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Lorentz Invariance proof

  1. Sep 15, 2016 #1
    1. The problem statement, all variables and given/known data
    I'm asked to prove that Et - p⋅r = E't' - p'⋅r'

    2. Relevant equations
    t = γ (t' + ux')
    x = γ (x' + ut')
    y = y'
    z = z'

    E = γ (E' + up'x)
    px = γ (p'x + uE')
    py = p'y
    pz = p'z

    3. The attempt at a solution
    Im still trying to figure out 4 vectors. I get close to the solution but I have some values hanging around.
    For the first two terms, E and t, i just multiple them out.
    (γ (E' + up'x))(γ (t' + ux') )

    Next I work with the p and r. The way i understand them is that that p is equal to the three different equations i have listed for px,py, and pz. And the same thing for r but with x,y, and z. Im guessing that because i don't a lorentz transformation formula for just p or r.

    I then multiply px with x, py with y, and pz with z. adding the products of each along the way.

    am i on the right track? I start canceling terms but ultimately I'm left with a γ2ut'uE' and γ2ux'up'. I'm also left with a bunch of γ2's.
     
  2. jcsd
  3. Sep 15, 2016 #2
    i just figured it out. the squared gamma factor helps me get rid of the left over terms. i forgot that gamma was something more than just a variable.
     
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