The concept of mass is such an abomination. Energy and momentum conservation follow from time and space translation symmetry. Beautiful. Geometric. Profound. Rest mass/baryon number conservation follows from some ad hoc U(1) internal symmetry. Horrible. Algebraic. Profane.

@IamSreeman It's perfectly possible to define matter configurations with no mass conservation (since it reduces to energy conservation), e.g. ultrarelativistic matter. This happens whenever there is no U(1) symmetry in the matter field equations.