If I have a closed box of length 299,792,458 metres fitted with mirrors on opposite sides inside the box that are reflecting light vertically (up down) again and again, then what will happen if I move the box to my right while the photon is halfway between the mirrors? Will the photon move with the box? If so, then how? The photon takes one second to travel from one mirror to another. What will happen if i move the box in the direction which light is going as in the diagram. Will the photon never reach the top mirror?Closed box with mirrors

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    $\begingroup$ The box need not be long. A laser is such a box, with one of the mirrors partially transparent. $\endgroup$
    – mmesser314
    Jan 21 '18 at 19:47
  • $\begingroup$ Actually what i asked is that photon reflects vertically -up down not right left $\endgroup$
    – Hark
    Jan 22 '18 at 3:15
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    $\begingroup$ Short answer: no, the photon will not move with the box when you move the box sideways. The photon will hit one of the side walls and (presumably) be absorbed. $\endgroup$ Jan 22 '18 at 4:31
  • $\begingroup$ I think the OP is asking about accelerating frames in relativity. $\endgroup$
    – Shing
    Jan 22 '18 at 10:52
  • $\begingroup$ And what will happen if i move the box vertically upwards at the speed of light while the photon is moving upwards like in the diagram. Will the photon never reach the top mirror? $\endgroup$
    – Hark
    Jan 22 '18 at 10:55

Spacetime diagram of photon bouncing in a moved box.

The easiest way of seeing what happens is to draw a space-time diagram. The stationary box walls form two vertical parallel lines with a 45 degree zigzag path for the photon as it bounces between them.

When you move the box the photon will not change speed - relativity tells us that light always move at lightspeed no matter what inertial coordinate system you use. The result is just that the approach to one side gets delayed (as seen by us who are not moving with the box) since the wall is receding as the photon tries to catch up, and the approach to the other side speeded up since the wall is approaching while the photon moves towards it. Overall there will be fewer bounces as the box is moving: we would say there has been a time dilation for the box.

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    $\begingroup$ I understood the question as moving the box orthogonally to the photon's way, not parallel. $\endgroup$ Jan 21 '18 at 22:24
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    $\begingroup$ @PaŭloEbermann that is correct, and is what the diagram shows. It’s a space time diagram. $\endgroup$
    – Tim
    Jan 21 '18 at 23:39
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    $\begingroup$ @Steve The fact that it violates your intuition doesn't make it wrong and experimental data agrees with all the prediction made under that assumption. Empirical results trump intuition. $\endgroup$ Jan 22 '18 at 2:20
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    $\begingroup$ I also think this doesn't answer the question as asked. The box is moving perpendicular to the light, so the light will end up colliding with a transverse side -- a long one without a mirror. It won't continue bouncing back and forth as shown in this diagram. $\endgroup$ Jan 22 '18 at 3:43
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    $\begingroup$ @Tim: If PauloEbermann is correct, then the diagram can't be correct, becaus Paulo's interpretation requires two spatial dimensions, and the diagram shows only one. $\endgroup$
    – WillO
    Jan 22 '18 at 5:42

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