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Homework Help: Doppler shift derivation from Lorentz Transformations

  1. Jan 29, 2017 #1
    1. The problem statement, all variables and given/known data
    Show how one can obtain the Doppler transformation for the frequency of a receding
    source just using the Lorentz transformations for the energy (where E=h).

    2. Relevant equations
    Relativistic transformations for momentum and energy:
    E = γ(E' + vp'x)
    pc/E = v/c = β

    3. The attempt at a solution
    E = γ(E' + vp'x)
    since p = Eβ/c, E = γ(E' + Eβ2) = γE' (1+β2).

    Which then would imply that = γ'(1+β2). But I have in my notes that the observed frequency = γ' (1-β). Where did I go wrong?
  2. jcsd
  3. Jan 29, 2017 #2


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    The speed ##\beta = \frac{pc}{E} = 1## for electromagnetic radiation. It's not the same as ##v##, the speed between the two reference frames.
  4. Jan 29, 2017 #3
    That makes sense, thanks.
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