- #1
Identity
- 152
- 0
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
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