Inertial Clocks and Remote Non-Simultaneity

A key prediction of Einstein’s Special Theory of Relativity (STR) is Remote Non-Simultaneity (RNS). It is derived from the equation below from the Lorentz transformation (LT), which is the cornerstone of STR:
Δt’ = γ(Δt –vΔx/c2) γ= (1 –v2c-2)-0.5
Einstein famously used the example of two lightning strikes on a moving train to illustrate RNS. The distance separating the strikes from the vantage point of the platform is Δx, the speed of the train relative to the platform is v and the time separating the strikes is Δt.
The corresponding time difference on the train is Δt’. We see that Δt can vanish without Δt’ doing the same. This has been assumed to prove RNS,i.e. that events which are simultaneous for one observer may not be so for another.


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