Problems Week 9
1. The spacetime position of a particle is given by ¯R(τ) where τ is the
proper time. It is observed by an observer with four-velocity ˆu. The
particle’s four-velocity is
ˆv = γ(ˆu + ¯v) .
Give corresponding expressions for the four-acceleration ¯A and ¯A2
.
2. A particle moves so that
d ¯A
dτ
= α2
ˆv ,
where ¯A is the four-acceleration and ˆv the four-velocity. Show that
¯A2
= α2
. Also show that α is constant along the the particle’s worldline.
What is the physical interpretation of this fact?
3. Assume that for a particle moving in a 2-plane in spacetime
¯A2
= α2
= constant .
Show that
d ¯A
dτ
= α2
ˆv .
This is the converse of the previous problem.
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