1. Consider the straight world line between two events O and P in Minkowski space with coordinates
$(t, x, y, z) = (0, 0, 0, 0)$ and $(2, 0, 0, 0)$, respectively, with proper time separation $\tau_{OP} = 2$. Let Q
with coordinates $(1, 1, 0, 0)$ be an intermediate event.
t P (0,2)
(0,1)
Q (1,1)
O
(1,0) x
(a) Find the proper times $\tau_{OQ}$ and $\tau_{QP}$.
(b) Show that the total proper time separation $\tau_{OQP}$ obeys
$\tau_{OQP} = \tau_{OQ} + \tau_{QP} < \tau_{OP}$.
