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

c = 1

. If

B

is in the future lightcone of

A

and

C

in that of

B

, then

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

Adding and using the triangle inequality gives

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

Thus the statement is true.

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