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!

Homework Help: Plane where clocks are synchronized in both frames

  1. Mar 20, 2013 #1
    1. The problem statement, all variables and given/known data

    What is the velocity of the plane where clocks in two different frames are synchronized?

    2. Relevant equations

    Lorentz Transformations:

    t' = γ(t - vx/(c^2))

    x' = γ(x - vt)

    Solution should be v(t = t') = (c^2)/v * (1 - 1/γ)

    3. The attempt at a solution

    I am getting the negative of the solution: v(t = t') = (c^2)/v * (1/γ - 1)

    If I contract to the frame of the plane, I get that

    γ_p(t - (v(t = t')/c^2)x) = γ_p(t' - (v(t = t')/c^2)x')

    Simplifying and solving for v(t = t'), I get

    v(t = t') = (c^2)(t - t')/(x -x')

    Transforming t' to t and x, I get

    v(t = t') = (c^2)(t - γt + γ(v/c^2)x)/(x - γx + γvt)

    Dividing through by t on both numerator and denominator and noting that x/t = 0, I get

    v(t = t') = (c^2)(1 - γ)/(γv)

    Which leads to the solution I obtained.

    EDIT: Never mind, I figured it out. I used the wrong form of the Lorentz transformation.

    If anyone is interested, it's supposed to be t' = γ(t + vx/(c^2)) and x' = γ(x + vt)
    Last edited: Mar 20, 2013
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

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