3.2.6  Mass-Energy Equivalence

It is commonly believed that the equivalence between mass and energy arose from the theory of relativity as described by Poincaré in 1900, and later by Einstein in 1905, in his famous paper “Does the inertia of a body depend upon its energy-content?”, in which he proposed the equivalence of mass and energy as a general principle and a consequence of the symmetries of space and time.

However, in the previous and many other related papers that he published in the next fifty years, Einstein gave various heuristic arguments for this relation without ever being able to prove it in any theoretical way Hecht (2011), as no one else also ever did. Based on Doppler effect and Maxwell’s theory of radiation, the reasoning that he gave in his 1905 original derivation was questioned by Planck and shown to be faulty. In 1907, Einstein acknowledged the controversy over his derivation. He later produced more than half dozen proofs that all suffer from unjustified assumptions or approximations. He never succeeded in producing a valid general proof Ohanian (2009). In 1955 he wrote in a letter to Carl Seelig (1894-1962): “I had already previously found that Maxwell’s theory did not account for the micro-structure of radiation and could therefore have no general validity.” Capria (2005).

Other physicists have tried to apply other methods, such as the relativistic Doppler shift, but all need to incorporate various approximations in order to reach the final equation. Until now there is no exact derivation of this famous formula.

As we already introduced in chapter I, an exact derivation of this experimentally verified relation is not possible without the inner levels of time, since it incorporates motion at the speed of light which leads to infinities on the physical level. Henceforth, based on the Duality of Time hypothesis, we will provide in chapter V several simple methods to derive this relation directly from the principles of classical Newtonian Mechanics. These simple methods would not have been possible without the metaphysical behavior in the inner levels of time, where the velocities of each individual geometrical points are perpetually and sequentially changing abruptly from rest to the speed of light, and vice versa, in literally “zero time” on the outer level. This is obviously not allowed on the normal level of time when dealing with physical objects that have mass, because it will lead to infinite acceleration and infinite energy.

The relation between mass and energy dates back to the 17th century, when the term vis viva, from the Latin for “living force”, is used for describing the kinetic energy in an early formulation of the principle of conservation of energy, proposed by Leibniz during the period 1676-1689. He noticed that in many mechanical systems of several masses, the quantity:was conserved, and he called this quantity the vis viva, or living force of the system. It was later realized that this observation is only accurate for the conservation of kinetic energy in elastic collisions, and it is independent of the conservation of momentum. In 1807, Thomas Young (1773-1829) was the first to use this term as energy, but it was later calibrated to include the coefficient of a half:

Einstein was not the first to have related energy with mass. In 1717, Newton speculated that light particles and matter particles were interconvertible. In 1734, in his own Principia, Emanuel Swedenborg (1688-1772) speculated that matter is ultimately composed of dimensionless points of “pure and total motion”.

Additionally, in the end of the 19th century, there were many attempts to understand how the mass of a charged object depends on the electrostatic field. The concept was called electromagnetic mass, and was considered as being dependent on velocity and direction as well, thus the object may have different longitudinal and transverse electromagnetic masses. One year before Einstein, in 1904, Lorentz expressed transverse electromagnetic mass as:

Shortly after that, Planck defined the relativistic momentum and gave the correct values for the longitudinal and transverse masses, but this concept of mass was redefined in 1909 as the ratio of momentum to velocity, instead of the ratio of force to acceleration. However, the concept of relativistic mass is not used anymore in Relativity, but it is considered as an invariant quantity, whereas the energy is relativistic.

In 1900, Poincaré also associated electromagnetic radiation energy with a “fictitious fluid” having momentum and mass related by:. By that, Poincaré tried to save the center-of-mass theorem in Lorentz’s theory, though his treatment led to radiation paradoxes. Like Poincaré, Einstein also concluded in 1906 that the inertia of electromagnetic energy is a necessary condition for the center-of-mass theorem to hold.

Back in 1873 also, Nikolay Umov (1846-1915) pointed out a relation between mass and energy for aether in the form of, where, and in 1903, Olinto De Pretto (1857-1921) published a paper in which he presented a mass-energy relation. De Pretto imagined that the Universe was filled with an aether of tiny particles that always move at the speed of light, thus each of these particles has a kinetic energy ofup to a small numerical factor.

After World War II, when huge energies released from nuclear fission, as demonstrated by the atomic bombs of Hiroshima and Nagasaki in 1945, the mass-energy equationbecame linked by the public with the power of nuclear weapons, but the equation was not strictly necessary to develop the weapons. As Robert Serber (1909-1997) put it: “Somehow the popular notion took hold long ago that Einstein’s theory of relativity, in particular his famous equation, plays some essential role in the theory of fission. Albert Einstein had a part in alerting the United States government to the possibility of building an atomic bomb, but his theory of relativity is not required in discussing fission. The theory of fission is what physicists call a non-relativistic theory, meaning that relativistic effects are too small to affect the dynamics of the fission process significantly.” Serber and Rhodes (1992)