The Mass-Energy Equivalence:
(Deduction of Einstein's Mass-Energy equivalence from first classical mechanics, and based on the Re-creation principle. Apart from the overwhelming experimental confirmation, neither Einstein, nor anyone else, had ever been able to construct a comprehensive prove for this famous relation from first fundamental principles ["How Einstein confirmed E0=mc2", American Journal of Physics, 79 (6): 591–600, Bibcode:2011AmJPh..79..591H, doi:10.1119/1.3549223]. With the re-creation principle everything is instantly popping into existence from zero speed into the speed of light, and collapsing again. Normal limited speeds that are much below the speed of light are explained in another section.)
Based on the new concept of re-creation, Einstein’s mass-energy equivalence relation is deduced directly from fundamental classical principles.
In normal classical mechanics, the kinetic energy is the work done in accelerating a particle during the infinitesimal time interval , and it is given by the dot product of force and displacement :
Now since the momentum: , and if we can assume mass is constant, so that: , we will get:
So in the classical view of apparently continuous existence, when we consider a continuous smooth change in speed from zero to , the result of this integration will give us the standard equation of kinetic energy:
This equation can be applied safely on macroscopic objects, in normal conditions, although in reality this incorporates some approximation, because we considered the change in speed to be infinitesimal, which is not correct in extreme conditions.
Note that if we want to consider mass to be variable with speed and distinguish between rest mass: , and relativistic mass: , according to the standard equation:
Then we can arrive to Einstein’s equation by calculating the derivative which in this case will not be equal to zero. However, the above relativistic mass in equation number (4) is only obtained based on the same Einstein’s equation that we are trying to prove here, so in this case it will be a circular argument. Actually there are various other methods to prove this equation, but all has been criticized because they are either applicable only in certain situations or rely on some relativistic concepts. Apart from the overwhelming experimental confirmation, neither Einstein, nor anyone else, had ever been able to construct a comprehensive prove for this famous relation from first fundamental principles [].
The only way to prove this relation classically is to suppose that velocity jumps from zero to in “no time”, and that is exactly what the Re-creation Principle is postulating. In this case the above integration in equation (2) will be converted back into summation of the two discrete states of zero and , because in calculus integration and derivation are only valid with infinitesimal change:
The difference between these two cases that result in equations (3) and (5) is demonstrated in Figure 1 below.
The difference between gradual change of speed and abrupt change.
So this would be a straightforward mathematical proof of the Re-Creation Principle, but we only need first to physically justify this abrupt change in velocity. Obviously, the problem is that with zero-time intervals, the acceleration would be infinite, and hence the force and energy. Light does in fact move from zero to and vice versa, for example when emitted or absorbed, but the photon is massless, unlike other particles and objects which have mass and suffer inertia and acceleration. In fact, we are now faced with the same dilemma of the wave-particle duality, or continuity versus discreteness, and as we said above, the only way out of this dilemma is “oneness”.
We shall see in the following [section 6] that on the primary level of oneness everything happens in “no time”, because the simple monads are naturally massless, so the task would be the other way around by explaining how massive particles and objects move with limited velocities on the normal level of space and time, or how do they acquire mass, or equally: how monads are coupled together to construct space-time itself, where multiplicity is hosted.
We can alternatively try to explain this zero-time interval in terms of quantum tunneling which has been reported to have occurred in zero-time [] or superluminally [], but since we are trying here to explain the reality, we want to discuss the general philosophical reasons that make all this possible. Once these reasons are clarified, zero-time tunneling and other nonlocal quantum phenomena would also be explained even outside the mathematical formulation of Quantum Mechanics, that would also gain stronger supporting logic.
When “particles” appear to maintain their motion at the speed of light, they are said to be massless, such as the photon for example, because its rest mass has been completely converted into energy. So this mass-energy equivalence is the usual operation that is always happening at the ontological level, as a result of exciting the vacuum field into waves and their eventual collapsing back into vacuum, which is the described perpetual alternation of monads between existence and nonexistence, that is always conveyed by the Single Monad.
On the other hand, on the phenomenological level, when during a time a monad or an object is moving at an average limited velocity that is a result of averaging the dual-state velocity or the average of various vector velocities of its elementary particles that are moving in all directions, so on average it is spending some time moving at (that corresponds to existence) and some time at zero (that corresponds to rest, nonexistence or vacuum), then in total it may move a distance:
Because it performed no distance during . Therefore, this average velocity is given by:
And its kinetic energy will be given by same standard classical equation (3): , because its change is smooth.
However, since this average velocity is the apparent velocity that is a “mixture” of its instantaneous dual-state velocity (), whenever this object or monad is measured or detected it will be necessarily at rest, at the real instance of measurement in the real flow of time, with its initial constant rest mass , as a result of the collapse of wave function. This is in fact the philosophical reason behind the first principle of Special Relativity, i.e. the laws of physics are invariant in all inertial systems that are non-accelerating frames of reference, because there is no difference at all if the monad or object is at rest or moving with any constant speed , since in reality it is always at rest at the time of measurement. This also means that even when it is moving at any speed that could be very close to c, at the time of measurement its mass will still be the same rest mass, because it is only detected as a particle, while its energy will be given by its relativistic mass, and then its total energy equivalence, with relation to an observer moving at a constant velocity , will be given by:
This is the only philosophical explanation that can account for the existence of “rest mass” and “relativistic mass” in the same equation. Mass itself is always the rest mass, it is not relativistic, but its effect, i.e. energy is.
Therefore, in conclusion, this notion of re-creation, or dual-state velocity, is able to explain at once all the three postulates of Special Relativity: the mass-energy equivalence, the invariance of physics laws in inertial frames, and the constancy of the speed of light, in addition to explaining the nature and collapse of the wave function into eigenstate. In a coming paper, we want to explore how we can apply this principle on General Relativity.
 Leaving aside that it continues to be affirmed experimentally, a rigorous proof of the mass-energy equivalence is probably beyond the purview of the special theory: Hecht, Eugene (2011), "How Einstein confirmed E0=mc2", American Journal of Physics, 79 (6): 591–600, Bibcode:2011AmJPh..79..591H, doi:10.1119/1.3549223.
 Low, F. E. (1998). "Comments on apparent superluminal propagation". Ann. Phys. Leipzig. 7 (7–8): 660–661. Bibcode:1998AnP...510..660L. doi:10.1002/(SICI)1521-3889(199812)7:7/8<660::AID-ANDP660>3.0.CO;2-0. Nimtz, G. (2011). "Tunneling Confronts Special Relativity". Found. Phys. 41 (7): 1193–1199. arXiv:1003.3944free to read. Bibcode:2011FoPh...41.1193N. doi:10.1007/s10701-011-9539-2.
 Razavy, Mohsen (2003). Quantum Theory of Tunneling. World Scientific. pp. 4, 462. ISBN 9812564888.