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Okay, so Einstein is on a train looking at a mirror. The train is moving at $c - 1 \frac ms$. Einstein is facing in the direction of motion.

All along the side of the train are stationary clocks. There are also clocks on the train, except that they show the same time as the stationary clocks instead of the trains time. Since the trains velocity is constant, there is only a constant factor of time dilation.

The distance between Einstein and the mirror, as measured from a stationary rod, is $1m$. It is obviously greater as measured on the train.

Light is emitted from Einstein face. As measured by stationary clocks, it takes $1s$ to hit the mirror. It is then reflected back to Einstein nearly instantaneously. The clocks on the train but in sync with stationary therefore read a greater amount of time for the light going from Einstein to the mirror then from the mirror to Einstein though. This is true of time from the train's reference frame as well, since time dilation is only a constant multiplicative factor.

This is a paradox though! Light travels the same distant in the same amount of time.

What is the resolution to this paradox?

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  • $\begingroup$ Could you explain the situation in more details? $\endgroup$ Commented Aug 12, 2015 at 2:37
  • $\begingroup$ @Hindsight I thought I was. What haven't I specified? $\endgroup$ Commented Aug 12, 2015 at 2:42
  • $\begingroup$ @diracpaul From Einstein's frame, it is going faster in one direction, apparently. $\endgroup$ Commented Aug 12, 2015 at 21:39

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The clocks are all in sync in the ground frame, but they are not in sync in the train's frame. An observer on the train would think that the clocks in the front of the train are ahead, while those to the rear are behind.

Measuring the forward traveling beam against the nearby clocks will show a long time difference, while measuring the rearward traveling beam shows a shorter elapsed time. The observer would think the actual time for the forward and rearward beams was the same and that the difference is because the clocks are not synchronized (in the observer's frame).

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