Suppose there are two stations A and B. There is an observer standing on station B. A train starts from station A and moves towards B at a constant speed V. Relative to the train speed of the observer at station B is V but in opposite direction of train i.e towards station A.

Lets say the train reaches station B after some time. Now since the observer at station B was moving towards point A(relative to the train), can't we say that the observer at B has reached the station A?

This is not something I have heard a lot but looks like I am missing some point here.

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    $\begingroup$ Note that relative to the train, observer A is also moving in the opposite direction of the train. Both A and B are moving in the same direction with the same speed. $\endgroup$ – garyp Apr 18 '17 at 18:32
  • $\begingroup$ Have you tried the experiment of standing at a train station while a train travels toward you, to see whether you end up at the station where the train started? $\endgroup$ – WillO Apr 18 '17 at 21:41
  • $\begingroup$ I don't understand is the observer walking or are they just standing at B? Anyway, from the point of view of the train everything moves, including the stations. They maintain their distance from each other. $\endgroup$ – Javier Apr 19 '17 at 22:54

The dilemma in the question, I guess, is: if everything appears to be moving with respect to each other (disregard the direction), who / what has actually moved?

Relativity tells us that there is no universally absolute frame of reference that can be used to determine which object is moving and which is stationary. The resolution therefore is: sticking to the Inertial frame of reference.

From the point of view of an observer on the train (if there was no way to tell whether the train ever left Station A), they won't be able to determine whether it was their train that moved towards Station B or the observer from Station B walked down to Station A. Likewise, from the point of view of a stationary observer on Station B (if their external view was occluded), they won't be able to determine whether their station moved towards the train (halfway? All the way up to Station A?) or the other way round.

The above narration could sound a bit absurd when dealing with things in the frame of reference (earth) that is naturally local to us and we assume parts of it to be somehow detached, which isn't really the case. However, a similar example could make much more sense if we considered another frame of reference, for instance, the earth-moon system.

Let's call one of earth's longitude as Station L and we then try to determine which of the two — earth or the moon — were moving when the moon passes by Station L.

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Let's look at the interpretation of the observers from three different point of views:

  • An observer on the moon: From a vantage point on the moon, the earth appears to rotate in the moon sky, but stays at nearly the same spot all through. An observer on the moon would therefore conclude that it was Earth's rotation that caused Station L to pass by the moon.

  • An observer on earth: Since the moon appears to move across the sky to observers on earth, the conclusion would read that moon's path in its orbit took it past Station L.

  • An external observer: An external observer would notice that both earth and moon were in motion (with respect to each other) and therefore it can't be said that any one of them was stationary when the said event of moon passing by a certain longitude occurred.

So, in the absence of an absolute frame of reference, every observer would make the measurements and derive the conclusions based on their own local reference frames, and each of them would be equally right — Equivalence Principle. The only thing then required to get the consistent results would be to ascertain that any conclusions that are derived pertain to that very reference frame which the assumptions were initially made and the experiments were carried out for.

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