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In other words, does the effect of relativistic length contraction affect all dimension of the moving object or only the direction parallel to the movement?

And if the effect affects only one dimension, then does the observer who aligning with the direction experience time dilation of other dimension?

Suppose I have a spaceship with laser beam bouncing between the parallel mirror inside vacuum chamber perpendicular to the moving of spaceship

enter image description here

Setup as the picture above, the red line is laser in vacuum chamber, should the observer see the length contraction between mirror, making the laser path smaller ?

And also, will the observer see speed of red laser slower than $c$ ?

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  • $\begingroup$ I don't see a general relativity aspect to your question. $\endgroup$
    – puppetsock
    Jan 10 '20 at 18:26
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You will see only the direction along the motion contracted, so the spaceship will look flatter and the distance between mirrors not contracted. The speed of light (laser or whatever) will be unchanged regardless of the light's direction of motion.

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  • $\begingroup$ The speed will be unchanged. But the observer sees moving mirrors. Therefore, the light has farther to go to get from one mirror to the other. And so, the observer will see the frequency of light bouncing between the mirrors as slower. That's the other side of the Lorentz transform. Those on the ship will also see light moving at its normal speed. But they will see a higher frequency than the observer behind the ship. It's essentially one arm of a Michelson-Morely experiment. $\endgroup$
    – puppetsock
    Jan 10 '20 at 18:30

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