In fact, both energy and mass are conserved. If you accept e=mc^2 as "true," it's easy to show.
If energy is conserved and mass is not, then what can E=mc^2 possibly mean? Is it a relation, like F=ma? Then if E is constant and of course c is constant, then m must be constant too.
Or is it an exchange rate: you can convert this much mass into that much energy? But then energy is no longer conserved, if you can make it from mass.
Last try. Maybe e=mc^2 means, within a given quantity of mass, there is necessarily a minimum energy? And this is true, but notice that the equation is phrased as an equality. Equalities go both ways: we can just as easily derive m=e/c^2, and now the "minimum energy" idea runs aground.
In modern interpretations, energy and mass are both conserved, and e=mc^2 is understood to be the energy in the rest frame of the system. Individually photons are massless, but multiple photon systems can and usually do have mass. The price we pay for conceiving of mass as conserved and invariant is that it no longer adds nicely.
If energy is conserved and mass is not, then what can E=mc^2 possibly mean? Is it a relation, like F=ma? Then if E is constant and of course c is constant, then m must be constant too.
Or is it an exchange rate: you can convert this much mass into that much energy? But then energy is no longer conserved, if you can make it from mass.
Last try. Maybe e=mc^2 means, within a given quantity of mass, there is necessarily a minimum energy? And this is true, but notice that the equation is phrased as an equality. Equalities go both ways: we can just as easily derive m=e/c^2, and now the "minimum energy" idea runs aground.
In modern interpretations, energy and mass are both conserved, and e=mc^2 is understood to be the energy in the rest frame of the system. Individually photons are massless, but multiple photon systems can and usually do have mass. The price we pay for conceiving of mass as conserved and invariant is that it no longer adds nicely.