The derivation, above, of the equation E = mc^{2} from E^{2} = p^{2}c^{2} + m^{2}c^{4 } (note that that is the correct form of the equation – the slightly different version quoted is dimensionally inconsistent) has one very important caveat – that “the object is not moving”. As such it will only work in the rest frame of the object, and cannot be used to model situations where a body gains energy by, say, absorbing or scattering a photon. In fact the interpretation of E = mc^{2} used by Einstein was somewhat different since he redefined mass as *mγ* – the “relativistic mass” – although he later regretted this. Relativistic mass is not used today, although some physicists still hold onto the concept.

Using this latter interpretation does indeed compel one to say that energy has mass. This is what is known as the “concomitance” view. Those who take this view will say that both energy and mass are conserved at all times, and they would not agree with the statement that by “measuring the mass of a radioactive atom, and all of its decay products, you will find that the decay products are slightly too light, by the amount of energy released divided by c^{2}”. They would say instead that the mass of the system, and its energy, are the same before and after the decay, they are just “rearranged”.

Taking the more modern line, that mass is Lorentz invariant, one arrives at the “interconvertibility” view, which is at odds with the idea of energy having mass. Which line you take depends on how you define momentum, and it is to some extent a free choice. The one sure thing is that you can’t have it both ways – you cannot say that energy and mass are interconvertible whilst simultaneously holding that energy has mass. Yet such confusion is widespread – not only on this forum but in the press, popular books and even textbooks.

One of the problems with the interpretation of special relativity is that Einstein’s models, from which he derived his equations, were incredibly simple. They were based on “rigid bodies” with no internal structure; they therefore had no capacity to heat up, and so one should not expect to be able to use them to model a situation where something is being heated. You only get out of a model what you put in. We might hope to be able to use SR to approximately model a simple collision between, say, a single photon and a single atom (although even a single atom is more complex than Einstein’s model allows, since it can absorb energy by excitation to a higher energy state, which again is not provided for in the model). But if we apply E^{2} = p^{2}c^{2} + m^{2}c^{4} to such a collision, then whichever reference frame we use, there will be motion, and hence momentum; so you can never say that “the object is not moving”, even at this simple level.