Absolute mass of photons based upon the Hamiltonian of energy content

: In this article, the mass-energy equivalence is analyzed based on the total energy content & inertia of a body. The analysis included quantum energy formalization with relativity. The finding suggests that photons have absolute mass to justify their momentum.


Introduction
Albert Einstein raised the question that does the inertia of a body depends upon its energy content? [1] and he concluded that if a body gives off the energy in the form of radiation, its mass diminished by / 2 (where is the speed of light). But here, we ask the question again in its reversal form that does the energy content of a body depend upon its inertia? It follows because of my recent work on de Broglie's hypothesis on the matter-waves, [2] in which I derived an equation of total energy (Hamiltonian) of a particle having rest (absolute) mass and relative velocity and a frequency because of matter-wave observed by an observer (in a relative frame of reference).
Now we know that Einstein never considers a quantum-energy in his theory of relativity. So how can it appear in his theory of special relativity? To analyze this, let have a look at his above paper in which he gives the change in kinetic energy by ∆ , If we expand the above in binomial terms, we get kinetic energy by and quantum-energy of matter-wave by , then work-done (by the force, which is the reason behind the motion) in the center of mass frame is given by the change in inertial energy, (1 − ) 2 = ( + ), and the work done (by the same force as stated above) in the relative frame is given by the change in kinetic energy by equation (1.2), which can be expressed as, ( − 1) 2 = ( + ), we can see that both are an equivalent statement.

Vis-Viva & Vis-Mortua [3]
The competition between two physical quantities (momentum & kinetic energy) to describe the changes in nature rise in late 1650 by two sides of philosophers. One side leaded by what is Newton's idea of force? "It is an agent, which produces a change in nature". The reason by which energy flows in an isolated system. The force can only change the inertia of a body and can't change the absolute or overall energy when applied to that body.

Factors for energy in special relativity
The equivalence factor for inertial energy is and for kinetic energy is Where is the equivalence factor for quantum energy, which has the value of (1 − − 2   2 ).
The table for values of these factors is given below as relative velocity increases 0 . In this table, we can see that how the quantum energy of matter-wave in a moving body evolves with kinetic energy and create a catastrophe in the relative energy for photons.

Photons
The relative energy is given by the expression, = 2 , if we manipulate this equation, And it is not mathematically right to derive, the total energy of photons by equation (4.1), because it is relative energy not the total energy of the photon. The total energy of a photon can be measure by equation (4.2) only. Obtaining momentum from equation (4.1) by ignoring term is a serious mathematical mistake, which is defiantly an obstacle for quantum energy to get formalize with relativity. It's just equivalent to saying that infinity or zero is equal to some real number. A photon has all its inertial (sleeping) energy in the awaken (vis-viva) state and contains an absolute mass, which causes momentum. The Lorentz transformation declares that the relative mass energy of photons must be infinite to hold the second postulate of special relativity. The rest mass notation 0 for photons create confusion and destroy the beauty of relativity. [4]

Conclusion:
From equation (1.1) it directly follows that if a body absorbs any radiation of frequency ( ), then its absolute mass get increases by 2ℎ / 2 or (1.4745 × 10 −50 ) .
The fact that mass energy withdraws from a body becomes the energy of radiation makes no difference, so we can conclude that the inertia of a body is the measure of its energy content and vice-versa.

Declaration:
The author has no conflict of interest.