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Derive lorentz transform for energy

  1. Mar 30, 2013 #1
    1. The problem statement, all variables and given/known data
    Derive the relation:
    [itex]E' = \gamma (E + \beta p c)[/itex]


    2. Relevant equations
    [itex]p' = \gamma p \\
    E^{2} = p^{2} c^{2} + M^{2}c^{4}[/itex]


    3. The attempt at a solution
    start off with stationary frame S [itex]E=mc^{2}[/itex]
    then in moving frame S' [itex]E'^{2} = p'^{2} c^{2} + E^{2}[/itex]:
    lorent transform momentum:
    [itex]E'^{2} = \gamma^{2} m^{2} v^{2}c^{2} + E^{2}[/itex]
    and that's as far as I get!
     
    Last edited by a moderator: Mar 30, 2013
  2. jcsd
  3. Mar 30, 2013 #2

    Simon Bridge

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    ##E=\gamma mc^2##

    That "p", in the equation you are supposed to prove, is unprimed.
    Is that significant?
     
  4. Mar 31, 2013 #3
    Yes the p is supposed to be unprimed.

    I've solved it now. Thanks anyway.
    Here it is for anyone who's having the same problem:
    You start off (or derive it as I had to, to understand it) with the lorentz transform for velocities in two frames [itex]u = \frac{u'+v}{1+frac{uv}{c^{2}}}[/itex]
    Know that [itex]E'=\gamma m_{0}c^{2}[/itex] because in the stationary frame S, only rest mass provides energy.
    You expand out gamma with u' given above and recognise that [itex]p'=\gamma p[/itex]
    simplify and you get an answer!
     
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