Problems Week 4
1. What is the condition for four orthogonal spacetime vectors to be linearly
independent?
2. Consider a situation where everything happens in a two-dimensional
plane in spacetime (containing both timelike and spacelike vectors).
The orthogonal space to an observer’s worldline in the plane is onedimensional.
Two observers in the plane follow worldlines with directions
ˆu and ˆv. They pass close to each other at an event which we take
as the origin. Another event P in the plane happens at time τ before
they pass according to U and at time τ after the pass according to V.
a) Find the spacetime point P.
b) How far away is P according to U and V?
3. Two spaceships which are out of fuel pass close by. At proper time τA
after they pass one ship sends out a radio signal which is received by
the other at proper time τB. Find the relative velocity of the ships.
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