I Simultaneity on a moving train

[sdkfz]

... Now whatever criteria Einstein used that he thought could establish for an observer on the train and one on the embankment that M and M' are at the same place at the same time, the same criteria could be used to establish that A and A' and B and B' are at the same place at the same time. So A', M', and B' align with A and M and B at the same time. ...

Don't forget the relative movement between M and M', and the finite speed of light. By the time the light reaches M and M' from A/A' and B/B', M and M' will no longer be adjacent. The situation at the start is not the situation a moment later.

...
Now we might imagine 4 clocks all set at 0 and made to trigger when they are hit by a light coming from A and B and to mark that moment. So a second way for an observer at M to tell if A and B were simultaneous would be to walk over to A and B, after the fact and see if they were triggered at the same time. And the same for an observer on the train at M'. He could decide not to trust his eyes but to go and examine the two clocks and use them to establish simultaneity. ...

Your setup here isn't clear to me, but I'd note that the issue has never been that M disagrees with what M' thinks, or vice versa. That is, if M' considers the events to be simultaneous, M may say "no they were not", but can agree that "well, they were for you".

A common way to visualise this is with M and M' wearing bombs that will explode if the light from the events reaches them at the same time. If the flashes are simultaneous for M', he or she explodes. M can see that, they can't claim the explosion did not occur! (Note that M did not explode in this case.)

 

[west-river]

Interesting! Thanks again. All this is very useful to me in my search for understanding and is much appreciated.

 

[Janus]

"Now, the next important event is the clock T reaching clock P2. If we analyse things in the platform frame we know that clock T is time-dilated. Let's assume by a factor of 0.8. Let's assume also that the train takes 1 second (in the platform frame) to travel from P1 to P2. Then, when T passes P2 we know that:
Clock P2 reads $1s$ and clock $T$ reads $0.8s$."

Does the fact that platform analysis shows clock T will read 0.8s and not 1s show that clock T will actually read 0.8s? -- I am thinking as a philosopher who has just trying to understand physics, so please take my comments and questions with a grain of salt.

"And, therefore, despite being synchronised in the platform frame, the clocks P1 and P2 are not synchronised in the train frame. Therefore, simultaneity is reference frame dependent."

Again, I wonder at my own thinking, but isn't an alternative reading of your argument be SR is incorrect in part?

I have another diagram for what may possibly be a distantly related thought. The image below was distorted in making a photo, but the idea should be clear.

It seems to me there are at least two ways of measuring simultaneity for a person on the platform and a person on the train. Start with the train observer: He could wait for the light to hit him at M' and make a judgment which would lead to him saying that A and B are not simultaneous (Einstein's point, I think). And the person on the bank at M can also judge in at least two ways. He can wait for the the light from A and B to hit him and then judge, in which case A and B will seem simultaneous.

View attachment 236784

Now whatever criteria Einstein used that he thought could establish for an observer on the train and one on the embankment that M and M' are at the same place at the same time, the same criteria could be used to establish that A and A' and B and B' are at the same place at the same time. So A', M', and B' align with A and M and B at the same time.

Now we might imagine 4 clocks all set at 0 and made to trigger when they are hit by a light coming from A and B and to mark that moment. So a second way for an observer at M to tell if A and B were simultaneous would be to walk over to A and B, after the fact and see if they were triggered at the same time. And the same for an observer on the train at M'. He could decide not to trust his eyes but to go and examine the two clocks and use them to establish simultaneity.

In this case it seems to me, both observers will pronounce that A and B were simultaneous, even if they will think the start and finish times of A and B are different.

Now you are going to have to deal with the length contraction issue I mentioned earlier.

Here's the original train experiment as it occurs according to the embankment.

Flashes are emitted from the red dots as the ends of the train reaches them and the trian observer is next to the embankment observer. Train observer runs into right flash before left flash catches up to him. One thing to keep in mind is that since the train is in motion with respect to the embankment, the train is length contracted according to the embankment and this length contraction is what allows the train to fit exactly between the red dots.

However, according to anyone at rest with respect to the train, the train is not length contracted, but instead, it is the embankment that it in motion and length contracted. Thus the train cannot fit between the red dots, the front of the train hit the right red dot before the back of the train reaches the left red dot. Since both the train and embankment have to agree that the flashes are emitted when the ends of the trains pass the red dots, the flashes cannot be emitted at the same time according to the train, like this:

Note that according to the train, the flashes still meet a the the embankment observer. Also note that the midpoint of the train is next to the same point of the tracks when each the light flashes reaches him in both animations.
A and A' being next to each other is simultaneous with B and B' being next to each other in the embankment frame, but this is not true for the Train frame. when A and A' are next to each other B and B' are apart,and B and B' are together A nd A' are apart.

 

[FactChecker]

Now whatever criteria Einstein used that he thought could establish for an observer on the train and one on the embankment that M and M' are at the same place at the same time, the same criteria could be used to establish that A and A' and B and B' are at the same place at the same time. So A', M', and B' align with A and M and B at the same time. (emphasis mine)

This is wrong. "at the same time" is dependent on the reference frame. Observer M will say that the clocks at A' and B' have been set out of synchronization. And M' will say the same thing about A and B. They can not agree on what "the same time" means.

Suppose M and M' both synchronize their respective clocks at the ends by flashing a light and saying that time 0 is when the light reaches the ends. Then M would say that M' has synchronized the A' and B' clocks wrong with clock B' time 0 being too late compared to clock A' time 0 (clock B' ran away from the light source and clock A' ran toward it). Similarly, M' would say that M has synchronized the A and B clocks wrong with clock A time 0 being too late compared to clock B time 0 (clock A ran away from the light source and clock B ran toward it). This is the root cause of the problem with agreeing on simultaneity.

You might object that there are better ways for M and M' to synchronize their respective clocks at the ends of the train. But the experiments measuring the speed of light contradict that. No one was ever able to detect any different speed of light no matter what the velocity of motion was. That means that any physical method of synchronizing clocks kept coming up with the same synchronization that they would have had if they had used light. It shows that synchronizing clocks using light travel time is deeply compatible all physical processes.
And you might say, as your diagram implies, that "at the same time" means when all the points are side-by-side. But don't forget that observer M sees that the length of the train has gotten shorter. So they no longer line up as you show it. Some points are side-by-side at different times from other points -- another example of "simultaneous" not being well-defined.
You can see how closely intertwined all this is. The mathematics and logic of SR all works together and is consistent. When thinking about it, one can not ignore any of its effects on simultaneity, time, or length.

 

[PeroK]

Interesting! Thanks again. All this is very useful to me in my search for understanding and is much appreciated.

If you really want to learn SR, then there is no substitute for a good-quality textbook. My recommendation would be Helliwell:

https://www.goodreads.com/book/show/6453378-special-relativity

You do need some high-school maths, of course, but the main conceptual issues require very little in the way of prerequisites.

 

[west-river]

I have just now put in an order for the Helliwell book (see the last post of PeroK)

If it isn't too much to ask, I would like to get your opinion about my method of learning SR up to here. A few months ago I downloaded a pdf of Robert W. Lawson's authorized translation of the 1916 "Relativity: The Special and General Theory." I read carefully the first 12 sections or so but most carefully Section 8 "On the Idea of Time in Physics" and Section 9 "The Relativity of Simultaneity." I always like, in doing any research, to start with original sources. I had some problems "keeping up with" some of the ideas in earlier sections (and in later ones), but I felt comfortable with the ideas in 8 and 9, felt I saw what Einstein was getting at, and felt I saw its genius and its truth. I did have two questions both of which I asked in this forum. From the responses, it seems I do not understand even what I thought was clear to me.

I have now ordered the Helliwell book. Is there a flaw in my approach, that is, starting with the original text? If there is, then maybe the textbook will help. However, I am very aware of my own limitations in many fields, in particular, in physics. I took undergraduate Physics and got either a B or C (I can't remember). If it was a B, I was lucky, as I never felt I grasped the basic ideas of mechanics (except, strangely enough, I did well on the section on Relativity in the class). As an aside, I have been playing the Japanese game of Go for maybe 5 years now. No matter how hard I try, I am not able to advance beyond a rather elementary level. Therefore, I am used to the idea that I have limitations that I can not overcome, even though I have decent abilities in my own field. So I am asking here your opinion about my method, that is, of starting with the original text. Is there a problem inherent in this that reading Helliwell might correct? I am confused if the problem is my approach or my inherent limitations.

In addition, I ask your patience to look at one more of my diagrams. I read every one of your posts written in this chain. I did not understand much of what you wrote, but I think I did understand a good chunk of it. (I had not reached the sections on contraction of time and space in Einstein's original text I have been studying, as I have been trying to go slowly and absorb only what I can). (It doesn't make sense to me that I have to read a few sections ahead in order to understand what I have been reading in these earlier sections.)

I sincerely do not want to ask you to respond to something that is, to you, clearly wrong. I don't like persistent elementary questions in my own field especially if they feel obstinate. I will not feel bad in any way if you feel you have written enough posts and have no wish to beat a dead horse, as it were. With this said, I think the following diagram expresses my thoughts more clearly and would like to know if there is a feeling I am understanding more or not.

I have dropped all references to clocks. Mirrors A', B', A, and B are set at 90 degree angles, so light hitting them is reflected to Mirror M and Mirror M'. I may still be missing something critical that you have all said more than once, but it seems to me that, according to Einstein's original text, it is possible that two strokes of lightening, one at A and one at B are simultaneous for an observer at M (that is, "with reference to the railway embankment") (we can imagine him with explosives attached that will go off when two beams of light hit Mirror M at the same time, and, in the way I have set it up, he does explode). This is true whether or not there is a train.

But now assume there is the train that is moving to the right in the picture. When lightning hits A and B (simultaneously, with reference to the embankment, it also moves towards the train. Clearly, if the train is moving, then A beam will arrive at M' after B beam arrives there, and M''s explosives will not be set off as the beams aren't arriving to him simultaneously.

But the two beams also will hit the two mirrors, Mirror A' and Mirror B'. It gets a little foggy for me here, but it seems to me that the reflected lights off these two mirrors will arrive at Mirror M' at the same time and set off the explosive at M'. So the light going directly from A and B to M' will not set off the explosive, but the light viewed indirectly, via Mirrors A' and B', will set it off. So the observers at M and M' will both suffer from an explosion, though (again this is foggy to me) neither would experience the other's explosion (if they were able to) as simultaneous with his own.

Thanks. Onward to Helliwell.

 

[sdkfz]

From the point of view of M, M' is moving towards B' and away from A'.

Even if, according to M, the lights somehow hit mirrors A' and B' simultaneously, they can't hit M' simultaneously.

 

[FactChecker]

I felt comfortable with the ideas in 8 and 9, felt I saw what Einstein was getting at, and felt I saw its genius and its truth. I did have two questions both of which I asked in this forum. From the responses, it seems I do not understand even what I thought was clear to me.

That is common. Things can be explained in one way that seems very clear and it is not till one looks at it in other ways that the complexity and consequences are apparent and confusing.

View attachment 236835

I have dropped all references to clocks.

IMHO, this is a mistake. So much of this depends on how an observer would set synchronized clocks in his inertial reference and how an observer in another frame would say that those clocks are set wrong.

Mirrors A', B', A, and B are set at 90 degree angles, so light hitting them is reflected to Mirror M and Mirror M'. I may still be missing something critical that you have all said more than once, but it seems to me that, according to Einstein's original text, it is possible that two strokes of lightening, one at A and one at B are simultaneous for an observer at M (that is, "with reference to the railway embankment") (we can imagine him with explosives attached that will go off when two beams of light hit Mirror M at the same time, and, in the way I have set it up, he does explode). This is true whether or not there is a train.

Yes

But now assume there is the train that is moving to the right in the picture. When lightning hits A and B (simultaneously, with reference to the embankment, it also moves towards the train. Clearly, if the train is moving, then A beam will arrive at M' after B beam arrives there, and M''s explosives will not be set off as the beams aren't arriving to him simultaneously.

But the two beams also will hit the two mirrors, Mirror A' and Mirror B'. It gets a little foggy for me here, but it seems to me that the reflected lights off these two mirrors will arrive at Mirror M' at the same time and set off the explosive at M'.

I disagree. M will see M' moving and the lights will not hit M' at the same time. M' will think that the lights did not hit A' and B' simultaneously, so he does not expect them to reach him at the same time. So both M and M' agree that M' will not explode.

So the light going directly from A and B to M' will not set off the explosive, but the light viewed indirectly, via Mirrors A' and B', will set it off.

That was wrong.

So the observers at M and M' will both suffer from an explosion, though (again this is foggy to me) neither would experience the other's explosion (if they were able to) as simultaneous with his own.

I don't understand what you are saying here.

 

[Ibix]

were synchronized

Which clocks were synchronised with which clocks according to who? Does each observer have a pair of clocks they synchronised themselves? Then each observer will say that the other observer's pair aren't correctly synchronised.

That is the one thing you are supposed to take away from this experiment.

 

[west-river]

Thanks for your response. Appreciated.

That is common. Things can be explained in one way that seems very clear and it is not till one looks at it in other ways that the complexity and consequences are apparent and confusing.IMHO, this is a mistake. So much of this depends on how an observer would set synchronized clocks in his inertial reference and how an observer in another frame would say that those clocks are set wrong.

Regarding clocks: What if, before the train set out, the clocks were made and set and synchronized by M and M'? Now the train sets out with clocks made and set and synchronized by both. Both M and M' know that, at least initially, the clocks were synchronized, because they synchronized them together. If possible, is this relevant to anything above?

Yes

OK

I disagree. M will see M' moving and the lights will not hit M' at the same time. M' will think that the lights did not hit A' and B' simultaneously, so he does not expect them to reach him at the same time. So both M and M' agree that M' will not explode.

But there is a separate set of beams from A and B that hit the mirrors, Mirror A' and Mirror B'. It is my understanding of such a situation that they would reflect their lights towards Mirror M' and would meet at the same time and set off the explosion.

That was wrong.I don't understand what you are saying here.

What I meant here is that there would be an explosion at M and one at M' (given the mirror reflection scenario), but neither M nor M' (if they were not damaged by the explosions) would think the other explosion happened at the same time.

 

[FactChecker]

Regarding clocks: What if, before the train set out, the clocks were made and set and synchronized by M and M'? Now the train sets out with clocks made and set and synchronized by both. Both M and M' know that, at least initially, the clocks were synchronized, because they synchronized them together. If possible, is this relevant to anything above?

That would be a another attempt to synchronize clocks using a different method. That would open the can of worms regarding what happens during acceleration. But the result of all the experiments that Einstein was trying to explain was that no valid method showed a change in the speed of light. So any valid method will end up with the same synchronization that one would get by M' shining light beams at A' and B'. The result of that would be that M would say that the M' clocks at A' and B' were unsynchronized.

 

[west-river]

Thanks.