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Time dilation with light clocks is affected by the constancy of the speed of light. Say we chose another type of clock, like a ball bouncing up and down instead of a beam of light. The speed of the ball is not constant for both of them. Therefore, if they both use clocks with a ball bouncing up and down, Alex will see John's ball going up a longer path just like in the light clock example. However, Alex will also observe the ball going up faster to compensate for the extra length. Therefore, although time dilation might occur here to, the amount of dilation should be different. Why then, does time dilate for all clocks on John's ship, in Alex's point of view, by the same factor of gamma? Shouldn't the factor be different depending on what type of clock is being used, and what the Lorenztian sum of the velocity is between the speed of John's ship and the speed of the clock?

If what I am saying is true, then the effects would be very strange: i.e. someone could go on a voyage at a very high speed with various clocks (including their biological clock) and come back with some of their clocks far behind those on earth, and other clocks only slightly out of sync.

Thank you.