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Einstein’s train-lightening thought experiment contains only inertial motion so SR says we can ascribe relative motion and relative rest to either reference frame. Although it is not stated in the description, we naturally ascribe motion to the train and rest to the landscape. But we are free to do the opposite.

Picture the train at rest while the landscape — including the tracks and the standing observer — rush past the train to its rear. The lightening strikes fore and aft in such a way that the conductor, being at the midpoint of the strikes, sees them as simultaneous. The standing observer, rushing toward the train’s rear, sees the rear strike first because of the shorter distance the flash must cover to reach him.

It seems that we have violated a major tenet of SR. We have caused two different physical outcomes merely by arbitrarily assigning motion and rest in accordance with SR. If the train is moving relative to the landscape the conductor sees the front flash first. If the train is at rest relative to a moving landscape the conductor sees the flashes as simultaneous. Two different physical results depending only on how we arbitrarily assign movement and rest to the two reference frames.

What is wrong with this argument?

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closed as off-topic by WillO, GiorgioP, ZeroTheHero, Jon Custer, M. Enns Mar 26 at 23:59

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    $\begingroup$ You can make the post self-contained by including a description of the thought experiment. $\endgroup$ – my2cts Mar 24 at 3:21
  • $\begingroup$ The answer by myself and CRDrost are essentially saying the same thing just in different language. I think either sufficiently answers your question. $\endgroup$ – Aaron Stevens Mar 24 at 10:41
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What is wrong with your version of the thought experiment is simply that you are not taking relativity sufficiently seriously.

Relativity says that the meaning of simultaneity is relative. That means we need to specify who thinks two things are simultaneous.

If the conductor thinks the lightning struck both sides of the train simultaneously, then at some later time, he or she will see both flashes as simultaneous. The person on the ground will see a time gap between the two flashes, and will not think that the lightning hit both sides of the train simultaneously. They are both right, because their definitions of “simultaneous” are different.

If the person on the ground thinks the lightning struck both sides of the train simultaneously, then at some later time, he or she will see both flashes as simultaneous. The conductor on the train will see a time gap between the two flashes, and will not think that the lightning hit both sides of the train simultaneously. They are both right, because their definitions of “simultaneous” are different.

When you are whimsically transferring between these two situations, you are blithely oblivious that for the conductor to see both flashes at the same time, the lightning strikes need to be fundamentally happening at different points in spacetime than they were when the person on the ground saw them and concluded that these events were simultaneous.

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The issue is that you are actually switching between two versions of the thought experiment.

One person (Alice) will see the flashes as simultaneous. One person (Bob) will see the flashes as occurring at different times (note I am not saying anything about on the ground or on the train). Furthermore, Alice will agree that the light reaches Bob at different times, and Bob will agree that the light reaches Alice at the same time. However, Alice will tell Bob "The light actually was emitted at the same time, but you moved into one flash first" whereas Bob will say to Alice "No! The light was emitted at different times, but you moved back into the later one so that your saw them at the same time."

The differing conclusions arise from each person thinking they are at rest and because the speed of light is independent of the speed of the source. Bob sees the the light at different times, and since he thinks he is at rest with the light traveling the same distance concludes they happen at different times. Alice sees the the light at the same time, and since she thinks she is at rest with the light traveling the same distance concludes they happen at the same time.

What you are doing in your question is changing reference frames while also interchanging the Alice and Bob roles. Thus you get different results. You are comparing two different (yet very similar) scenarios.

In other words, you are trying to use a sort of relativity of perception (which isn't a thing) rather than the actual relativity of simultaneity. The perceptions aren't the issue. The issue is between who thinks they are at rest and then applies this reasoning to their perception of when they see the light. This is sometimes not stated in these thought experiments. We assume the observers have already done the calculations based on the perceptions. We don't have ignorant observers here.

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