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 Incoming links: Past exam of the symmetry and relativity course of the University of Oxford / 2015 / 4 / a

Past exam of the symmetry and relativity course of the University of Oxford / 2015 / 4 / b / ii / Solution 2026-10-25

Use the same event pair already made simultaneous in the rear instantaneous rest frame. Its proper spatial separation is the Minkowski interval length, so

[h (t_{B}) - f (t_{A})]^{2} - c^{2} (t_{B} - t_{A})^{2} = L^{2}, h (t_{B}) - f (t_{A}) > 0.

(1)

The inequality selects the front rocket rather than the equally long backward extension. Equivalently the Lorentz-transformed spatial difference obeys

γ [h (t_{B}) - f (t_{A}) - v (t_{B} - t_{A})] = L

. This is not the condition

h (t) - f (t) = L

at equal laboratory times, which would describe the stretching arrangement in a.

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