This is an excerpt fom R. Wald's book on General Relativity (page 61). I'm not able to understand how he deduces that $E$ must be the time component of $p^a$ with only the assertions made before this part of the book.
The four velocity ($u^a$) is defined as the tangent to a timelike curve parametrized by the proper time ($\tau$) defined as $ \tau = \int \left(-\eta_{ab}T^a T^b\right)^{1/2} dt $
where $T^a$ is the tangent to the curve parametrized by any arbitrary parameter $t$.
$u^a u_a = -1$ is implied by the above parametrization.
That is the only information available. He says it like its obvious without giving any reason for it. What am I missing?
