This example shows that the equation E=mc² expresses the equivalence of mass and energy and not the generation of energy as a reaction product from mass. The confusion that sometimes arises can often be traced back to the mix-up between the words “mass“ and “matter“. Matter can be transformed into radiation. Matter is taking the role of energy container, radiation is some sort of released, “free“ energy, that must fly through space. [...]
The smaller the length scales, the stronger the forces involved and the higher the (binding) energies, and hence the corresponding masses, relative to the rest masses of the constituents. We could wonder whether this finds it climax at a point where an elementary material particle is build of constituents that have zero rest mass, with only kinetic and potential energy to make up for its mass. That this should be the case for the electron, but at the same time seems quite impossible [3], is well known [4].
What is intriguing is that matter’s most basic building blocks, the elementary particles, all have non-zero spin, intrinsic angular momentum, which seems to imply that they all must have some sort of intrinsic dynamics. Hypothetical structures which do not have internal dynamics, such as point particles and hard spheres, do not exist. So what is matter really made of then? In the Dirac theory, the electron is like electromagnetic energy quivering at light speed, just like a photon in a box [5]. If really so, matter is light. [...]
Rest mass never applies to a system at complete rest, because such systems do not exist; there will always be internal dynamics.

As we remember, at the beginning of wave mechanics there was the idea to regard every particle of the mass m as the origin of a periodical phenomenon of the frequency v. In order to express this in a quantitative way: De Broglie linked Einstein's formula E=mc²; with Planck's formula
and thus received the formula m c ² = h v
This formula tries to link, in a very general form, the quantum postulate with the principle of relativity.

To meet the principle of relativity means that this law has to be the same for all observers which move parallel and uniformly with respect to each other. Nevertheless, neither the mass nor the frequency can be called relativistic invariants, i.e. values which do not change from one observer to another. Thus, they have to change in a way to meet the equation they are in. But a severe difficulty arises within that. Indeed: If mass has a certain value m_o for an observer who is at rest with relation to the particle, its value is bigger for any observer who is moving. On the other hand, if the observer at rest defines the frequency v_o of the periodic movement which is linked to the particle, for any other observer it will have an inferior value. This is the famous effect of the clock difference. From this, it has to be followed that the law mentioned above can be true for a special observer who then defines the cyclic frequency which is linked to the particle. Nevertheless, it has then to be wrong for all other observers. It can be said that such a law is relativistically covariant.

In a certain sense, wave mechanics rose from a theorem of de Broglie, according to which everything elapses in a way as if there was a wave which propagates at a velocity much higher than the velocity of the particle. It must be stationary and have the frequency v_o for the observer at rest. For any other observer it must continuously be in phase with the inner cyclic movement of the particle. He showed that the frequency of this wave is transformed as well as the mass from one observer to the other, and that therefore the quantum relation m c ² = h v becomes relativistically covariant, if the cyclic frequency in it, which from now on is designated v_c , is substituted by the frequency v of that wave.