  We study $f(R,T)$ gravity, in which the curvature $R$ appearing in the
gravitational Lagrangian is replaced by an arbitrary function of the curvature
and the trace $T$ of the stress-energy tensor. We focus primarily on situations
where $f$ is separable, so that $f(R,T) = f_1(R) + f_2(T)$. We argue that the
term $f_2(T)$ should be included in the matter Lagrangian ${\cal L}_m$, and
therefore has no physical significance. We demonstrate explicitly how this can
be done for the cases of free fields and for perfect fluids. We argue that all
uses of $f_2(T)$ for cosmological modeling and all attempts to place limits on
parameters describing $f_2(T)$ are misguided.
