The evolution of mass-energy equivalence principle goes rather deep into history of physics. By Umberto Bartocci, the famous equation E=mc^2 was derived an at least two years before Einstein by Italian physicist Olinto De Pretto. The true is, De Pretto has derived a somewhat different version of E=mc^2 equation in his original article.
By AWT the Universe appears as being formed by nested density fluctuations of hypothetical particle environment, so called the Aether. This environment is similar to dynamic foam and it behaves similarly. It means, the Aether condenses into more dense phase temporarily, whenever some energy wave travels through it, by the same way, like soap foam, which gets more dense under shaking. You can play with this behavior by using of mouse in the following Java applet:
It means, in vacuum foam the mass density is always proportional to energy density - and vice-versa. Therefore every isolated wave packet (a soliton) propagates through vacuum as a less or more dense blob of Aether foam. From this the concept of particle-wave duality follows, so we can see, the AWT can explain the fundamental concepts of both relativity, both quantum mechanics by the model of foam, based on Newtonian physics.