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Lorentz's identity, relative speed

  1. Dec 1, 2007 #1
    1. The problem statement, all variables and given/known data
    start from:
    x = [x' + vt']/sqrt[1 - v^2/c^2]
    ct = [v/cx' +ct']/sqrt[1 - v^2/c^2]
    y = y'
    z = z'

    2. Relevant equations
    show that

    ( 1 - [tex]\frac{u^{2}}{c^{2}}[/tex])(1+[tex]\frac{vux'^{2}}{c^{2}}[/tex]) = ( 1 - [tex]\frac{v^{2}}{c^{2}}[/tex])(1-[tex]\frac{u'^{2}}{c^{2}}[/tex])


    3. The attempt at a solution

    ok, I have spent many hours on this crappy thing. We have no book in class so.....
    I derived the lorentz transformation for ux, uy, and uz... as well as u'x', u'y', u'z'.... then i computed the velocities in each fram using u = sqrt[ ux^2 + uy^2 + uz^2] and the same for u'. Nevertheless I end up in some mess of algebraic letters that get me nowhere close to the answer. I just need some sort of hit as to how to approach this problem.

    thansk for any hints.
     
    Last edited: Dec 1, 2007
  2. jcsd
  3. Dec 2, 2007 #2

    siddharth

    User Avatar
    Homework Helper
    Gold Member

    What are u,v,u' ? Is -v the velocity of unprimed system wrt the primed system? Then what's u? I suggest that you post the entire problem as it was given. That way, there's no scope for confusion.
     
  4. Dec 2, 2007 #3
    yeah, I know it is confusing..... but that is the whole problem... exactly as it was given to us.
    For what understand it is like this

    u = speed of particle 1 in S frame of reference
    u = sqrt[ux^2 + uy^2 + uz^2]
    u' = speed of same particle after a lorentz transformation in the S' frame of reference
    u' = sqrt[u'x^2 + u'y^2 + u'z^2]

    now, v would be the speed of one reference with respect to the other. I assume it is the v that carries over from the gamma sqrt[1-v^2/c^2] from the lorentz transformation.

    sorry about my notation, but I can't understand how to use latex yet.

    thanks for the reply
     
  5. Dec 2, 2007 #4
    this the actual equation

    [text]1+u_{x}single-quoteV/c^2=\sqrt(1-usingle-quote^2/c^2)*\sqrt(1-V^2/c^2)/\sqrt(1-u^2/c^2)[/text]
     
    Last edited: Dec 2, 2007
  6. Dec 2, 2007 #5
    never mind guys, i found the answer.... i will post the stepwise solution when i get a chance to write it on latex or scan it
     
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