In this post, I shall reveal the reason behind the appearance of the speed of light [c], in Einstein’s equation and explain why it has to be squared. This, I shall do with reference to the fabric of space and the nature of matter and energy as quantities derived from that fabric. And in order to save the reader going over previous posts for the relevant information, I shall begin by defining those parameter. However, for the sake of brevity, I shall not explain why those definitions hold true.
The fabric of space is a medium of oscillating homogenous spherical elements. The size of an element is of the order of the Planck length, with an invariable period of oscillation, so that the greater the amplitude of oscillation, the greater the acceleration they experience on the rebound. In other words, the greater they are pulled apart, the faster they rebound. This property is most important for explaining the nature and structure of light and its constant speed [c]. It is also very important for explaining the behaviour of matter in both classical and quantum mechanics.
Stable matter particles are localised dynamic structures that develop from the elements of the fabric of space. In a particle, they maintain perpetual angular motion as a group, so that the particle they form appears as a single spinning object. In the process they expose a given volume of the background vacuum, which represents the particle’s mass. Thus, mass is a void or a collection of voids in the medium.
Energy is the motion of the elements of the fabric of space, which in a given field could be oscillatory, acceleratory or constant angular speed, reflecting heat, gravitational and magnetic fields respectively. Angular motion diminishes with increased radial distance away from the source and therefore the same field is considered accelerating in radial direction, hence General Relativity’s definition of gravity as warped space-time. All three types of motion are induced by matter by virtue of the mechanics and interaction with the fabric of space and they all coexist in one field around molecular matter. However, considered from different perspectives, they may appear as different fields. In fact, an object entering the field of another may also experience spin as a result of the combination of curvilinear and acceleratory components of motion.
Energy could also be quantised as localised impulse-waves propagating in straight lines. Each such an impulse-wave is a photon.
In the absence of matter, the medium exists under neutral pressure. Therefore, the void (mass) developed by a particle has negative pressure proportional to its volume, while condensed elements forming the structure of a particle around the mass are under positive pressure. As such, elements in the surroundings are continually attracted to the mass, but are expelled by the spin of the particle. This mechanism is in fact one of two sources of the observed photon emission by matter. The mechanism also produces a weak vortex action around the particle, which represents the source of gravity in molecular matter. It intensifies with increased number of particles.
The void (mass) is essentially an intrinsic potential for greater dynamics in the medium, if it were to collapse. On the other hand, the perpetual motion of the elements forming a particle represents the particle’s intrinsic energy. Furthermore, when translating in space the particle’s motion relative to the surrounding field represents the particle’s kinetic energy. This is all we need to know about the fabric of space, matter, mass and energy in order to fully understand the reinterpretation of [E = mc2].
The current consensus amongst physicist is that mass is some form of condensed energy. However, according to the definitions I have given here that is not the case. Mass and energy are complementary phenomenon, but they are definitely not the same thing.
From the relativistic mass equation used to derive [E = mc2], we have:
m = mo (1- β2)-1/2, β = v/c eq. (2.1)
Where m, is referred to as the dilated mass, mo is the rest mass, and β is the dynamic ratio of the mass.
In the binomial expansion of eq. (2.1) we obtain:
m = mo [1 + (β2/2) + (3β4/8) + (5β6/16) + …..
m = mo [1 + (v2/2c2) + (3v4/8c4) + (5v6/16c6) + ……..
mc2 = moc2 + mo (v2/2) + mo (3v4/8 c2) + mo (5v6/16c4) +…..
E = moc2 +mo (v2/2) +(3v2/4c2) mo (v2/2) +(5v4/8c4) mo (v2/2) +… eq.(2.2)
The accepted interpretation of eq. (2.2) is that the total energy in matter is the sum of its potential energy [moc2] given by the first term, its kinetic energy [mo (v2/2)] given by the second term, and its relativistic kinetic energy, given by the third and higher order terms. Whilst this expansion represents the sum of the different components of energy in a given mass, its current interpretation with respect to a moving particle is incorrect.
According to current interpretation of eq. (2.1), if a particle approaches the speed of light [v → c], its mass approach infinity [m → ∞]. However, if the particle could reach that speed, it would develop infinite inertia— i.e., resistance to motion. Imagine a particle having mass greater than that of the universe in a particle accelerator! In reality, no increase in particle mass has been observed when particles accelerated close to the speed of light. For example, protons accelerated in particle accelerators reach speeds of [99.9999 c], but show no increase in their mass. And although physicists like to interpreted the increase predicted from the equation in terms of increased kinetic energy of the particles, that too does not resolve the issue, for even then the energy of the particle should be approaching infinity, which is not the case. So, what is the correct interpretation of the equation?
Here is the interpretation!
The increase in mass created by a particle as it accelerates is not part of the particle. Rather, it is created in the surroundings in the form of energy, so that the greater the speed of the particle, the more energetic and intense the photons it generates. Therefore, in addition to the simplified definition of a photon that I gave above as an energy quanta in the form of an impulse-wave, as a photon propagates through the fabric of space it is continuously exposing an element of the background vacuum at the speed of light [c]. Thus, the mass dissipated as photons is non-gravitational. It is electromagnetic mass.
When a particle reaches the speed of light, the excessive uneven pressure distribution on its structure distorts it, then causes it to collapse. The distortion of the mass itself could be verified with reference to the equations for longitudinal and transverse masses of slowly accelerated electron referred to in Einstein’s paper of 1905. On collapse, mass of the particle becomes part of the infinite background vacuum, hence the infinite mass. However, the energy generated in the collapse does not all materialise at once. Instead, it is produced in cycles as the mass gradually dissipates into photons. In effect, the collapsed elements rebound following their initial collapse, then continue to oscillate indefinitely about the centre of mass, producing less photos in each successive oscillation. The process as described by the equation is as follows:
When a particle collapses, the elements forming its structure collapse into the mass producing the first term in the expansion [moc2], which represents the initial energy release from the mass. They then rebound and collapse repeatedly producing the subsequent terms in the binomial expansion. In effect, the binomial expansion represents the infinite summation of energy generated cyclically as three-dimensional under-damped vibration. As such, the original mass becomes progressively smaller in successive collapses and rebounds as it is converted into energy (photons). This is reflected by the value of factors in the second and subsequent terms [1, (3v2/4c2), (5v4/8c4),……..] in eq. (2.2) which are effectively amplitude reduction factors. That is, the amplitudes of the elements oscillating about the centre of the collapsed mass are reduced successively as under-damped vibration propagating indefinitely in space-time.
Therefore, the speed of light in Einstein’s equation E = mc2, signifies the dissipation of mass into energy as photons travelling as spherical two-dimensional wave-fronts, hence the square of the speed of light. Expressed as E/m = c^2, gives the relationship between energy and mass a significant meaning as a constant of nature, just like the Planck constant.