Simultaneity on a moving train

[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.