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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
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