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The zeroth component of the four-momentum

  1. Nov 12, 2011 #1
    Why is it that the Energy of a system is identified with [itex]p_0[/itex] and not [itex]p^0[/itex]?

    This is especially concerning to me in non-Minkowski metrics, such as the Schwarzschild metric, where the difference between [itex]p^0[/itex] and [itex]p_0[/itex] can be quite dramatic.

    In the schwarzschild metric, we have:

    [tex]p_0 = -\tilde{E}\,m[/tex]

    where [itex]\tilde{E}[/itex] is energy per unit mass, and for a photon, [itex]p_0=-E[/itex]

    But that means that for a massive particle,

    [tex]p^0 = m\left(1-\frac{2M}{r}\right)^{-1}\tilde{E}[/tex]

    and for a photon,

    [tex]p^0 = \left(1-\frac{2M}{r}\right)^{-1}E[/tex]

    Clearly [itex]p_0[/itex] has been more closely related with energy than its contravariant form
  2. jcsd
  3. Nov 12, 2011 #2


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  4. Nov 12, 2011 #3
    thanks :)
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