1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Discussions: Why is the longest worldline the unaccelerated one?
  1. Longest Straw (Replies: 4)

  2. Longest Straw (Replies: 2)

  3. Longest Wavelengths (Replies: 1)