Paper 4, Section I, B

Dynamics and Relativity | Part IA, 2012

Let SS and SS^{\prime} be inertial frames in 2-dimensional spacetime with coordinate systems (t,x)(t, x) and (t,x)\left(t^{\prime}, x^{\prime}\right) respectively. Suppose that SS^{\prime} moves with positive velocity vv relative to SS and the spacetime origins of SS and SS^{\prime} coincide. Write down the Lorentz transformation relating the coordinates of any event relative to the two frames.

Show that events which occur simultaneously in SS are not generally seen to be simultaneous when viewed in SS^{\prime}.

In SS two light sources AA and BB are at rest and placed a distance dd apart. They simultaneously each emit a photon in the positive xx direction. Show that in SS^{\prime} the photons are separated by a constant distance dc+vcvd \sqrt{\frac{c+v}{c-v}}.

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