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How to obtain the Lorentz space contraction formula for a moving rod from knowledge of the positions of its ends a different times.

My question is:

Consider a rod at rest in I', located along the x' axis. Its ends 1 and 2 are characterized by the space coordinates x'(1) and x'(2). The proper length of the rod is

x'(2)-x'(1)

independent of the time when the mentioned coordinates are measured.

Is it possible that observers from I measure the coordinates of ends 1 and 2 at different times, taking into account that their clocks read the same running time as a consequjence of the fact that the clocks they use are standard synchronized? At each end of the rod we find an observer from I characterized by the space coordinates x(1) and x(2) respectively.

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# Simultaneous detection of the space coordinates of the ends of a moving rod?

Can you offer guidance or do you also need help?

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