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Homework Help: Why is the longest worldline the unaccelerated one?

  1. Aug 25, 2010 #1
    1. The problem statement, all variables and given/known data

    How does one prove that, of all timelike worldlines connecting two events A and B, the accelerated one is the longest.

    2. Relevant equations

    dT^2 = dt^2 - dx^2
    (accelerated reference frames:
    t = (sinh aT)/a
    x = (cosh aT)/a
    c = speed of light = 1)

    3. The attempt at a solution

    If there is no acceleration, then x = vt, therefore T = t(1 - v^2)^0.5
    I don't know where to go from there.

    Conceptually, I understand this, however, I can't seem to prove this with mathematics. Any ideas?
  2. jcsd
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