Worldlines of two clocks 2. The figure shows the worldlines of two identical clo

Question

Worldlines of two clocks 2. The figure shows the worldlines of two identical clocks that move from A to B. The first clock has a straight worldline x= v where v, is a constant. The second clock has the worldline x = a., where ao is a constant. For each clock, find the elapsed proper time between A and B. Which clock shows the longer proper time? Hint: it might be difficult to directly compare the proper times. A clever way is to compare them in the rest frame of clock 1. The proper time is frame invariant, so this comparison holds in any !

Explanation / Answer

Both the clock shows same proper time.

For the first case, dx= v0 dt and for the second case it is dx= a0 t dt = v0 dt, hence both have same proper time.

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