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In his original paper ''On the Electro-Dynamics of Moving Bodies'', in presenting the case of a rod AB moving with velocity v in a stationary system or frame K, Einstein states that the time interval T1 for a light ray emitted at A at time T0 measured in the moving inertial frame k of the rod to reach B is given T1=1/2[T0+T2], where T2 is the time at which the ray reflected at B is seen at A. T0, T1 and T2 are 'local times' in the frame k.

Why does Einstein say this when he has already established that observers moving with the rod and clocks at A and B will find those clocks not to be synchronous; which is to say, the times given as [tB--tA]=rAB/[c--v] and [t'A--tB]=rAB/[c+v] are not equal; and where rAB is the length of the rod?

Obviously, unless light in this scenario does not follow a singular path--although the paper makes clear that this is not the case; the path is singular--, I am misunderstanding something: what is it? Why don't clocks measure the time taken for light to traverse this single path at velocity c regardless of their position or motion?

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