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ID: past-exam-of-the-symmetry-and-relativity-course-of-the-university-of-oxford/2017/2/b/solution

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Past exam of the symmetry and relativity course of the University of Oxford / 2017 / 2 / b / Solution by

Codex  0 2026-10-25

Let

Δ t = t_{d} - t_{g}

and

Δ x = x_{d} - x_{g}

. A spacelike separation obeys

c^{2} Δ t^{2} - ∣Δ x ∣^{2} < 0.

Under a boost with velocity

V

, the time separation is

Δ t^{'} = Γ (Δ t - V \cdot Δ x / c^{2})

. Choose

V = \frac{c ^{2} Δ t}{∣Δ x ∣ ^{2}} Δ x .

Then

Δ t^{'} = 0

, while

∣ V ∣/ c = c ∣Δ t ∣/∣Δ x ∣ < 1

follows from the spacelike inequality. Therefore an inertial simultaneity frame exists. This choice has no transverse boost component and is not claimed to be the unique such frame. If the events are already simultaneous,

V = 0

suffices.

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