On page 61 of his book “General Relativity”, Robert Wald says that the energy of a particle with $4$-momentum $p^a = mu^a$ measured by an observer with $4$-velocity $v^a$ is given by $E=-p_av^a$. How can I see that?
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See Why is the first component of the energy-momentum tensor $-p_av^a$? for some remarks. You can take that as a definition of the phrase “energy of a particle measured by an observer”, but to see that this is a reasonable definition I like the approach presented in Landau and Lifshitz, starting with the Lagrangian for a point particle. – peek-a-boo Jun 13 '23 at 13:50
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Possible duplicate: https://physics.stackexchange.com/q/761369/2451 – Qmechanic Jun 13 '23 at 13:56