Einstein's light clock with mirrors experiment involves mirrors on top and bottom of a moving train and light reflecting back and forth. To a stationary observer, it would seem that the light is traveling more distance and since the speed of light is the same for both stationary and moving observors, we conclude that moving clock runs slower relatively. My doubt is what if we are placing the mirrors outside the train horizontally to the train? Assume that the train is made of glass. Now to the stationary observer, the light beam would be traveling in a straight line but to the observer in the train, the light beam would move in a curved path and hence covers more distance. Hence to the stationary observer, time moves at the same speed inside the train but for the observer inside the train, time moves slower. Could you please explain the difference in the point of view of the stationary observer in the 2 experiments and doesn't it conflict with each other?

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    $\begingroup$ Why would the light move in a curved path in the train’s frame? Putting the mirrors inside or outside doesn’t change anything. $\endgroup$ – Dale Nov 2 '19 at 3:27
  • $\begingroup$ By "outside the train" do you mean that the light clock is stationary? $\endgroup$ – probably_someone Nov 2 '19 at 4:01
  • $\begingroup$ @Dale since the observer inside the train would see the light move diagonally due to the motion of the train $\endgroup$ – Shamy Nov 2 '19 at 4:58
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    $\begingroup$ @probably_someone yes the light clock in stationary $\endgroup$ – Shamy Nov 2 '19 at 4:58
  • $\begingroup$ Hey @Shamy, I don't understand your reply to Dale's question. If a person at rest inside the train turned on a torch briefly to let out a photon, then that person would observe the photon to go up and down only (Train frame is an inertial frame : therefore, the emitted photon would behave the same way it behaves when a person on the ground turns on the torch briefly). Mirror's motion is not going to determine the photon's path. $\endgroup$ – Ajay Mohan Nov 2 '19 at 6:33

To the observer standing on the ground, time moves slower on the train (since the light bouncing in a light clock on a train, which is moving in this observer's frame, has to cover a longer distance between bounces). To an observer standing in the train, time moves slower on the ground (since the light bouncing in a light clock on the ground, which is moving in this observer's frame, has to cover a longer distance between bounces).

There is no contradiction because you can't be in two reference frames at once. You cannot be both moving and not moving in any one reference frame.

  • $\begingroup$ but shouldn't time always move slower then you are in motion? $\endgroup$ – Shamy Nov 2 '19 at 17:14
  • $\begingroup$ @Shamy How do you know you're in motion? What experimental test can you do to verify this? $\endgroup$ – probably_someone Nov 2 '19 at 17:27

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