Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 4 / 4C / a / iii / Solution

True. The assumptions give

t_{B} - t_{A} \geq ∣ x_{B} - x_{A} ∣, t_{A} - t_{C} \geq ∣ x_{A} - x_{C} ∣.

Adding and applying the triangle inequality proves

t_{B} - t_{C} \geq ∣ x_{B} - x_{A} ∣ + ∣ x_{A} - x_{C} ∣ \geq ∣ x_{B} - x_{C} ∣,

so

B

is in the future lightcone of

C

.

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