Why does E/m = c^2?

Einstein’s famous equation E = mc^2 encapsulates the relationship between mass and energy. However, explaining the appearance of the square of the speed of light as a constant of proportionality proved to be an insurmountable challenge for physicists. They could only point out the colossal energy contained in a small amount of mass, which is immediately obvious from the magnitude of the speed of light. But, why the speed of light? What is its significance in the relationship? And why squared?
These and many other questions in physics remain unanswered, because the source of physical reality and the effect it has on all physical phenomena have been totally discarded. Therefore, phenomena such as matter, mass, energy, electric charge, light, gravity, time, etc., treated as independent quantities that arise out of nothing!


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  [0.9999 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.


Author: PhysicalRealityBlog

I am a structural design engineer with a passion for science and mathematics.

9 thoughts on “Why does E/m = c^2?”

  1. I must admit beyond me yet you strike a similar chord within me … I have a passion for mathematics, or at least I used to. I have transferred that passion into my photography. Angels, shadow, light, quatuam physics, patterns, sychroniciites, balance, infinity …. and so much more. I don’t think about it … it just happens. 🙂

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    1. Thanks for dropping by AmyRose. You may have gathered from the number of posts in my blog that I am quite new to WordPress. My posts are dedicated to a concept that I have been developing over the past ten years, in the hope of finding people who share my understanding of physical reality. I visited your blog and I loved your photography subjects and the photos… I too feel that you strike a similar chord within me. I have a great passion for photography and only recently I began, though very slowly, to organise some of the photos I have. A few weeks ago I opened a flickr account for the purpose: https://www.flickr.com/photos/abdul_tresh/ .. It only has three photos so far, but I am hoping to add more 

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      1. Physical reality and Life itself fascinate me. I “see” and “feel” beyond what the human eye can see and I have learned how to “see” beyond what most people deem reality to be. I know how to soften my gaze and go within as I look out. Hard to explain. I know all of Life to be created mathematically for it is perfect in its symmetry and form. I’ve watched trees for example who grow towards the other as if seeking family. When I studied anatomy and physiology when going to school for nursing, I walked away from that experience in such wonder at how these bodies of ours are put together. Complex, so complex all of Life is and it just boggles my mind. No coincidence this week I have some extremely deep posts coming which again leaves me in awe because if you view them you will understand of what I speak of. I “flow” and as I do with both camera and pen, I document mysteries as they are presented to me. I know not where this Journey is taking me, yet I do know I am on a specific Journey. I’m thrilled you “see” in my photography math and the message of “Life”. I do not have a flickr account. I only focus on WP and that beleive me, is enough. My blog has exploded. I look forward in learning from you. I will read your posts slowly and even if I don’t understand them, I may be able to “intuit” them. Yes I do that too. (Smile) Much Love, ❤ … SO many I interact with here which leaves me to tell you the best way for me to get to your blog is for you to comment on mine. Forgive me if that sounds selfish, but the sheer volume I deal with is at times overwhelming. I'm serious when I say I want to learn from you. Thank you.

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        1. Thank you AmyRose. I get the sense of what you mean by “seeing” beyond what most people deem reality to be. I guess that is what drives you to explore and learn more. The challenge of the mind boggling complexity of life you mentioned has driven me to search for what lies behind it. I came to realize the existence of a very simple, yet a well-hidden reality underlying all forms of physical existence; a reality which is fully accessible to us through logic (mathematics) to understand and contemplate. I also discovered that understanding how life comes about— that is how groups of inanimate atoms become self-regulating and arrange themselves to perform complex tasks, is surely beyond my grasp. As a biological cell, they definitely contain an element of a nonphysical reality, which any physical brain would find mind boggling, to say the least. However, with regard to physical reality, it is in essence counterintuitive, for what we perceive as being empty space is in fact a physical medium that permeates all space, and what we perceive as being physical matter particles are bubble of vacuum within the physical medium. I do realize that I have much to learn, and like you wanting to learn from me, I want to learn from you. I am looking forward to your upcoming posts. And by the way, I do not see it as selfish at all to ask of me to comment on your posts. I will do my best to find the right words. I wish you all the best in your journey with your camera and pen, wherever it may take you 

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  2. Hello professor (physicalrealityblog), I enjoyed your finite thoughts of math and precision. When I approach all that unknown as perceived versus your actual calculated reality, I much laugh on how a chemical change physically can impart a different dimension per se’. Thanks for giving me a look at seeing your interpretation. You must have spent about the same or more in amount of determination through training to gain a reality of your own. Please check out a scientificfishermans41’s glance at life after break, restrospection, and writing down my thoughts.

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    1. Hello and thank you for your comment and your invite to visit your blog scientificfishrman41, which I have done and found very interesting. I agree with your thoughts on reality. In fact, I share your appreciation of its complexity, though that may not be immediately apparent from my approach to its physical aspects. Since perception of reality takes place in the mind, and since the mind involves consciousness, I believe that understanding its complexity demands understanding consciousness, which is something I feel is beyond my capacity for understanding. I thank you again for your visiting my blog and look forward to reading more of yours.

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  3. “In reality, no increase in particle mass has been observed when particles accelerated close to the speed of light.” – Wrong. J.J. Thompson knew this in 1881.
    (Source: https://en.wikisource.org/wiki/On_the_Electric_and_Magnetic_Effects_produced_by_the_Motion_of_Electrified_Bodies )

    “For example, protons accelerated in particle accelerators reach speeds of [99.9999 c], but show no increase in their mass.” Wrong. Speeds do not go above c. Furthermore, these protons HAVE increased in mass. How else can particles of (rest) energies less than 1GeV create Higgs bosons of (rest) energies greater than 125GeV?

    “…even then the energy of the particle should be approaching infinity” – Here (probably) lies your misunderstanding. Masses do tend to infinity as \beta tends to 1. But, as discussed in my previous point, this can’t happen; particles can never reach this limit precisely because mass tends to infinity and we would have to put in a physically unreasonable amount of work to accelerate particles to \beta = 1.

    Please read a book on relativity – I recommend ‘Relativity Made Relatively Easy’ by Andrew Steane. The relevant lecture notes based off this book can be found here: https://users.physics.ox.ac.uk/~Steane/teaching/rel_A.pdf


    1. Thank you so much for your comment Matthew. I have now correct the error of (99.9999 c), which is supposed to read (0.9999 c) or 99.999% C. As to the rest of the contents, you may wish to dispute them, but I maintain that energy and mass are no more than the motion of the elements of the fabric of space and the background vacuum respectively.


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