right you can move the mirror closer to the other type front end of the train so it's simultaneous for a person on the ground but then it's not simultaneous for you so it is still true that you could not agree on what simultaneous yes yeah you gotta be careful the only speed that is same for everybody is the speed of light okay a train going at 1/4 the speed of light will not like you appear to have that speed for everybody some people can say it's less than 1/4 some people can't is more than 1/4 so it's not that any formula that has a scene it doesn't change it's got to be really at speed speed of C so the velocity of light is the only speed that is same for all people half the velocity of light is not the same for all people oh one here and then one there yes yes well a gravity wave is so maybe one way one way to think about gravity waves is that we are supposed to be in a in a space-time in which there is something called a curvature of space-time so that the distance between points can be stretched or contracted it's like saying maybe here's your on a rubber sheet and you mark some dots okay and the dots are spaced uniformly so of course the ripple goes past the rubber sheet you realize that when the ripple goes past you some points will move further away and some will be closer so that's a real wave on a real diaphragm producing the distance it returns out in free space if you take two points which you think are a meter apart when a gravity wave goes past it's a change in the underlying fabric of space-time so that for that short time they will seem to be the closer out further so gravity wave is one in which the actual distance between points changes when the wave goes fast yeah if they act they accelerate it like yes your question is is only the accelerated portion that you think will make a difference that what you're saying no it will actually also remember how long you went on a straight line also yes whether okay so the Doppler effect is the phenomenon that when waves are emitted towards you so a crest comes in a trough comes in a crest comes you time them that's the frequency of sound but if as I talk to you I also walk towards you which I can do after some practice then you will find out that the crest appeared to come to you a lot quicker because I emit a crest then I move and emit the next one so they're squashed that's the Doppler shift and that is nothing to do with relativity we can understand that in Newtonian mechanics but in relativistic mechanics that's the added fact that when I'm moving my clock is different from your clock that's called the transverse a Doppler effect and you can one way to see that I mean that's an extra contribution to Doppler effect but you can best see it when you are going around another person when you go around another person you're not emitting waves towards them or away from him and yet there will be a shift that's because when you're moving in a circle your clocks are different from mine and your frequency will be different from my you think you're singing at some frequency I will hear it at a different frequency but with light is a constant yeah the emitter is moving toward you talk about the redshift yeah the expanding right yeah that shift is really that really can be understood as a classical Newtonian shift if a galaxy is receding from you the light adem it's shifted towards the red because the crests are further apart than they normally would be so the color looks redder than the actual color yeah okay first I gotta tell you I don't know what a warp is okay because we don't know okay what point is speed of light okay speed of light as far as I understand definitely not possible for any material object the only thing the traveling speed of light is light that's what roosevelt said only thing traveling at the speed of light is light itself nothing fund me ah here's a question if you can go faster than light a lot of things will happen one of them will be that you will see the effect appear before the cause and that will lead to logical contradiction that's one of the consequences so that you will find that if I if I fire a bullet can you move away a little bit yes like and it hits that door okay hits him then this is the cause that's the effect you will find another observer if you go faster than light that he got shot and I've not even pulled out my gun meanwhile somebody grabs my gun that's poor guy has been shot for no reason ok-hee he is on a risky mission here right okay any other things oh yes yeah okay now you cannot go at the speed of light but imagine you are going at point nine nine nine nine nine times the speed of light everything will be the same the minute you turn on the light bulb light will spread out and illuminate the room as if you were not moving you will not know in fact here's a point you somehow say I am going at that speed right with respect to whom how do you know you're going at the speed because there's no it's always relative to somebody else you're going at that speed normally you may mean with respect to mother earth but that is an arbitrary human interest right normally the speed of some system is defined only relative to other systems in the claim is that you cannot deduce any intrinsic effects due to their speed so you won't know as long as is less than the speed of light everything will look exactly the same but when you make a long trip and here's another thing how far can we explore our universe suppose a star is 200 light years away that means even if you travel at the speed of light it's going to take you 200 years to go into 200 years to come back and brag about it right can you do it if your lifetime is only a hundred years the answer is you can because if you go fast enough you stop aging you can go you can go to the planet you can turn around and come back and you could have aged only two days but you won't have anybody to brag to because everybody is gone there 400 years old but you can do it so there is no limit it's very interesting the speed of light imposes a limit on how fast we can travel so it looks like in a hundred years you can go only a hundred light years and that's wrong because as you travel you slow down your clock your own biological clock that's the other thing if you worried about the biological clock and you're waiting for mr. right or mr. right now mr. mrs. right whatever it is get on a rocket ship and tell them to call you when somebody reasonable comes along

Channel: YaleUniversity

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Rating: 4.8851871 out of 5

Keywords: Yale University, Association of Yale Alumni, Ramamurti Shankar, Einstein, physics, mathematics, theory of relativity

Id: 3enwR6e9V9A

Length: 62min 30sec (3750 seconds)

Published: Fri Jun 11 2010