Hello everyone, thanks for reading.
This might be a little more math than physics (don't run away though!), but it's an excercise on my General relativity text :)
I need to prove that there exists an analog formula, like a*b = abcos(theta) for 3-vectors, only for 4-vectors, in which:
a*b = abcosh(theta), where a and b are 4-vectors, a and b are defined: a = (-a*a)^-0.5, b = (-b*b)^-0.5, and theta is a parameter that describes lorenz boost between the frame where an observer whose world line points along a is at rest and the frame where an observer whose world line points along b is at rest.
I have no idea how to work with this theta :-\
p.s. a and b are time-like 4 vectors.
a*b = -a0*b0 + a1*b1 + a2*b2 = a3*b3
The Attempt at a Solution
I just tried to look for examples in the book and work with the definition... But I got nowhere :-\