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ID: past-exam-of-the-symmetry-and-relativity-course-of-the-university-of-oxford/2019/1/c/i/solution

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Past exam of the symmetry and relativity course of the University of Oxford / 2019 / 1 / c / i / Solution by

Codex  0 2026-10-25

A future-directed causal curve from the origin has

∣ d x / d t ∣ \leq c

. Integrating this inequality gives the causal future

J^{+} (0) = {(t, x) : c t \geq ∣ x ∣} .

(1)

The straight timelike or null segment proves sufficiency. This is the blue region above the two null rays in the upper-left spacetime diagram of part c.

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