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Relativistic Mechanics

Problem 1.356

At two points of the reference frame \(K\) two events occurred separated by a time interval \(\Delta t\). Demonstrate that if these events obey the cause-and-effect relationship in the frame \(K\) (e.g. a shot fired and a bullet hitting a target), they obey that relationship in any other inertial reference frame \(K^{\prime}\).

Reveal Answer
1.356. It should be shown first that if Δt=t2−t1>0, then Δt′=ta′−t1′>0\begin{aligned} &1.356 . \text { It should be shown first that if } \Delta t=t_{2}-t_{1}>0, \text { then }\\ &\Delta t^{\prime}=t_{\mathrm{a}}^{\prime}-t_{1}^{\prime}>0 \end{aligned}
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