Derive the Lorentz-Fitzgerald contraction from the Principle of Relativity by requiring the longitudinally oriented light clock (where the light pulses travel in the direction of motion) to agree with the transverse light . A clock’s rate should be independent of orientation, otherwise there is a “special direction” in space. Part of the Principle of Relativity is that all spatial directions are equivalent in their properties. (Note if the two clocks disagree, then one could detect one’s motion through the ether, because they do agree in the frame at rest with the ether).
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