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Confused about Lorentz Transformations

  1. Sep 4, 2012 #1

    BWV

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    I thought Lorentz Transformations left Δt2-Δx2 invariant
    but, for example a frame moving at .5C for Δt =1 has Δx = .5 so
    Δt2-Δx2 = .75

    If this is transformed by :


    d3140dec18ab1103cc4aebe3fe182f98.png


    to a rest frame
    Δt =0.65 has Δx = 0 and Δt2-Δx2≠ 0.75

    not sure where I have gone wrong here, any help would be appreciated
     
  2. jcsd
  3. Sep 4, 2012 #2
    You made a mistake with your arithmetic. If you plug your numbers into the Lorentz Transformation equation that you quoted, the result is Δt' = sqrt(0.75) and Δx' = 0, so the quantity Δt'2-Δx'2 equals 0.75, just as before.
     
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