Train Simulation: Observer A and B Contradiction?

[Besso]

TL;DR Summary

Simultaneity measurement on train equipped with synchronized clocks at each end.

I have not seen this exact configuration discussed. Observer A in middle of train. Observer B at station. Both A and B think the other is moving. Observer A synchronizes two clocks and puts one at each end of train. Lightning strikes both clocks stopping them when A passes B. B says strikes were simultaneous. A says flash from front is seen first so must have occurred first. But then A checks clocks. Clocks read that they were stopped at the same instant. Contradiction?

 

[Ibix]

Contradiction?

I think you have specified that the clocks stopped simultaneously according to B, but read as if they were stopped simultaneously according to A. So the problem is that you are contradicting yourself (i.e. your result is impossible given the setup you specified), not with relativity.

 

[PeroK]

TL;DR Summary: Simultaneity measurement on train equipped with synchronized clocks at each end.

I have not seen this exact configuration discussed. Observer A in middle of train. Observer B at station. Both A and B think the other is moving.

What does that mean? Do you mean the train and station are moving relative to each other?

Observer A synchronizes two clocks and puts one at each end of train.

Okay.

Lightning strikes both clocks stopping them when A passes B.

"When" according to the train frame or the platfform frame?

B says strikes were simultaneous.

They are, if they were simultaneous in the platform frame.

A says flash from front is seen first so must have occurred first.

If the strikes are simultaneous in the platform frame, then in the train frame the strike at front of the train happens first. You can calculate this from the Lorentz Transformation.

But then A checks clocks. Clocks read that they were stopped at the same instant.

Same instant according to which frame? If the same instant in the platform frame, then the front clock was stopped first in the train frame.

Contradiction?

No. Only a basic lack of understanding of reference frames.

 

[Sagittarius A-Star]

TL;DR Summary: Simultaneity measurement on train equipped with synchronized clocks at each end.

You can find a presumably correct description and solution for this scenario in chapter 1.3.1 "Loss of simultaneity" (page 12), in the book "Special Relativity: For the Enthusiastic Beginner" (D. Morin), see free PDF link "Chapter 1" under:
https://scholar.harvard.edu/david-morin/special-relativity

 

[PAllen]

TL;DR Summary: Simultaneity measurement on train equipped with synchronized clocks at each end.

I have not seen this exact configuration discussed. Observer A in middle of train. Observer B at station. Both A and B think the other is moving. Observer A synchronizes two clocks and puts one at each end of train. Lightning strikes both clocks stopping them when A passes B. B says strikes were simultaneous. A says flash from front is seen first so must have occurred first. But then A checks clocks. Clocks read that they were stopped at the same instant. Contradiction?

I thought you died in 1955 (Einstein's early friend and collaborator, Michele Besso).

 

[FactChecker]

TL;DR Summary: Simultaneity measurement on train equipped with synchronized clocks at each end.

I have not seen this exact configuration discussed. Observer A in middle of train. Observer B at station. Both A and B think the other is moving. Observer A synchronizes two clocks and puts one at each end of train. Lightning strikes both clocks stopping them when A passes B. B says strikes were simultaneous. A says flash from front is seen first so must have occurred first. But then A checks clocks. Clocks read that they were stopped at the same instant. Contradiction?

This is impossible. If A synchronized his co-moving clocks and he sees the front flash was first, then A's clocks can not indicate the same time of the strikes.

 

[Ibix]

I thought you died in 1955 (Einstein's early friend and collaborator, Michele Besso).

Well, it makes a change from endless variations on Einstein, Feynman and Hawking.

 

[Besso]

What does that mean? Do you mean the train and station are moving relative to each other?

Okay.

"When" according to the train frame or the platfform frame?

They are, if they were simultaneous in the platform frame.

If the strikes are simultaneous in the platform frame, then in the train frame the strike at front of the train happens first. You can calculate this from the Lorentz Transformation.

Same instant according to which frame? If the same instant in the platform frame, then the front clock was stopped first in the train frame.

No. Only a basic lack of understanding of reference frames.

Thanks for the comments. I know this can be unraveled. Just trying to be provocative with the “contradiction?” comment. But it would be helpful to me to discuss a little more detail about what’s happening. As the frames pass, the lightning bolts strike in B’s frame. What if B has two clocks that were just below the train‘s two clocks at the instant of the strikes which show B that the bolts struck simultaneously in B’s frame. That is, both pairs of clocks are lined up and receive the strikes at the same instant. I know this last statement is probably an impossible configuration, but I can’t quite visualize what is happening in detail.

 

[PeroK]

Thanks for the comments. I know this can be unraveled. Just trying to be provocative with the “contradiction?” comment. But it would be helpful to me to discuss a little more detail about what’s happening. As the frames pass, the lightning bolts strike in B’s frame. What if B has two clocks that were just below the train‘s two clocks at the instant of the strikes which show B that the bolts struck simultaneously in B’s frame. That is, both pairs of clocks are lined up and receive the strikes at the same instant. I know this last statement is probably an impossible configuration, but I can’t quite visualize what is happening in detail.

That essentially is the heart of SR. One way to look at it is to use the concept of length contraction, if you are familiar with that.

We have a train of length $l$ and a platform of length $L$, say. If $l = L$ then in the platform frame the train will be shorter than the platform. And in the train frame the platform will be shorter than the train. The clocks at the ends of the train and ends of the platform won't line up in that case.

Suppose now you make the train longer, so that in the platform frame it just fits neatly with the length of the platform and the two sets of clocks do indeed line up in the platform frame.

But, in the train frame, the platform is now even shorter than the train and the two sets of clocks don't line up. The ones at the front line up first, when the front of the train reaches the far end of the platform (in the train frame). The rear ones line up later, when the rear of the train reaches the near end of the platform.

This highlights the relativity of simultaneity, and shows that you cannot have a pair of clocks at rest in one frame and synchonised in both frames. If they are synchronised in one frame, they are out of sync in the other.

 

[Ibix]

You mean that you want the lightning bolts to be simultaneous in both A's frame and B's? Yes, that's impossible.

The best way to visualise relativity is a Minkowski diagram. I produced an interactive diagram uears ago. Go to https://ibises.org.uk/Minkowski.html, scroll near the bottom, and click "Make Einstein's train". You get a displacement-time diagram showing the positions of the embankment observer and clocks (black) and train observer and clocks (green) and the light from the lightning flashes travelling to the center. Tap on a green line and click "Boost to selected line rest frame" to animate a frame change.

 

[Besso]

That essentially is the heart of SR. One way to look at it is to use the concept of length contraction, if you are familiar with that.

We have a train of length $l$ and a platform of length $L$, say. If $l = L$ then in the platform frame the train will be shorter than the platform. And in the train frame the platform will be shorter than the train. The clocks at the ends of the train and ends of the platform won't line up in that case.

Suppose now you make the train longer, so that in the platform frame it just fits neatly with the length of the platform and the two sets of clocks do indeed line up in the platform frame.

But, in the train frame, the platform is now even shorter than the train and the two sets of clocks don't line up. The ones at the front line up first, when the front of the train reaches the far end of the platform (in the train frame). The rear ones line up later, when the rear of the train reaches the near end of the platform.

This highlights the relativity of simultaneity, and shows that you cannot have a pair of clocks at rest in one frame and synchonised in both frames. If they are synchronised in one frame, they are out of sync in the other.

Thanks. This kind of detail is helpful.

 

[Mister T]

TL;DR Summary: Simultaneity measurement on train equipped with synchronized clocks at each end.

Clocks read that they were stopped at the same instant. Contradiction?

No. The clocks reading the same is explained by B, that they were in fact never synchronized properly in B's rest frame.