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Frame S' travels at speed V_1 along the x axis of frame S (in the standard configuration). Frame S'' travels at speed V_2 along the x'' axis of frame S'; (also in the standard configuration). By applying the standard Lorentz transformation twice find the coordinates x'', y'', z'', t'' of any event in terms of x, y, z, t. Show that this transformation is in fact the standard Lorentz transformation with velocity V given by the relativistic sum of V_1 and V_2.

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