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Question in 4-vectors.

  1. Jun 14, 2008 #1
    1. The problem statement, all variables and given/known data
    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 :-\

    Thanks!

    p.s. a and b are time-like 4 vectors.


    2. Relevant equations

    a*b = -a0*b0 + a1*b1 + a2*b2 = a3*b3



    3. The attempt at a solution

    I just tried to look for examples in the book and work with the definition... But I got nowhere :-\
     
  2. jcsd
  3. Jun 14, 2008 #2

    tiny-tim

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    Homework Helper

    Hi cosmic_tears! :smile:

    (btw, its ^1/2, not ^-1/2)

    Let's rephrase the question:

    For every two timelike 4-vectors a and b, you know how to make the dot-product a.b.

    Since they are timelike, there will be two observers with velocities for which a and b, respectively, are at rest.

    Let their relative speed be v.

    Find a.b as an expression in a b and v, show how the v part can be written as cosh of something, and explain why that's an advantage. :smile:
     
  4. Jun 15, 2008 #3
    Thank you very very much!
    It's done!
     
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