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I apologize in advance for my severe lack of understanding regarding this topic. Here goes nothing:

My understanding of Einsteins first postulate is that every inertial reference frame is equal. If I'm on a moving train, I should be able to do all the necessary math as if the train were still and the train station moving in the opposite direction.

With this in the back of my mind, I started to consider one of the classic examples of special relativity (at least as far as my education is concerned). If one person gets on a train that is moving close to the speed of light, he will age slower and thereby, by the time the train stops and both people meet each other, be younger than someone who is simply standing still (assuming of course that both started with the same age).

Now apply the aforementioned postulate to the situation. Considering not the train as moving, but the train station as moving, someone inside the train would expect that the people outside, since they are now moving relative to his reference frame, would age slower and thereby be younger than him when both people meet.

If this happens to two people (again, with the same age initially), after they meet again, who would be older? For one person, the other should be younger, but for the other person, the opposite should be true. Which reality is the real one?

Nik Tedig
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  • Does this answer your question? What is the proper way to explain the twin paradox? – John Rennie Apr 01 '22 at 16:25
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    This is the famous twin paradox, about as old as special relativity itself. If Wikipedia doesn't answer your question, one of the >100 questions on this site on the twin paradox probably will. – Puk Apr 01 '22 at 16:27
  • The set-up you describe in your question is vague in an important sense. If two people are together and then move apart at some speed, then they can only meet again if at least one of them reverses their direction of motion. If one of them reverses, while the other continues moving at the same speed, then the one who has reversed will have aged less than the other when they re-meet- that is the so-called 'twin paradox'. If they both reverse their direction of motion (in an exactly symmetrical way) then when they remelt they will each have aged by the same amount. – Marco Ocram Apr 01 '22 at 17:16
  • The effects of SR are entirely symmetrical. If you are on a train at noon passing a friend on a platform, and the train is moving at such a speed that you are time-dilated by 50% relative to the platform, then after a minute on your watch the time on the train will be 12:01 while alongside you on the platform the time will be 12.02. However, after a minute on your friend's watch, the time on the platform will be 12.01 while the time alongside her on the train will be 12.02. So both you and your friend will think your watches are running slow. – Marco Ocram Apr 01 '22 at 17:22
  • In fact neither of your watches is running slower than the other- what is happening is that time on the train is out of synch with time on the platform. That is the relativity of simultaneity, and it is essential that you understand it if you are to understand the rest of SR. – Marco Ocram Apr 01 '22 at 17:24
  • @Puk Thank you. I apologize for not seeing my question's duplicates sooner. I didn't know the proper name for the paradox before your answer, so that's probably why I was under the impression that no resources were available. – Nik Tedig Apr 01 '22 at 18:07

1 Answers1

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Remind that velocity is a vector, and therefore, its direction matters.

We can model the train as a one dimensional motion, and thus the time measured by any observer is:

$ t' = \gamma \Bigl(t - \frac{vx}{c^2}\Bigr) $

For the first case (moving train), the velocity is positive, which means that the time in the train ($t'$) is shorter. For the second case (moving station), the velocity of the station is negative, from the train's perspective. Therefore, $t'$ will be greater than $t$. There is no contradiction, but it's a really good question.

tonetillo 4
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