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Lorentz Transformation Question

  1. Sep 28, 2016 #1
    1. The problem statement, all variables and given/known data
    For an event occurring at (x,t),
    consider the quantity I = x^2 - (ct)^2
    Find a simple expression for this in the S' frame: I' = x'^2 - (ct')^2
    How are I and I' related, and why is this noteworthy?

    3. The attempt at a solution
    So the question is under "Lorentz Transformation" and I must
    simplify I' = x'^2 - (ct')^2.

    I am not sure if this is the way to go about it, but should I find
    the equation in the form of "c =" ?
     
  2. jcsd
  3. Sep 28, 2016 #2
    You should write x' and t' in terms of x and t by using Lorentz transformations (specifically, what is called a boost in the ##x## direction).
     
  4. Sep 29, 2016 #3
    When I do, do I find the quantities equal?
     
  5. Sep 29, 2016 #4
    I plugged into
    I' = x'^2 - (ct')^2

    x' = y(x - ct)
    t' = y(t - cx/c^2)
    * y is Lorentz Factor

    and I get that I' = 0
     
  6. Sep 29, 2016 #5
    Yes, you should find that they are equal, I=I'. You got 0 because you wrote c instead of v in the Lorentz transformations. They are:

    x' = y(x - vt)
    t' = y(t - vx/c^2).
     
  7. Sep 29, 2016 #6
    I see, thank you!
     
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