European Journal of Scientific Research
ISSN 1450-216X Vol.26 No.2 (2009), pp.161-175
© EuroJournals Publishing, Inc. 2009
New Concept of Mass-Energy Equivalence
Bahjat R. J. Muhyedeen
Department of Chemistry, College of Science
University of Baghdad, Jadriyah, Baghdad, Iraq
Contact e-mail email@example.com
The correct meaning of E=mvv and E=mcc have been discussed. The discussion has shown that
the second v and c are conversion factors and not v2 and c2 in these two equations respectively. These
velocities (v and c) are used to convert the momentum units to energy units. The first v and c in both
equations should be multiplied with the mass to form the momentum term. The essential issue is the
momentum and not the mass where it is an absolute quantity and it will not give any indication while
the momentum gives a clear vision about the moving mass. The speculative Lorentz factor has also
discussed to be incorrect when used in special relativity to increase the mass of the materials through
changing their velocities.
The concept of conversion between mass and energy is discussed in chemical and nuclear
reactions to show it is incorrect and the annihilation reactions of electron-positron are pseudo
A new non-relativistic mass-energy equivalence is used E=mbc as an alternative, where b is a
derived universal constant and equal to 0.603797 x 108 m/s which gives E/m= 1.8101351214 x 1016
J/kg or 1u= 187.607 MeV/bc. The ratio of mbc/mc2 is equal to (187.607) / (931.49) = 0.2014 which
gave 41.7 MeV/bc for the Total Kinetic Energy (TKE) of fission fragments of experimental value 29.4-
37.8 MeV/bc rather than 200 MeV/c2 given by E=mc2. The magnetic constant of charged field μb was
calculated from Maxwell formula and found to be equal to 3.265 x 10-6 N/A2 and it was larger than
magnetic constant of electromagnetic field μo by 24.65.
Keywords: E=mc2, E=mbc, Mass-Energy Equivalence, new mass-energy equivalence,
photon-frequenton, states of matter, speed of light-charged particle velocity
constant, b, magnetic constant μb, relativistic mass, relativity, types of energy.
Our present understanding of energy comes from different time periods, different experimental results
of science and different theories and models. The substantial concepts of mass and energy and their
relationship in the universe were continually changed throughout history by Greek, Roman, Arab,
Indian and Chinese Philosophers. The inertia of motion was described in the 3rd century BC by the
Chinese philosopher Mo Tzu, and in the 11th AC century by the Muslim scientist, Ibn al-Haytham
Alhazen who stated Newton's first and second law of motion in 965-1039, Risala fi’l-makan (Treatise
on Place) (i.e. 650 years before Newton laws), (Salam, 1984) and Avicenna also stated Newton's first
and second law of motion in 980-1037 in his book: Ibn Sīnā's, Kitab al mayl (Theory of Inclination)
New Concept of Mass-Energy Equivalence 162
But the most acceptable mathematical definition for mass and energy was written by Gottfried
Leibniz over the period 1676-1689 to express his theory vis viva of conservation of energy
(from Latin for living force) (Mackie’s, 1845) and the theory of the conservation of momentum
by Isaac Newton (British) in 1687 and René Decartes (French) in 1645 (Gullberg, 1997).
These two theories were considered as controversial at that time but later they were understood as
The mass concept is usually related to the energy. The mass is a fundamental concept in
chemistry and it is a central concept of classical mechanics and related subjects. The concept of energy
and its transformations is extremely useful in explaining and predicting most natural phenomena.
Energy transformations in the universe over time are characterized by various kinds of potential energy
which has been available since the Big Bang, later being released (i.e. transformed to more active types
of energy such as kinetic or radiant energy) when a triggering mechanism is available.
In the duration from the 19th century to the 20th century the mass-energy concept became more
realistic for both issues when many scientists shared in crystallization of the concepts to understand
deeply the secret of the universe. In 1804 John Dalton stated his five main points of his Atomic Theory.
The discovery of the electron by J. J. Thomson (1897), the discovery of the proton by Ernest
Rutherford (1919) and the discovery of neutron by James Chadwick (1932) in the first two decades of
the twentieth century has set the real foundations of the atomic and nuclear structure. The subsequent
theoretical and experimental researches on the energy, atom, nuclei, isotopes, waves and particles led
to the branch of fundamental sciences that deals with atomic and subatomic systems which we today
call quantum mechanics. It is the basic mathematical framework of many fields of physics and
chemistry, including condensed matter physics, solid-state physics, atomic physics, molecular physics,
computational chemistry, quantum chemistry, particle physics, nuclear physics, quantum
chromodynamics and quantum gravity. The foundations of quantum mechanics were established during
the first half of the 20th century by Max Planck, Curie, Albert Einstein, Ernest Rutherford, Niels Bohr,
Louis de Broglie, Max Born, Werner Heisenberg, Erwin Schrödinger, John von Neumann, Paul Dirac,
Wolfgang Pauli and others (Planck M. 1901-1908, Einstein, 1905, Rutherford, 1904-1933, Bohr, 1913,
De Broglie, 1924, Bernstein, 2005, Heisenberg, 1925-1927, Schrödinger, 1926, Macrae, 1999, Dirac,
1928, Pauli, Wolfgang and Jung, 1955).
The theories and discoveries of thousands of nuclear physicists and chemists since the 1910s
have resulted in a notable understanding into the fundamental structure of matter. These findings
explained to us several facts about how the matter is composed of elementary and composite particles
and how the forces control these particles. The Standard Model has integrated all these efforts and
concepts to crystalize them for use in the data explanations of most of the experimental results
(Bromley, 2000; Kane, 1987). The experts of CERN said “Even though the Standard Model is
currently the best description there is of the subatomic world, it does not explain the complete picture.
The theory incorporates only three out of the four fundamental forces, omitting gravity”.
Other speculative theories tried to remedy these deficiencies such as Preon Theory which is
coined by Jogesh Pati and Abdus Salam in 1974- (Pati and Salam, 1974; Dugne et al, 2002). This
theory believes that there are one or more orders of particles more fundamental than those found in the
Standard Model called preons, which are derived from "pre-quarks" and look like “particle zoo model”
that came before it. The interest in preons has vanished also since the simplest models were
experimentally ruled out in the 1980s. More theories have been suggested such as Supersymmetry
theory, string theory and grand unification theory. Supersymmetry theory states that for every type of
boson there exists a corresponding type of fermion such as sleptons, squarks, neutralinos and charginos
(Martin, 1999; Lykken, 1996; Drees, 1996; Bilal, 2001; Arygres, 2001). The Grand Unification Theory
is a theory that searches for precise explanations to all physical phenomena in the universe starting with
the combining of the three fundamental forces: the electromagnetic force, the strong force and the weak
force at high energies. It failed to combine the forth force due the lack of understanding of gravity
(Ross, 1984, Parker, 1993; Hawking, 1988).
163 Bahjat R. J. Muhyedeen
A more recent model is the string theory which suggests that all "particles" that make up matter
and energy are comprised of strings, measuring at the Planck length (Arygres, 2001; Cooper et al,
1995; Junker, 1996). These strings exist in an 11-dimensional universe to prevent tears in the "fabric"
of space using the uncertainty principle, whereas our own existence is merely a 4-brane, inside which
exist the 3 space dimensions and the 1 time dimension that we observe. It predicts the existence of a
massless spin-2 particle behaving like the graviton (Schwartz, 1998; Troost, 2005; Witten, 2005).
In my previous article I proposed a novel nuclear model to depict the nuclear structure and to
explain the nuclear reactions. The model proposes new elementary particles called conservons and sub-
quarks called magnetons. The magnetons are basic building blocks of the fermions while the
conservons control the conservation of mass number, linear momentum, total energy, charge and spins
during the nuclear reactions law of conservations. The electron, protons and neutrons are composed of
the integer multiple of sub-quarks elementary particles magnetons. The protons have certain stable
mass and the neutron have several stables masses depending on the isotope Z and N. The neutron will
have unstable masses in the radioactive nuclides.
I also have discussed the idea of conversion of mass to energy and vice versa and I showed it is
incorrect as it is neither in the chemical nor in nuclear reactions. The annihilation reactions of electron-
positron are disintegration processes rather than annihilation processes, because the annihilation will
break the laws of conservations (Muhyedeen, 2008).
In addition to that I proposed the fifth and sixth states of matter. The fifth state represents the
Nuclear Transparency in which the nuclear components are loosely bound and free to endure a nuclear
reaction due to the weakness of the electromagnetic belt surrounding the nucleus. Beyond this region
toward the sun core the fermions will be crashed and disintegrated into to their elementary particles,
magnetons, which accumulated in hazy form which I called nuclear magma. The nuclear magma
starts getting cold and dark because no heat can be absorbed or emitted due to the amorphous
structure. The nuclear magma is denser than the nuclei and of high magnetic property and they bind
each other through very strong charged nuclear forces. This nuclear magma will be born in the core of
the sun and it moves down and up toward the surface as “cold and dark” mass, so called a sunspot,
therefore, their appearance will be fluctuated to the observer. These sunspots (nuclear magma) are
collected together through a million of years to form a black hole state and this nuclear magma state of
matter may be called the sixth state of matter.
Moreover, I discussed the nature of light and I explained it is composed of wave discrete
packets of "frequentons" to differentiate them from discrete packets of photons of particle nature. I
concluded that light is not of dual character (Muhyedeen, 2008). Of course, Bohr refused the photons
existence and had a long debate with Einstein known as Bohr–Einstein debates.
Furthermore, I explained both the photoelectric effect and Compton’s effect (Compton, 1923)
based on the new wave concept of light represented by frequentons. I also proved that the Heisenberg
uncertainty Principle (Heisenberg, 1927) became invalid and there is complete certainty in the
measurement. I confirmed that the fermions generate its charged electromagnetic field due to its
magnetons. This structure grants the particles the duality. I as well confirmed that the radiating body
will not lose any mass. Finally, I derived a simple semi-empirical formula for non-relativistic mass-
energy equivalence E=mbc, where b is new derived universal constant in term of speed units and
equals to 0.603797 x 108 m/s. This b constant is equal to 0.2014 of speed of light. In my opinion, that
this b constant represents the optimum speed to be reached by the moving charged particles.
In this paper I would like to correct some ideas regarding the mass-energy relationship such as
kinetic and potential energy. In addition to explain the correct meaning of E=mc2 which was deeply
treated by Einstein. I also will submit a novel wave-particle relation to explain the charged
electromagnetic field of the fermion.
New Concept of Mass-Energy Equivalence 164
2. The mass-energy relationship in E=mv2 equation
The coupled behavior of mass and energy is a very old idea since Thales of Miletus (Greek
philosopher, 624 BC–ca. 546 BC) then Galileo (Italian) in 1638 (Singer, 1941) then in 1676
mathematically formulated by Gottfried W. Leibniz (German) (E=mv2), to express his theory Vis Viva
of conservation of energy (from Latin for living force) (Mackie’s, 1845). Of course, later another
theory, dubbed as Caloric theory, was discussed that motion can be converted to heat and how it was
achieved. Some scientists study these two competing theories such as Antoine Lavoisier in 1783 and
Rumford in 1798 and others to prove that the mechanical motion could be converted into heat. In 1807,
Thomas Young changed the name from Vis Viva to Energy. At that time there was also another theory
in the mechanics which was called the theory of the conservation of momentum suggested by René
Decartes (French) in 1645 (Gullberg, 1997) and formulated as (p=mv) by Isaac Newton (English) in
1687. The scientists at that time were focused on the stars and planets and they thought that the
energy emitted from stars is finally converted to the mass and vice versa to keep the eternity of the
universe and they also thought that when body emits radiation it will loss some of its weight. For
example, in 1717 Isaac Newton (England) speculated that gross bodies and light are convertible into
one another (Newton, 1704, Cohen et al, 1999). These confused ideas grew up gradually and they were
well crystallized as concepts of classical mechanics from 1800-1920. It became very common in
physics that mass–energy equivalence refers to the concept that any mass has an associated energy and
vice versa. From the relativity point of view that mass and energy are two forms of the same thing and
neither one appears without the other and even a single photon moving in empty space has a relativistic
mass, which is its energy divided by c2.
3. The mass-energy relationship in E=mc2 equation
The E=mc2 equation usually overestimates the produced energy due to its non-logical comprehension
that made c2 as a conversion factor and this disclosure appeared since the atomic bombs explosion
tests in early 1940. For example, the nuclear scientists said that in nuclear fission roughly 0.1% of the
mass of fissioned atoms is converted to heat energy and radiation. In turn, the mass of fissioned atoms
is only part of the mass of the fissionable material: e.g. in a nuclear fission weapon, the efficiency is
40% at most, meaning that 40% of fissionable atoms actually fission. In nuclear fusion roughly 0.3% of
the mass of fused atoms is converted to active energy. I will explain in the forthcoming paper that these
percentages of the mass will not actually convert to an energy because this concept it completely
wrong. The E=mc2 equation is also still not confirmed in the chemical reaction and the reason cited for
this is that current equipment are not sufficiently sensitive (Beiser, 1987). It may be not being regarded
as precisely true in such cases from the scientific point of view. It also did not work well with the
investigation of the Big Bang theory because the creation of mass or energy in the formation of
‘primeval atom’ is not consistent with E=mc2. The same thing can be said about the efficiency of the
nuclear weapons as well as nuclear reactors which are far less than the theoretical value predicted by
E=mc2. Robert Serber (a member of the first American team to enter Hiroshima and Nagasaki in
September 1945 to assess loses), has indicated that the efficiency of “Little Boy” weapon [U-235,
49kg] that was used against Hiroshima was about 2% only (Serber, R. 1943). Similarly Recent work
led by Antimo Palano (Palano, 2003) and his collaborators, at Stanford Linear Accelerator Centre,
SLAC using BABAR detector, confirmed discovery of a new particle labeled as
mass 2,317 mega-electron volts (or 2.32 GeV/c2). But this mass is far less than current estimates based
Generally, I can say that the inherited incorrect ideas about understanding the energy and mass
bred out two main imprecise concepts in modern physics that firstly, that mass and energy are
165 Bahjat R. J. Muhyedeen
convertible; secondly, the radiation has mass. In my perception these ideas are utterly incorrect and the
mass and the energy are inconvertible.
I may classify the energy in the universe into two types of energy. These are primitive and
a- The primitive energy: since the Big Bang, the energy was stored mainly in two big
reservoirs; 1- binding energies of the electrons in the quantized atomic orbitals of the atoms and 2-
binding energies of the fermions in the quantized nuclear shells of the nuclei of the atoms. We daily
use these stored energies in various chemical and nuclear transformations and there is no mass
converted to energy or vice versa. In nuclear fission processes one can say that these processes lead to
some spallation for very light particles carrying energies caused huge heat. These processes may be
calculated by the new equation E=mbc.
b- The incited energy: this type of energy appears when any force is applied on anybody or
particle. For example: an earthquake rolls a rock down from a mountain, a researcher accelerates a
particle or an atom and so on. These processes may be calculated by E=mv2.
4. The correct meaning of E=1/2mv2
I think that the real meaning of the kinetic energy equation is based on the deep understanding of the
relationship between the energy (as scalar or numerical quantity) and the moving mass. In point of fact,
no clear vision for this relationship has been published in the literature for 330 years since Leibniz
was published in 1676-1689.
The scientists do understand the equation as they read and write it, which means they believe
the kinetic energy just comes from multiplication of mass of the moving particle (or body) by its
velocity square v2. At the same time they do not think that the particle needs to move with a velocity
equal to a value of its square. They looked at it as kinematic energy (which describes the motion of
objects without consideration of the circumstances leading to the motion) rather than kinetic energy
because they focused on the whole term and not on the momentum term, which is the central issue in
Actually, this is an unclear concept. In addition to that the scientists look at the concept of
energy (E=mv2) calculated from the mass of particle nature in a similar way to that energy (E=hν)
calculated from electromagnetic spectrum of wave nature. This obscure and misleading
misunderstanding resulted in the creation of the same deceptive ideas that have historically led the
scientists to the serious errors about E=mc2.
In my opinion, the kinetic energy calculated from the moving mass is just a mathematical
equivalent function, which indicates the equivalent amount of energy that corresponds to any reaction
because of the momentum p of moving particle m with its environment. Therefore, it is a function of
momentum and not a function of movement as said in the literature. It is incited energy and not
primitive energy. Of course, the heat formed due to friction of moving body with material is another
issue and can be related to outer electrons physical interaction and it does not concern E=mv2 formula
concept. The mathematical function of the kinetic energy may be written as a simple multiplication of
p times the velocity;
E=pv (should be understood so)
E=mvv (should be read so)
E=mv2 (should be written so);
the second velocity here should be considered as conversion factor from momentum units to energy
units where v is conversion factor but not v2. This is a general rule for the calculation all types of
energy from any moving mass.
Normally, the anticipated energy from a wave or particle cannot be calculated directly unless
there is a conversion factor. For example, the energy calculated from the electromagnetic wave is used
New Concept of Mass-Energy Equivalence 166
in Planck conversion constants E=hν and E=kT. More examples are clear in electric, magnetic,
potential, thermal, nuclear and chemical energy.
The calibration factor 1/2 which added to the kinetic energy to be 1/2mv2 by Gaspard-Gustav
Coriolis (who coined the work for the product of force and distance, W=F.D) (Persson, 1998) and Jean-
Victor Poncelet in 1819-1839 (Didion, 1870) is not necessary and not essential because it is based on
engineering works data and not based on physical concept. It may depreciate the actual value of the
momentum acquired by the external force. The Coriolis-Poncelet calibration factor idea might come
from the incorrect understating of the kinetic energy equation as just coming from multiplication of
mass of the moving particle by its velocity square v2 and the momentum is just the first derivative of
the energy. Therefore, I suggest to remove this calibration factor and to write kinetic energy equation
Of course, in the same way we can discuss the potential energy E=1/2Kx2. The second x is a
conversion factor. We can write it without the calibration factor to be E=Kx2 (William Rankine in
1853 who was the first man coined potential energy).
5. The correct meaning of E=mc2
Since the appearance of the empirical formula E=mc2 in the works of S. Tolver Preston in 1875 (E
mc2) (Preston, 1875), it was once more misinterpreted in the same manner of that of kinetic energy.
The scientists look at this equation in a vague manner that the energy simply comes from multiplication
of mass by c2 as conversion factor. This delusive understanding lead to the great disaster to science as
the 20th century has brought out strange thoughts such as the mass and energy are convertible and the
energy has a mass. These concepts were clearly shown in the works of Jules Henri Poincarè in 1900
(mv= (E/c2)c, (Poincare’, 1900) ) Olinto De Pretto who speculated E=mc2 in 1903-1904, (Pretto, 1904;
Bartocci, 1999) Fritz Hasenőhrl in 1904 (m= 4E/3c2), (Ohrl and Sitzungen, 1904; Ohrl, 1905) Einstein
in 1905 (Δm=L/c2 or E=mc2, from speculative origin and the c2 as a conversion factor), (Einstein,
1905) and Max Planck in 1907 [(m-M)= E/c2 in which the mass increased by absorbing heat],
(Planck, 1907, 1908) and Einstein also in 1909 [(m-M)=L/c2], (Einstein, 1909). In spite of the great
work submitted by those scientists not one of them ever focused on the real meaning of the energy
which is the main gate to all sciences. Those scientists had inherited the misconception regarding the
understanding of the kinetic equation. They exceeded the science fiction to the extent that Preston said
that one grain could lift a 100,000 tons object up to a height of 1.9 miles. This wrong thought came due
to consideration of c2 as a conversion factor and the mass refers to any kind of mass. I am very sorry
to find out the great scientist of last century thinks in this way. The wrong understanding misleads the
researchers for one century over the entire world that it costs them time and money. They let the
scientists dream to create energy from the mass just by using the c2 as a conversion factor. Up to this
date there is no clear picture about the nucleus and its components and still they interpret the nuclear
reaction as virtual processes due to the absence of the fact.
Among those scientists is Einstein who wrote a new philosophy which crystallized in the theory
of special relativity to include his new concept about the speed of light as a universal constant which
can be used to convert the mass to energy in the simple equation E=mc2. The incorrect interpretation of
E=mc2 through accepting c2 can be used as the conversion factor lead him to do several accumulated
errors. Einstein laid down the special relativity to warrant how c2 can convert the mass to the energy,
but he was unlucky in his new theory because it was based on arbitrary speculative mathematical factor
of Lorentz–Fitzgerald γ which is named after the Dutch physicist Hendrik Lorentz. It is defined as:
β is the velocity in terms of the speed of light, u is the velocity as observed in the reference frame
where time t is measured, τ is the proper time, and c is the speed of light.
167 Bahjat R. J. Muhyedeen
Originally, in the two papers of 1888 and 1889, Oliver Heaviside (English), [after reading Maxwell 20-
equations and converted to 4-equations only, (Maxwell, 1861-65)] calculated the deformations of
electric and magnetic fields surrounding a moving charge, as well as the effects of it entering a denser
medium using Heaviside correction factor which he derived by himself (Heaviside, 1885-
1893). This included a prediction of what is now known as Cherenkov radiation.
The Heaviside idea of deformations of electric and magnetic fields surrounding a moving
charge inspired George Francis Fitzgerald (Irish) in 1888 and later Hendrik Lorentz (Dutch) in 1891
(Lorentz, 1904) independently to suggest what now is known as the Lorentz-Fitzgerald contraction in
bodies rather than in waves and they changed the Heaviside correction factor form to the speculative γ.
The Lorentz–FitzGerald contraction hypothesis was used to explain the negative result of the
Michelson–Morley experiment, in which they attempted to detect Earth's motion relative to the
luminiferous aether (Michelson and Morley, 1887). For Earth moving in its orbit at about 30 km/s
(18.5 mile/s), the contraction would amount to about one part in 200,000,000, which would be about 6
cm (2.5 inches) on the diameter of Earth. This small change accounts for Michelson and Morley's
negative result by making the source of light and the mirror draw closer together when the system is
moving lengthwise. Henri Poincare was not completely satisfied with contraction hypothesis. Of
course, Lorentz later believed that relativity had introduced some doubt about whether the length was
apparent or real?
Whatever the case may be, I probably accept (actually I don’t), as nuclear and quantum
chemist, Fitzgerald and Lorentz used this speculative γ-factor to bodies' contraction rather than waves
field contraction (as Heaviside originally used) to explain the body length contraction which might be
acceptable because length contraction and extension or expansion is one of the properties of the
material whatever is? But I cannot accept is to use γ-factor to increase mass (to add/or create/ more
grams) due to changes in its velocity.
Anyhow, the Lorentz factor was one of the fundamental postulates of Einstein's special theory
of relativity is that all inertial observers will measure the same speed of light in vacuum regardless of
their relative motion with respect to each other or the source. The use of such arbitrary mathematical
Lorentz factor resulted in additional misguiding concepts such as time dilation (T=Toγ), length
contraction (L=Lo/γ) and relativistic mass relative to rest mass (m=moγ) (i.e. mass increment due to its
speed). I think the arbitrary mathematical factor should not be used to control the essential concepts
like time, length and mass. I will let the length contraction and time dilation aside to the prudent
scientists to reassess and I will discuss what the so called rest and relativistic mass as a chemist.
Of these three delusive concepts is the mass increment (relativistic mass). This concept, for me
as a chemist, is a big disaster in science since there is no way for any moving mass to increase by
increasing its speed. The increment in mass means to the nuclear chemist that some new mass (even of
femto-grams or atto-moles) should be created from nihility or nonexistence. For example the rest mass
(mo) of 1 gram will be increased by 1/4 grams if it moves with 0.6c, that means the relativistic mass
(m) will be 1.25 grams (since γ has the following values when v approaches c in the following ratio :
0.2c→1.021, 0.4c→1.09, 0.6c→1.25, 0.8c→1.667 and 0.98c→5.025). This increment concept in mass
is nonsense. A simple question is directed to the special relativity that how is the mass of the moving
particle increased? Is that through creation of atoms or increase in the mass of elemental particles such
as electrons or protons or neutrons? And when the moving mass decrease its velocity Will its mass
decrease? What type of science is this?
All these labyrinths came from the misunderstanding of the equation E=mc2 since Einstein said
c2 is a universal conversion factor.
Anyhow, the correct visualization and understanding to this equation should be realized in the
same way of that we explained for the kinetic energy where c is conversion factor but not c2 as
Einstein alleged as shown below:
E=pc (should be understood so)
E=mcc (should be read so) (although there is no mass can move with speed of light)
New Concept of Mass-Energy Equivalence 168
E=mc2 (should be written so)
This means that the energy equation should be interpreted as p times c and not m times c2. In this case
the conversion factor is c but not c2. Nevertheless, this equation becomes useless because no mass can
move with speed of light
After this new understanding we can stop the international imaginary example that one gram of
mass is equivalent to the following amounts of energy:
24.9 million kilowatt-hours (≈25 GW·h)
21.5 billion kilocalories (≈21 Tcal)
21.5 kilotons of TNT-equivalent energy (≈21 kt)
85.2 billion BTUs.
If now we apply our new understanding to this equation then we need to write E=pc first. Then
we need to know the velocity of this mass (of one gram) to calculate the momentum. Then we can
convert the value to the energy unit using the speed of light.
The mass-energy equation can be written in different ways depending on the velocity of the
moving particle and the second velocity as the conversion factor. In my previous article I derived a new
mass-energy equivalence which can be reviewed in the following section.
6. Non-relativistic quantum mass-energy equivalence E=mbc:
In this regard, I had derived a new conversion factor b in E=mbc, rather than c2 in E=mc2, based on
experimental principles, semi-empirical formula, wave quantized character and the universal constants
which reflect the frequentons character, which were called energy resonators by Max Planck. I started
from black body treatment of Max Planck (Planck, 1901) which related the emission radiation from the
black body with the temperature radiation. I used the two universal experimental constants of Max
Planck (hP= 6.62606957x10-34 J.s), (kP= 3.806488x 10-23 J/oK) in addition to the Wien constant to
derive the new conversion factor b. Please note that Planck constant 3.806488x 10-23 J/oK is wrongly
known as Boltzmann constant kB (Boltzmann, 1877). In the literature, this kP is called Boltzmann
constant kB which is given by R/NA, i.e. the gas constant divided by the Avogadro constant, where
value is already given by R= kBNA. It is a trivial substitution loop i.e. k= kBNA/NA. The success of Max
Planck treatment, which results in finding the two constants h and k, was based on three assumptions:
that the energy is composed of oscillators, the temperature is set to one Kelvin and the wavelength at
its max value. These assumptions, in addition to some theorem and some experimental values, led him
to an historical success of black body radiation.
During the derivation of the new formula E=mbc I explained that when the radiation energy is
in equilibrium with the temperature this means that the emitted energy from the electron is equal to the
absorbed energy. I realized that the electromagnetic field (EMF) of the electron absorbs and emits the
electromagnetic energy through interference of both fields. The excited EMF of the electron is confined
by its mass m due to its internal basic component which called magnetons, me=∑mmagneton. Thus, I
attributed the wavelength λmax of the thermal spectrum to the energy absorbed by the EMF of the
excited electrons. Finally, I related the wavelength λmax of the excited EMF with the mass m of the
electrons through De Broglie expression (De Broglie, 1924) i.e. p=h/λmax to reach the final expression
for the energy as follow:
The detailed derivation of eq. no. 1 is explained in my previous article (Muhyedeen, 2008). Equation
no.1 gives the final non-relativistic quantum mass-energy equivalence as follow:
169 Bahjat R. J. Muhyedeen
b is new universal constant and equals to 0.603797 x 108 m/s which may represent the optimum speed
for electrons or any light charged particle. Now, I can write the mass-energy equivalent as follow:
The mass-energy equivalence will gets its final value if we substitute for the velocity of light
2.99792458 x108 m/s, as follow:
For one atomic unit, amu, the mass-energy equivalent is calculated as follow:
1u = (1.660538921 x 10-27 kg) x (1.810137886817 x 1016 J/kg) (5)
1u = 3.0058 x10-11 J (6)
The equivalent energy to one amu in MeV is calculated as follow:
1 u (in MeV) = 3.0058x10-11 J x MeV/1.60218x10-13 J (7)
1 u = (187.607) MeV (8)
This novel non-relativistic mass-energy equivalence will help in measuring the masses of the various
particles in low and high energies and to replace the problematic relativistic mass-energy equivalent
which result in various difficulties in the field of nuclear physics and chemistry. The derived universal
particle speed constant b, describing the speed of the electron, is more realistic than Dirac value where
he found the electron speed is equal to the speed of light
7. Application of E=∆mbc in Nuclear Reactions and Decays
Nuclear Reactions Calculation
The ratio of mbc/mc2 is equal to (187.607 MeV/ 931.49 MeV) = 0.2014. This energy equivalent
187.607 MeV/bc will be used in the calculation of all nuclear processes and reactions rather than
931.49 MeV/c2 of the speculative equation of Einstein E=mc2 which overestimates the Q-value. The
new equation E=mbc gives 41.7 MeV/bc of the Total Kinetic Energy (TKE) of fission fragments of the
mass=3.55 x 10-28Kg, (E=3.55 x 10-28Kg x 0.603797 x 108 m/s x 2.99792 x 108 m/s) / 1.60218 x 10-13
J/MeV=41.7 MeV/bc). Bakhoum found that the maximum velocity v of the oscillating fragments is v =
0.45 × 108 m/s which is very near to the b value (b=0.604 x 108 m/s). Bakhoum has attempted to
calculate the TKE using the wave mechanical equation H=mv2, at this velocity, and got 4.5 MeV/v2
(Bakhoum, 2002). Other experimental works showed that Total Kinetic Energy (TKE) of fission
fragments (of the mass=3.55x10-28Kg) using thermal neutron (25 KeV) that results from of U-235 and
Pu-239 is 20-60MeV less than Q-value of reaction predicted by Einstein’s equation E=mc2 (200MeV
for U-235) (Hambsch,1989; Thiereus, 1981). The new non-relativistic quantum mass-energy
equivalence E=mbc gives reasonable Q-values for the nuclear fission reactions. For example, the Q-
is 34.901 MeV/bc (compared to 173.29 MeV/c2) and the Q-
is 38.523 MeV/bc (compared to 191.274 MeV/c2). The
Q-value for the nuclear fusion
is 4.506 MeV/bc (compared to 22.37 MeV/c2) and the
Q-value for the nuclear fusion
is 1.012 MeV/bc (compared to 5.0 MeV/c2).
Dirac attempted to derive a relativistic wave equation. He obtained a Hamiltonian of the form:
where c is the velocity of light, mo is the rest mass of the particle, [α] is a 4×4 matrix, and ξ and p are 1×4 vectors, p being
the momentum vector. Dirac calculated the x component of the velocity of the particle, x˙, from the Poisson bracket,
, Since α11 = ±1, he concluded that must be always equal to ±c.
New Concept of Mass-Energy Equivalence 170
The Q-value for the nuclear reaction 10B(d,n)11C
is 1.3020 MeV/bc (compared to
Beta rays Calculation
The energy of beta decay may be calculated from E=∆mbc directly, where ∆m came from the mass
defect. The difference in atomic masses ∆m of the mother and daughter will determine the energy of
the emitted beta rays. For example, the mass defect ∆m for the beta decay emitted from Neptunium i.e.
is equal to 0.0007756 u. The Q-value is 0.7225 MeV/c2 (based on 931.5
MeV/c2 relativistic) or 0.1455 MeV/bc (based on non-relativistic 187.607MeV/bc). The Q-value for
beta decay for
is 0.11 MeV/bc (compared to 0.54595 MeV/c2). The velocity
of beta particle emitted from the nuclear process cannot be calculated from E=mbc directly because of
Alpha rays Calculation
The energy of alpha particle emitted from 238U can be calculated from the mass defect, E=∆mbc,
M = 0.004583314 u. The Q-value is 0.8599 MeV/bc (compared to 4.2698
MeV/c2). Another example is that, the Q-value for alpha decay for
MeV/bc (compared to 6.405 MeV/c2).
The velocity of alpha emitted from 238U (m=6.6446567 x 10-27 kg) of 4.27 MeV/c2 can be calculated
from E=mvb. The calculated velocity is 1.70514 x 106 m/s while E=1/2mv2 gives 1.435 x 107 m/s
which is relatively high.
8. Some derived equations for wave-particle duality
In my previous article I concluded that there are three difference concepts for the energy given by the
E=mbc. Firstly, E=mbc is used to describe the mathematical energy corresponding to the momentum
p=mb of the particle rather than the kinetic energy formula E=1/2mv2. Secondly, E=mbc is used to
describe the energy generated by the fermion. Thirdly, E=mbc is used to describe the energy of any
nuclear reaction or decay process such beta decay may be calculated directly from E=∆mbc where ∆m
came from the mass defect.
I also stated that the universal particle speed constant b represents the maximum velocity can be
reached by all particles (like leptons) when they are emitted from nuclear reactions or processes and no
particle can exceed this value unless it is accelerated. Therefore, this constant can be used to calculate
the momentum of the elemental charged particles such as electron, muon, tau lepton and hadrons as
The momentum of the fermion
The momentum p of the fermion can be given by the following equation:
This momentum can describe any moving fermions. In current physics we usually use speed of light to
describe the fermions and other nuclear particles (p=mc) but now we can use this universal particle
speed constant b in all formula that are used for the fermions.
The wavelength of the fermion
In my previous article (Muhyedeen, 2008) I described the wavelength that is corresponding to the
momentum of the fermion where we interpreted this wavelength which given by λ=h/mb is to
represents the excited radius of the fermion mass, due to the flexibility of the sub-structure (magnetons)
of the fermion and not due to the duality concept. For example, the active radius of the electron is
given by the following equation:
171 Bahjat R. J. Muhyedeen
For example, the wavelength λ (or excited radius) of the electron is 1.2044 x 10-11 m, the muon
particle is 5.835 x 10-14 m, proton particle is 6.552 x 10-15 m, neutron particle is 6.561 x 10-15 m, tau
particle is 3.4694 x 10-15 m and alpha particle is 1.652 x 10-15 m. This type of wavelength λ can be
measured when the fermion impact the target.
The frequency of the charged field of the fermion
The frequency of the electromagnetic field of the fermion generated by its mass can be calculated from
equation no. 3.
The frequencies of the electromagnetic field of some particle are calculated from this equation. For
example the ν for the electron is equal to 24.909 x 1018 Hz, for muon is 5.147 x 1021 Hz, for proton is
4.571 x 1022 Hz, for neutron is 4.577 x 1022 Hz, for tau is 8.656 x 1022 Hz, and for alpha is 1.816 x1023
Hz. The electromagnetic field of the fermion will dissipate only when it impacts its anti-fermion and
result in the disintegration process. The wavelength of the electromagnetic field of these fermions can
be calculated electron can be calculated from the following equation as follow:
For example, the corresponding λ for υ of the electron (24.909 x 1018 Hz) is equal to 2.424 x 10-
12 m or 2.424 pm. This wavelength (2.424 pm) describes the strength of the charged field of the
electron. Of course, this wavelength 2.4240 x 10-12 m is measured by Compton and he attributed it
incorrectly to the photon. The b constant may represent the optimum velocity of the elementary
particles, and can be used to relate the wavelength and the frequency of the field of the fermions as
below: As I stated previously that this equation no.3 can be used in particle physics for any fermion
moving with velocities less than speed of light. In particle physics we usually use c=λυ to describe both
waves and particles but now we can use b=λυ for the particle and c=λυ for waves. The wavelength λ
and the frequency υ for waves describe the electromagnetic field property while the wavelength λ and
the frequency υ for particles describe the particle charged field property. This charged electromagnetic
field cannot move with speed of light c but it moves with particle speed b. Equation no.3 can be used
for any particle moving with velocities less than velocity of light. The energy of the field at the
circumference of the fermion or the particle can be calculated as follow:
For example, the energy at the circumference of the electron (at 2.424 pm) is 20.7 eV and the
energy at the circumference of alpha (at 1.11 pm) is 151.171 MeV. These figures well explain the
difference in the ionization strength of the electron and alpha particle when they penetrate the matter.
The energy equation E=hb/λ can be used in particles physics for heavy particles based on its speed. The
speed should be near the b-value.
More relation can be derived such as E=mb2, which can be applied for heavy hadrons but less
than alpha, and E=mv2, which can be applied for heavy hadrons, E=mvb, which can be applied for
heavy hadrons but equal or more than alpha, E=mbc, which can be applied for light particles such as
electron, muon and neutrino and others produced from nuclear fission reactions and E=mvc, which can
be applied for any accelerated particles with velocity v that exceed 0.5 of speed of light. This formula
can be used in any accelerator. Also this equation can be used for fast neutral particle like neutrons.
We can use the universal particle speed constant b in all of equations that describe the behavior of the
electrons as seen below:
We can use this universal particle speed constant b to calculate the linear stopping power for the
electrons with high velocity which described by Bethe as follow:
New Concept of Mass-Energy Equivalence 172
If we set the electron velocity v=b we can simplify the equation to the following form:
Where N is the number of the atom of the absorber in cm3 (=NLρ/A), Z is the atomic number of the
absorber and I is the average of the ionization potential of the absorber (≈11.5x Z eV). This formula is
valid for non-accelerated electrons, muons and any similar particles.
We can use universal particle speed constant b also in the reduced formula for the electron with low
energy. We believe that the electron speed mostly move with this b value whether during the excitation
process in the atomic orbital or when it is emitted from radioisotope as beta ray. The reduced formula
can be written as follow:
The approximate formula for critical energy of the electron Ec (Bethe and Heitler) is given by:
Ec=1600mec2/Z. We can replace c speed with b speed, as the electron cannot move with speed of light,
to get the new formula Ec=1600meb2/Z. The following Table-2 shows the difference in the calculated
Table-2: The critical energies for some material
b -constant components
In my previous article (Muhyedeen, 2008) I showed that the two components of the electromagnetic
field (εo and μb) of the fermion can be related to universal particle speed constant b in a similar manner
to that of light or the electromagnetic ray (the magnetic constant, μo 12.56637061 x 10-7 N/A2 and
electric constant, εo 8.854187817 x 10-12 F/m) through Maxwell formula c=1/√(μo εo) as follow:
, then the new value of μb of the field of
charged particle is equal to 3.265 x 10-6 N/A2.
So, the ratio of the magnetic constant μb=3.0979 x 10-5 N/A2 of the charged particle is larger
than that of light μo=1.256637061 x 10-6 N/A2 by 24.65 and this gives a special magnetic property to
field of the charged particles. For example, the strong bonds in the chemical interactions are due to the
strong interference of electromagnetic ray with the electromagnetic field of the electron. It also
explains the deflection of gamma, beta and alpha rays through passing the magnetic field. Of course,
this concept is novel in the field of electrodynamics quantum science.
8. Summary and concluding remarks
The concept of conversion between mass and energy is discussed in chemical and nuclear reactions to
show it is incorrect and the annihilation reactions of electron-positron are pseudo processes. The source
of the energy in the universe has been classified into two types of energy. These are primitive and
incited energy. The correct meaning of E=mvv and E=mcc have been discussed. The discussion has
173 Bahjat R. J. Muhyedeen
shown that the second v and c are conversion factors and not v2 and c2 in these two equations
respectively. These velocities are used to convert the momentum units to energy units. The first v and c
should be multiplied with the mass to form the momentum term. The essential issue is the momentum
and not the mass where it is an absolute quantity and it will not give any physical indication while the
momentum gives a clear vision about the moving mass. The speculative Lorentz factor has also
discussed as incorrect to be used in special relativity to increase the mass of the materials through
changing their velocities. The relative mass, time dilation, length contraction were shown as a delusive
Finally, a new semi-empirical formula has been used for non-relativistic mass-energy
equivalence E=mbc, where b is universal constant in term of speed units and equals to 0.603797 x 108
m/s. This constant is equal to 0.2085 of speed of light. Finally, we can use this constant to relate the
wavelength and the frequency of the elementary particles in such that b=λυ. The magnetic constant of
charged field μb was calculated from the Maxwell formula and found to be equal to 3.265 x 10-6 N/A2
and it was larger than magnetic constant of light μo by 2.56
Other non-relativistic quantum equation are derived for high speed charged particles such as
p=mb, λ=h/mb, E=hb/λ, E=mb2, E=mvb and E=mbb.
I suggest to use 1 amu=187.607MeV/bc from E=mbc rather than 1 amu=931.49 MeV/c2 from
E=mc2 because this equation overestimates the value. I also suggest deleting Lorentz factor from all
mass calculation in nuclear sciences because it gives non logical values due to change of the mass
owing to its velocity.
The author is highly indebted to Professor Dr. G. A. W. Derwish, B.Sc. Ph.D. CChem., FRSC, for his
valuable and fruitful discussions, suggestion and comments.
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