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Assume you're in outer-space and a spaceship flies past you at a very high speed. In the ship, the pilot is shooting a light beam from the ground to the ceiling, and a mirror on the ceiling reflects the beam back to the ground. The pilot sees the beam move in a straight line going up and down, but you would see the beam moving in a triangle path going up then down (due to the ship quickly flying past you).

The speed of light is constant, but the length of the beam is shorter for the pilot moving at fast speeds than it is for you. Therefore, the pilot's time must be running slower than yours, in order to satisfy v = d/t

Does this analogy verify that time dilation and length contraction happen when moving at faster speeds? A book I was reading used this thought experiment to prove time dilation, but it seems like it also proves length contraction as well.

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  • $\begingroup$ Yes, it is a correct analogy for time dilation and it is also used in many books. But can you elaborate on why do you think this also explains length contraction. $\endgroup$ – SR810 Feb 15 '18 at 9:11
  • $\begingroup$ That proves nothing, real experiments prove, or better disprove, something. Thought experiments give you hints about what should happen assuming the laws of physics to be valid, and they help you to understand it better and find paradoxes and absurdities in the known physics sometimes. They are very important for the understanding of physics, but they cannot prove anything. $\endgroup$ – Run like hell Feb 15 '18 at 9:45
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This does not prove length contraction because lengths contract only in the direction of motion and the line joining the ground to the mirror on the ceiling is normal to the direction of motion.

Be cautious about length contraction because it is not really a contraction. Instead it is a form of rotation, but it is a rotation in spacetime not just in space. For more on this see my answer to "Reality" of length contraction in SR.

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  • $\begingroup$ And, readers, note that "rotation" involving time presents a little bit like an image on a progressive-scan LCD - it's cause is that not all parts of the image (the length of the object, even a stationary one) present simultaneously (because of differing path lengths to each point), and so any movement during scans changes the impression of length that is seen. It might be a bit of a clumsy analogy, but this is the physical reality described by such a "rotation in time". $\endgroup$ – Steve Feb 15 '18 at 11:52

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