# I Problems with Einstein's 1920 "Relativity"

#### bengoodspeed

Hi, I have been reading and watching a lot of physics lately but I have come across this problem.

I have the basics of special relativity down, and it all seems clear to me. This is not in question to me. For example, I am reading a book on string theory by Brain Greene, and in it he covers relativity. All the explanations are clear and I can easily understand exactly what logic he is using and how it works.

However upon reading Einsteins 1920 publication on relativity (which you can read here for reference: https://www.bartleby.com/173/
I am having a trainload of problems

Chapter 7 became extremely aggravating as I spent about an hour reading the same page over 10 times, and feeling everything contradicted or that the explanations were terribly given. however I was able to find a way to just write it off as bad explanations,
but then Chapter 9 got worse, as it just seemed downright wrong, and I can't find a way of looking at it that explains it. So help me out here..

This is the passage in question:

 UP to now our considerations have been referred to a particular body of reference, which we have styled a “railway embankment.” We suppose a very long train travelling along the rails with the constant velocity v and in the direction indicated in Fig. 1. People travelling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment. As a natural consequence, however, the following question arises: 1​ Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train? We shall show directly that the answer must be in the negative. FIG. 1.​ 2​ When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length A —> B of the embankment. But the events A and B also correspond to positions A and B on the train. Let M' be the mid-point of the distance A —> B on the travelling train. Just when the flashes of lightning occur, this point M' naturally coincides with the point M, but it moves towards the right in the diagram with the velocity v of the train. If an observer sitting in the position M’ in the train did not possess this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated. Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A.

My problems comes with the statement: "Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A."

Um, no he wouldn't?

My thinking is this: if the speed of light is constant for all observers, then let us imagine from the perspective of M' (the man on the train) he is stationary while A & B are moving by him. First A passes him, and then when he is in the middle the lightning strikes and pulses light toward him. A & B continue moving by as the light travels, but since he was in the middle (M) at the moment they pulsed, from his view the beams both travel to him at the same exact rate accross the equal distance to him, since there will be no added (or subtracted) velocity due to the points (A&B) motion past him. If there was, that would mean that he could rush towards an object and measure the speed of light as c+v where v is his own velocity relative to it, (or it to him.) hence, VISUALLY at the very least he would see both pulses at the same moment no matter how fast he goes by the embankment?

I thought this over and over, I've searched the text for some misunderstanding, I cant find anything, what am I missing? My only thought was that maybe this was described from the perspective of the embankment watching the observer on the train, but in the last two sentences the text makes it clear that they mean the observers from their own perspective on the train.

My second problem is this:

If you described this experiment say with cannons instead of lightning, and had two cannons aimed at M, and had them both fire at the moment lightning strikes them, then this experiments description would hold true, if we considered the arrival of the cannonballs at the observers to be our method of judging simultanaety of firing. This would be because the observer on the train would be adding his velocity towards the cannonball in front of him to its speed toward him, thus it would fly by his face before the cannonball behind him reaches him, just as this chapter describes what light supposedly would do?
But this scenario I've invented is a description involving objects that can be described in a Newtonian manner, (adding velocities, etc) therefore what is the point of this experiment in trying to undermine our Newtonian notions of time? We all know that velocities add to an object in motion so if light did the same thing it would only demonstrate and reinforce the Newtonian dynamics.

I can't possibly think that Relativity is wrong, nor do I, nor can I think that this book wasn't carefully thought through and read and analyzed by many people, yet I can't for the life of me figure out what I'm missing.

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#### Ibix

My problems comes with the statement: "Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A."

Um, no he wouldn't?
Some care is needed with language - by "see", Einstein (or his translator) means "subtract out the travel time of light from the time he actually receives the pulses to deduce their emission times". As long as you have that in mind...

Start in the frame of the embankment. The flashes are emitted simultaneous with and equidistant from the observer at the centre of the embankment, at the same time as the observer in the train passes by. The embankment observer, therefore, receives the light from the pulses at the same time and calculates that the flashes were emitted at the same time.

However, when the embankment observer receives the flashes, the train observer has moved. So obviously the train observer receives the front flash first - he moved towards the source and away from the other source. So he receives the light from the front flash first. This is invariant: you could use the flashes of light to illuminate each observer's watch and take a photo, and if one person says that there's only one photo of the embankment observer's watch but two of the train observer's, everyone had better agree.

So the train observer sees the front flash first. How does he interpret this from bis perspective? The speed of light is constant, the distance to the front and back of the train is equal. But he did not receive the flashes at the same time. The only possibility is that they were emitted at different times.
First A passes him, and then when he is in the middle the lightning strikes and pulses light toward him.
This is where you've gone wrong. By saying "he's in the middle when the lightning strikes" you are implicitly assuming that the strikes are simultaneous in this frame. That leads you into a contradiction when the thought experiment is set up so the strikes are not simultaneous in this frame.

#### lomidrevo

@bengoodspeed , welcome to Physics Forums!

I have the basics of special relativity down, and it all seems clear to me. This is not in question to me. For example, I am reading a book on string theory by Brain Greene, and in it he covers relativity. All the explanations are clear and I can easily understand exactly what logic he is using and how it works.
If you mean one of his pop-sci books, you cannot really learn any theory from this kind of books. Don't get me wrong, those books might be interesting to read and they have its own role, but you need a textbook to immerse yourself in a real study of the topic. Especially for topics like theory of relativity!
I am not sure that Einstein's publication from 1920 is the best way to begin with. Have you tried to read any of the Feynman lectures? They are for free, and I think this one does a great job for introduction:

EDIT: I forgot, one drawback of the lecture is mentioning the concept of relativistic mass, which is obsolete by now. So I would ignore that one in the lecture...

#### bengoodspeed

Thanks for the thoughts.

Although this still isn't clear to me. For simplicity, let's first just talk about the light that the observers actually visually receive, without back-calculating:

So you say:
when the embankment observer receives the flashes, the train observer has moved. So obviously the train observer receives the front flash first - he moved towards the source and away from the other source. So he receives the light from the front flash first.
Well, yes, from the perspective of the embankment observer.
But from the train observer in his own reference frame, his motion does not change the rate relative to him at which the light travels to him across the distance from which it was first emitted, all that matters is that it covered a certain distance per second relative to him from the time it pulsed. If he could somehow receive it earlier than this by flying towards it, then this means that when he actually receives it, he would measure a speed for the light faster than the speed of light. In his own "stationary" reference frame, the light propagated to him at a set rate exactly the same as the stationary/embankment observer measured.

Or am I confusing things a little here? If we could somehow view the train man's OWN perspective from the outside, we would say that the light "slowed down" at a rate equal to his own velocity towards it. I suppose within that time that it is "slowed down" he is still covering distance, and so will still be reducing the distance between him and the source which the light has to traverse, and therefore could receive it earlier in that sense? Maybe? But does that make sense? It would have to "slow down" exactly according to his own rate of motion in order to be measured by him at a constant rate (c). In other words if it takes one second to reach the embankment observer, it would take one second to reach him as well, despite his motion, as the distance he covers would in essence be "subtracted" from the rate of the light coming at him, "slowing it down" in a way which is exactly proportional for him to measure it at a constant rate when he receives it at his own velocity. Ah this is breaking my mind.

When you say:
By saying "he's in the middle when the lightning strikes" you are implicitly assuming that the strikes are simultaneous in this frame. That leads you into a contradiction when the thought experiment is set up so the strikes are not simultaneous in this frame.
Are you referring to things like future light cones or whatever? Or space contraction? I mean because this is very early in the book and he has only just dived into the subject really so I find it hard to believe all this is meant to be assumed. He passes by the middle just as the lightning strikes as judged by the back-calculation the embankment observer makes.. how else can we define when it occurs? The lightning struck just as the man in the train passes the midpoint, how else can we even set up the experiment? If we can't say that the lightning struck just as the man in the train passed it then how can we even remotely sensibly make a discussion about when he should receive the ray?

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#### bengoodspeed

@bengoodspeed , welcome to Physics Forums!

If you mean one of his pop-sci books, you cannot really learn any theory from this kind of books. Don't get me wrong, those books might be interesting to read and they have its own role, but you need a textbook to immerse yourself in a real study of the topic. Especially for topics like theory of relativity!
I am not sure that Einstein's publication from 1920 is the best way to begin with. Have you tried to read any of the Feynman lectures? They are for free, and I think this one does a great job for introduction:

EDIT: I forgot, one drawback of the lecture is mentioning the concept of relativistic mass, which is obsolete by now. So I would ignore that one in the lecture...
It's funny, considering the 1920 book is lauded as being meant for the layperson and easy to grasp without confusing math. All it's done is make me frustrated with Einstein for explaining everything in the most haggard and extraneous way hahaha

Thanks, feynman is an enjoyable speaker so maybe I could give that a listen. Though I think I have the material mostly down with Brain Greene's "The Elegant Universe". I just wanted to hear Einstein in his own (translated) words. In Brian's book he describes a sort of similar thought experiment involving a moving train with two observers equidistant from a single light source, and also some stationary observers outside the train. It's absolutely crystal clear.. which is why this is so ridiculous that I can't make heads or tails of Einsteins lightning thought experiment.

#### Ibix

Well, yes, from the perspective of the embankment observer.
But from the train observer in his own reference frame, his motion does not change the rate relative to him at which the light travels to him across the distance from which it was first emitted, all that matters is that it covered a certain distance per second relative to him from the time it pulsed.
Not quite. It also matters whether the flashes were emitted at the same time. If they weren't, he won't receive them at the same time even though they were emitted at the same distance.

The analysis in the embankment frame shows that the train observer does not receive the flashes simultaneously if the embankment observer does. Thus the train observer does not receive the flashes simultaneously. Full stop. So how does the train observer interpret not seeing the two flashes at the same time? The speed of light is the same in both directions and the distance covered is the same, as you say. Therefore they must have been emitted at different times.

"At the same time", for things that don't happen in the same place, is not an absolute statement in relativity. You - and about 99% of students - seem to be struggling to let go of the idea that "at the same time" is a universal statement. My suggestion is that you review anything you write or think, and any time you say "at the same time" or "simultaneous", think "have I said for who this is simultaneous?"
He passes by the middle just as the lightning strikes as judged by the back-calculation the embankment observer makes.
This is fine. But in your original post you didn't add the bit about who does the judging.
If we can't say that the lightning struck just as the man in the train passed it then how can we even remotely sensibly make a discussion about when he should receive the ray?
It's simplest to start in the frame where the strikes are simultaneous, show that only one observer receives them simultaneously, argue that both observers would see the flashes simultaneously if they were emitted simultaneously by their own calculations, and conclude that they disagree about whether the flashes were emitted simultaneously or not.

You can work in the frame where the flashes are not emitted simultaneously, simply stipulating that they are emitted such that the other observer receives them simultaneously. It's just messier.

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#### SiennaTheGr8

Though I think I have the material mostly down with Brain Greene's "The Elegant Universe".

But also some good news: it takes only high-school algebra and a bit of study to understand basic relativistic mechanics, and it's a worthwhile endeavor. Here are two very approachable books on the subject:

Taylor and Wheeler's Spacetime Physics (a classic that emphasizes the geometric nature of the theory from the start; the writing style is idiosyncratic but this book is great)

David Morin's Special Relativity: For the Enthusiastic Beginner (a newer one that does a particularly good job of introducing the relativity of simultaneity, which seems to be tripping you up somewhat)

#### bengoodspeed

The analysis in the embankment frame shows that the train observer does not receive the flashes simultaneously if the embankment observer does. Thus the train observer does not receive the flashes simultaneously. Full stop. So how does the train observer interpret not seeing the two flashes at the same time? The speed of light is the same in both directions and the distance covered is the same, as you say. Therefore they must have been emitted at different times.
Ok, I can kinda see where this is going. Inferring from the reference frame of the embankment, watching how the light hits the train guy, and extrapolating backwards to infer that his 'now' at that moment must be different from the 'now' of the embankment fellow. The issue of how the man on the train himself perceives this, however still remains:

"At the same time", for things that don't happen in the same place, is not an absolute statement in relativity.
But they were in the same place. (M and M') As the text states: "Just when the flashes of lightning occur, this point M' naturally coincides with the point M"
He could even reach out the window to the other guy, if need be, or to confer with each other that both flashes of lightning are striking in that instant.

#### bengoodspeed

But also some good news: it takes only high-school algebra and a bit of study to understand basic relativistic mechanics, and it's a worthwhile endeavor. Here are two very approachable books on the subject:

Taylor and Wheeler's Spacetime Physics (a classic that emphasizes the geometric nature of the theory from the start; the writing style is idiosyncratic but this book is great)

David Morin's Special Relativity: For the Enthusiastic Beginner (a newer one that does a particularly good job of introducing the relativity of simultaneity, which seems to be tripping you up somewhat)
thanks much

#### bengoodspeed

I have read what I just wrote a few times and pondered it. Yes they were in the same spot when the text states that lightning struck. But they weren't in the same places THAT the lightning struck. So those could be different instants for them, from far away, since they are not in the same stationary frame with each other. Is this the answer? But how am I supposed to assume that when he only just started talking about motion-and-light-measurement experiments and hasn't gotten into anything else about time dilation or light cones or anything else? To make it worse the text even says the lightning struck "just when" when M and M' were together. I guess I was just supposed to mindlessly take it at face value from the perspective of the embankment observer watching the man on the train receive the light rays, and not even question whether it's possible that the man on the train could have had a different experience. ugh einstein you're killing me

In other words, lightning did NOT strike when M' was at M, from his own "now" perspective, even though he was in the same "now" locally with M, for whom lightning WAS striking. Right?

#### FactChecker

Gold Member
2018 Award
But they were in the same place. (M and M') As the text states: "Just when the flashes of lightning occur, this point M' naturally coincides with the point M"
All observers will agree that both flashes reach M at the same time. Those are events at the same place. Likewise, all observers will agree that the flashes do not reach M' at the same time. Those are events that would be at the same place, M', if they reached simultaneously (they don't). But A and B are never in the same place at the same time by anyone's perspective, and those places are where the events happen whose simultaneity is debatable. The observer on the bank will say that the flashes at A and B were simultaneous and the observer on the train will say that the flashes were not simultaneous.

#### FactChecker

Gold Member
2018 Award
If one observer says that two events at the same location happened at the same time, then all observers will agree. Even if their clocks are set differently, they only have one clock time at that location. They see the two events happen at the same time in their clock setting. However, if two events happen at different locations for one observer, then he is comparing two of his clocks to judge if they are simultaneous. Other observers can also have two clocks, synchronized differently, to judge if the events are simultaneous. That is very different from one clock at one location.

#### bengoodspeed

All observers will agree that both flashes reach M at the same time.
Not sure how you can say that unless we're already taking time dilation or length contraction or anything else apart from the constancy of light as a proven concept into account, (which can't be since this is the first chapter that's really even beginning to create a thought experiment to form the basis of it, which is the whole idea of the thought experiment.) Allow me to elaborate: If we take the perspective of the embankment guy and watch the light ray from B hit the train man at a certain point forward from M, then if we assume this is the correct place the light indeed hit him from his own perspective too, (which is what I'm now coming to see is the assumed infallible truth for him from his own perspective too which the text was trying to instill in me. grrr) Then from the train mans perspective at that moment he will see that light ray continue on to M, however measured at his own rate c, therefore reaching M a little bit later since that speed c will be slower relative to the embankment from his perspective than for embankment man.

Going on to just simply say that all observers agree the flashes don't reach M' doesn't really go on to explain your reasoning for how that occurs for M' if the flashes both occurred when he was at M, which is what the text states. And those aren't events at the same place. (M and M' when M' has received any light)

But I see now. A and B were not at M when M and M' were at M, and therefore can be in different moments for each observer at M.

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#### bengoodspeed

I think this makes sense now. I'll have to mull it over a little I suppose but I think it's consistent. Thanks guys

#### bengoodspeed

I still think it's a terribly written book, but maybe it's just that I consider everything too much. If the man on the embankment sees the light rays hit train man at two different points, then I was just supposed to accept that as the infallible truth for all observers and not even question what train man's experience might have been, or keep in mind that einstein specifically stated that both strikes occurred when M' was at M, or the way in which he keeps making it terribly unclear which reference frame is being talked about

but, in having this discussion I have had a moment of pondering that really makes the nature of the way time moves clearer and more intuitive to me, as I imagine the light moving from one observer to another. Which is what I'm after..

#### vanhees71

Gold Member
It's funny, considering the 1920 book is lauded as being meant for the layperson and easy to grasp without confusing math. All it's done is make me frustrated with Einstein for explaining everything in the most haggard and extraneous way hahaha
The problem is the attitude towards math reflected in this quote. Physics becomes confusing without math. Math, to the contrary, is the only way to talk about physics in a non-confusing way. That's why in Einstein's writings there's a minimum of math used to "explain things as simple as possible but not simpler".

A classic, written in 1920, "semi-popularization" of this kind, i.e., using a minimum of math that is even better than Einstein's popularizations is

https://www.amazon.com/dp/B00CC0NSKU/?tag=pfamazon01-20

#### Ibix

But they were in the same place. (M and M')
But the flash emissions aren't, and it's whether or not they are simultaneous that's at issue.
He could even reach out the window to the other guy, if need be, or to confer with each other that both flashes of lightning are striking in that instant.
No he can't - the light from the strikes hasn't reached them. So they have no basis for discussion at the time they pass each other.

#### Ibix

I still think it's a terribly written book,
How to teach this stuff is still a topic of debate. The maths is fairly straightforward (as long as you deal only with constant velocities and instantaneous accelerations), but getting people to accept what the maths means requires them to understand that a lot of their deep-seated understanding of "how the world works" is hopelessly wrong at anything above a tiny fraction of light speed. And then to accept that what the maths says is consistent, just strange. That seems to be hard.

My personal favourite tool is the Minkowski diagram, which is basically just a displacement-time diagram with rules on how to work out what other frames see. But since we take the notion of spacetime seriously, it's actually a Euclidean representation of a slice through spacetime.

#### Janus

Staff Emeritus
Gold Member
 ​ ​

Um, no he wouldn't?

My thinking is this: if the speed of light is constant for all observers, then let us imagine from the perspective of M' (the man on the train) he is stationary while A & B are moving by him. First A passes him, and then when he is in the middle the lightning strikes and pulses light toward him. A & B continue moving by as the light travels, but since he was in the middle (M) at the moment they pulsed, from his view the beams both travel to him at the same exact rate accross the equal distance to him, since there will be no added (or subtracted) velocity due to the points (A&B) motion past him. If there was, that would mean that he could rush towards an object and measure the speed of light as c+v where v is his own velocity relative to it, (or it to him.) hence, VISUALLY at the very least he would see both pulses at the same moment no matter how fast he goes by the embankment?
If you look at things from the Embankment frame, it is obvious that the light from B strikes the train observer first according in this frame. This is a key point, as the Embankment observer and train observer cannot disagree on this fact. ( allowing this to happen would also allow for the creation of physical contradictions. Thus, from in the Train's frame, you have to start from the fact that he doesn't see the flashes at the same time, and being halfway between the emission points (ends of the Train) the travel time for these falshes must be equal and ergo, according to the Train observer, the lightning strikes were not simultaneous.
While it is not brought up in the passage by Einstein, you also have to take into

My second problem is this:

If you described this experiment say with cannons instead of lightning, and had two cannons aimed at M, and had them both fire at the moment lightning strikes them, then this experiments description would hold true, if we considered the arrival of the cannonballs at the observers to be our method of judging simultanaety of firing. This would be because the observer on the train would be adding his velocity towards the cannonball in front of him to its speed toward him, thus it would fly by his face before the cannonball behind him reaches him, just as this chapter describes what light supposedly would do?
But this scenario I've invented is a description involving objects that can be described in a Newtonian manner, (adding velocities, etc) therefore what is the point of this experiment in trying to undermine our Newtonian notions of time? We all know that velocities add to an object in motion so if light did the same thing it would only demonstrate and reinforce the Newtonian dynamics.
The difference here is that with the cannon balls, our train observer could measure a difference in the speeds of the balls relative to the train and himself. When he takes this into account, he would conclude that both cannons were fired simulataneously, even though the balls reached him at different times as one ball was in flight for a longer time. This is different than the light example, where the flashes arrived at different times, but spent equal times "in flight".
With the light example, each observer measures the light as moving at c relative to himself and at v +/-c relative to the other observer, while with the Newtonian cannonball example, both observers agree on how fast the cannonballs are moving with respect to either observer.
I can't possibly think that Relativity is wrong, nor do I, nor can I think that this book wasn't carefully thought through and read and analyzed by many people, yet I can't for the life of me figure out what I'm missing.
This might help. It similar to the train experiment above, except we have arranged things so the light flashes
arrive at the same time as the observers pass each other. Thus both observers see the both flashes at the same time.
Here we have the events in the embankment frame:

The light flashes ( expanding circles) leave the emission point simultaneously, expand outward at c and arrive at the observers just as they meet.
If we switch to the railway car frame:

The light flashes again expand outward at c equally in all directions, but relative to the railway car. The red dots do not stay in the centers of the expanding centers, but move off to the left.
The flashes still arrive at both observers as they pass each other. However, since both flashes have to originate before the observers meet and the train observer is halfway between the dots, The observer has to be closer to the left dot then he is the right dot when either flash is first emitted. Thus the only way for the flash from the right dot to arrive at both observers at the same time as the flash from the left dot, is for it to have left first. Thus according to the train observer, the light flashes could not originated at the same time.

#### Nugatory

Mentor
He could even reach out the window to the other guy, if need be, or to confer with each other that both flashes of lightning are striking in that instant.
Set it up so that the light from the two strikes and the two observers' eyes all meet at the same point in time and space. We could even add an electronic light detector wired so that if it is struck by two flashes of light arriving from opposite directions at the same time, it will trigger a circuit that rings a bell. Both observers agree that the bell rings (of course - the universe would be hopelessly inconsistent otherwise) and that the light from the two strikes reached their eyes at the same time, and that the middle of the train was lined up with the platform observer at that moment.

Now, they ask themselves what time the two lightning strikes happened. If the strike happened at a distance $D$ away from me and the light from the strike reached my eyes at time $T$, my only sensible answer is that the strike happened at time $T-D/c$ because $D/c$ is the time it took for light travelling at speed $c$ to travel the distance $D$.

But when they actually do this calculation, one of them finds that the two strikes are simultaneous and the other finds that they were not. To see this you have to consider the distance traveled by the light from the two flashes, as measured by each observer. We've assumed from the beginning that the two lightning bolts strike the front and back of the train, so that makes the distances for the train observer easy - it's just half the length $L$ of the train, the light from both flashes covers a distance $L/2$ in a time $L/(2c)$ and the train observer properly concludes that the two strikes happened at the same time, $T-L/(2c)$.

But how about the platform observer? To measure the distances they have to know where to start measuring from, so let's say that the lightning bolts leave scorch marks on the tracks when they strike. These marks identify the locations where the light from the strikes started out, so the platform observer uses the distance from scorch mark to themself to calculate the time it took for that light to reach him. But these two scorch marks are not equidistant from the platform observer - they can't be, because they were equidistant from the train observer when they were made, and the train observer wasn't yet lined up with the platform observer. The platform observer finds that light from the two strikes traveled different distances yet reached their eyes at the same time; they properly conclude that the light started out at different times, which is to say that two lightning strikes were not simultaneous.

To calculate the exact results (that is, what are the distances from platform observer to scorch marks, and hence what times platform observer says the strikes happen) we'd need to use the Lorentz transformations and allow for time dilation and length contraction. The argument above is just enough to show that they will disagree about simultaneity, but not by how much.

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#### vanhees71

Gold Member
For an explanation of the train problem in terms of a simple Minkowski diagram, see

#### bengoodspeed

For an explanation of the train problem in terms of a simple Minkowski diagram, see

good stuff

#### bengoodspeed

Set it up so that the light from the two strikes and the two observers' eyes all meet at the same point in time and space. We could even add an electronic light detector wired so that if it is struck by two flashes of light arriving from opposite directions at the same time, it will trigger a circuit that rings a bell. Both observers agree that the bell rings (of course - the universe would be hopelessly inconsistent otherwise) and that the light from the two strikes reached their eyes at the same time, and that the middle of the train was lined up with the platform observer at that moment.

Now, they ask themselves what time the two lightning strikes happened. If the strike happened at a distance $D$ away from me and the light from the strike reached my eyes at time $T$, my only sensible answer is that the strike happened at time $T-D/c$ because $D/c$ is the time it took for light travelling at speed $c$ to travel the distance $D$.

But when they actually do this calculation, one of them finds that the two strikes are simultaneous and the other finds that they were not. To see this you have to consider the distance traveled by the light from the two flashes, as measured by each observer. We've assumed from the beginning that the two lightning bolts strike the front and back of the train, so that makes the distances for the train observer easy - it's just half the length $L$ of the train, the light from both flashes covers a distance $L/2$ in a time $L/(2c)$ and the train observer properly concludes that the two strikes happened at the same time, $T-L/(2c)$.

But how about the platform observer? To measure the distances they have to know where to start measuring from, so let's say that the lightning bolts leave scorch marks on the tracks when they strike. These marks identify the locations where the light from the strikes started out, so the platform observer uses the distance from scorch mark to themself to calculate the time it took for that light to reach him. But these two scorch marks are not equidistant from the platform observer - they can't be, because they were equidistant from the train observer when they were made, and the train observer wasn't yet lined up with the platform observer. The platform observer finds that light from the two strikes traveled different distances yet reached their eyes at the same time; they properly conclude that the light started out at different times, which is to say that two lightning strikes were not simultaneous.

To calculate the exact results (that is, what are the distances from platform observer to scorch marks, and hence what times platform observer says the strikes happen) we'd need to use the Lorentz transformations and allow for time dilation and length contraction. The argument above is just enough to show that they will disagree about simultaneity, but not by how much.
that's a good way of putting it. with the scorch marks especially.

yes, a good way, much better than the text hah

#### bengoodspeed

How to teach this stuff is still a topic of debate. The maths is fairly straightforward (as long as you deal only with constant velocities and instantaneous accelerations), but getting people to accept what the maths means requires them to understand that a lot of their deep-seated understanding of "how the world works" is hopelessly wrong at anything above a tiny fraction of light speed. And then to accept that what the maths says is consistent, just strange. That seems to be hard.

My personal favourite tool is the Minkowski diagram, which is basically just a displacement-time diagram with rules on how to work out what other frames see. But since we take the notion of spacetime seriously, it's actually a Euclidean representation of a slice through spacetime.
minkowski diagram is beautiful once i understand how it slides. And I have become accustomed to picturing time as a sort of 'spatial' dimension that moves through the 3rd dimension even before I picked up this book, and yet this book still confused me

#### bengoodspeed

If you look at things from the Embankment frame, it is obvious that the light from B strikes the train observer first according in this frame. This is a key point, as the Embankment observer and train observer cannot disagree on this fact. ( allowing this to happen would also allow for the creation of physical contradictions. Thus, from in the Train's frame, you have to start from the fact that he doesn't see the flashes at the same time, and being halfway between the emission points (ends of the Train) the travel time for these falshes must be equal and ergo, according to the Train observer, the lightning strikes were not simultaneous.The difference here is that with the cannon balls, our train observer could measure a difference in the speeds of the balls relative to the train and himself. When he takes this into account, he would conclude that both cannons were fired simulataneously, even though the balls reached him at different times as one ball was in flight for a longer time. This is different than the light example, where the flashes arrived at different times, but spent equal times "in flight".
With the light example, each observer measures the light as moving at c relative to himself and at v +/-c relative to the other observer, while with the Newtonian cannonball example, both observers agree on how fast the cannonballs are moving with respect to either observer.
This might help. It similar to the train experiment above, except we have arranged things so the light flashes
arrive at the same time as the observers pass each other. Thus both observers see the both flashes at the same time.
Here we have the events in the embankment frame:
View attachment 243753
The light flashes ( expanding circles) leave the emission point simultaneously, expand outward at c and arrive at the observers just as they meet.
If we switch to the railway car frame:
View attachment 243754
The light flashes again expand outward at c equally in all directions, but relative to the railway car. The red dots do not stay in the centers of the expanding centers, but move off to the left.
The flashes still arrive at both observers as they pass each other. However, since both flashes have to originate before the observers meet and the train observer is halfway between the dots, The observer has to be closer to the left dot then he is the right dot when either flash is first emitted. Thus the only way for the flash from the right dot to arrive at both observers at the same time as the flash from the left dot, is for it to have left first. Thus according to the train observer, the light flashes could not originated at the same time.
very nice animations, this works better than the text too, thank you

"Problems with Einstein's 1920 "Relativity""

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