There's an equation from Dirac's book on General Relativity that I don't get at all. It isn't derived; instead it's treated as almost self-evident, when it isn't.(adsbygoogle = window.adsbygoogle || []).push({});

Dirac begins by defining ##p^\mu## to be the "mass 4-current" of a continuous distribution of matter (matter in this case really being matter, ie not including the E&M field). This is defined such that ##p^\mu=\rho_0 v^\mu##, where ##\rho_0## is the mass density of a particular element of matter in that element's rest frame, and ##v^\mu## is just the four-velocity of the matter at the same point. Basically, ##p^\mu## is just the mass flux, in the same way as ##J^\mu## is the charge flux.

Dirac is trying to derive the equations of motion for a distribution of matter using the action principle. He does this by first making "arbitrary variations in the position of an element of matter" and seeing how it affects ##p^\mu##. He then asserts that if each element of matter is displaced from ##x^\mu## to ##x^\mu +b^\mu##, where ##b^\mu## is small, then ##\delta p^\mu=(p^\nu b^\mu - p^\mu b^\nu),_{\nu}##.

As I stated at the beginning, he doesn't derive this equation. I was hoping that someone else could describe where this equation comes from. Thanks.

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# I don't understand this equation from Dirac's General Relativity

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