= Physical momentum
{title2=$p_\perp^\mu=(\delta^\mu{}_{\nu}+u^\mu u_\nu)p^\nu$}
An observer with future-directed unit velocity $u^\mu$ measures particle energy $E=-u_\mu p^\mu$ and spatial <physical momentum> given by the orthogonal projection of its <four-momentum> in the displayed formula. With signature $(-+++)$ and $p_\mu p^\mu=-m^2$, its squared magnitude is $p_{\perp\mu}p_\perp^\mu=E^2-m^2$. Components in the observer's orthonormal spatial frame agree with $\gamma m\mathbf v$. They differ in general from coordinate <canonical momentum> components. For a comoving observer in flat FRW, a conserved conventional spatial comoving covector has locally measured magnitude divided by the scale factor.
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