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Energy in different frames.

  1. Apr 2, 2009 #1
    something which seems so fundamental that i can't find anywhere that derives it is the following:

    E' = gamma * (E - p.v)

    where E is the energy in one frame, p the momentum, v the relative velocity of the other frame, and E' the energy in the other frame.

    i.e. energy transforms like time. i can't quite see where this comes from though.. help?
  2. jcsd
  3. Apr 2, 2009 #2


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    Staff: Mentor

    It comes from the fact that energy is the "zeroth" component of the momentum four-vector [itex](p_0, p_1, p_2, p_3) = (E/c, p_x, p_y, p_z)[/itex], just like time is the "zeroth" component of the position four-vector [itex](x_0, x_1, x_2, x_3) = (ct, x, y, z)[/itex].
  4. Apr 2, 2009 #3


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    Welcome to PF!

    Hi chewwy! Welcome to PF! :smile:

    (have a gamma: γ :wink:)
    Yes, it's because (E,p) is defined as the derivative of (t,x),

    so E' = γE - γ(p.v),

    just as t' = γt - γ(x.v)
  5. Apr 2, 2009 #4
    okie doke. thanks everyone!
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