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The vertical clock is ticking faster than the horizontal clock. This
cannot be right. The clocks tick together when they are not moving,
and for someone moving along with them they continue to tick together.
If they tick together for one observer they must tick together for all
observers. This is because of the
second relativity postulate, which says the outcomes of experiments don't depend on the
experiments' state of motion. Here the experiment is to observe
whether or not the clocks tick together.
The only way to keep them ticking together is to length contract the horizontal clock along the direction of motion. Then the light pulse has less distance to travel and can keep up with the vertical light pulse. This allows the light pulse in the horizontal clock to cover the round trip in the same time as that in the vertical clock. This is shown in the next animation. This animation, and the next, are to scale. The speed of the clocks is half the speed of light. This gives time dilation and length contraction factors of the square root of 3/4, or about 0.866c. |