I have recently read that the laws of energy conservation, impulse conservation, angular momentum conservation and electric charge conservation can't " forbid " the proton decay and proton annihilation in nuclei ( the ref is from 1988 but I think it's still valid in that ).
22.
Examples of continuity equations often written in this form include electric charge conservation \ partial _ \ mu J ^ \ mu = 0 where " J " is the electric 4-current; and energy-momentum conservation \ partial _ \ nu T ^ { \ mu \ nu } = 0 where " T " is the stress-energy tensor.
23.
Maxwell's equations " seem " overdetermined, in that they involve six unknowns ( the three components of and ) but eight equations ( one for each of the two Gauss's laws, three vector components each for Faraday's and Ampere's laws ) . ( The currents and charges are not unknowns, being freely specifiable subject to charge conservation . ) This is related to a certain limited kind of redundancy in Maxwell's equations : It can be proven that any system satisfying Faraday's law and Ampere's law " automatically " also satisfies the two Gauss's laws, as long as the system's initial condition does.
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