Problems Week 5
1. A spaceship travels unaccelerated from event A to event B and another
one from B to C. Show that a third could go directly from A to C.
2. An observer U measures the events P1 and P2 to be simultaneous and
a distance l apart. Another observer V is traveling from P1 towards
the spatial point where P2 occurs, with relative velocity v according to
U. What is the spatial distance between P1 and P2 according to V?
3. The timelike unit vectors ˆu, ˆv and unit vectors ˆa,ˆb with ˆu· ˆa = ˆv ·ˆb = 0
all lie in the same 2-plane. ˆu · ˆv < 0. Calculate ˆa · ˆb.
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