Download New Concept of Mass-Energy Equivalence

European Journal of Scientific Research
ISSN 1450-216X Vol.26 No.2 (2009), pp.161-175
© EuroJournals Publishing, Inc. 2009
http://www.eurojournals.com/ejsr.htm
New Concept of Mass-Energy Equivalence
Bahjat R. J. Muhyedeen
Department of Chemistry, College of Science, University of Baghdad, Jadriyah
Baghdad, Iraq, Amman, Jordan, Retired in August 2007, Previously
Professor of Quantum and Nuclear Chemistry, MRSC
E-mail: [email protected]
Abstract
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 give a clear
vision about the moving mass. The speculative Lorentz factor has also discussed to be
incorrect to be 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 processes.
A new non-relativistic mass-energy equivalence is used E=mbc as an alternative,
where b is a derived universal constant and equal to 0.624942 x 108 m/s which gives
to E m = 1.87354 x1016 J / Kg or 1AMU= 194.18 MeV. The ratio of mbc/mc2 is equal to
(194.18) / (931.49) = 0.209 which gave 41.7 MeV for the Total Kinetic Energy (TKE) of
fission fragments of experimental value 29.4-37.8 MeV rather than 200 MeV given by
E=mc2. The magnetic constant of charged field µoB 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 2.56
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 µoB, relativistic mass, relativity, types of energy
1. Introduction
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 through the history since the philosophers of the
Greek, Roman, Arab, India and China. 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. before 650 year Newton laws), (Salam, 1984) and Avicenna he also stated Newton's first
New Concept of Mass-Energy Equivalence
162
and second law of motion in 980-1037 in his book: Ibn Sīnā's, Kitab al mayl (Theory of Inclination)
(Espinoza, 2005).
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 a controversial at that time but later they were understood as a complementary.
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 19th century to 20th century the mass-energy concept became more realistic
for both issues and a lot of scientists shared in crystallization of the concepts to understand deeply the
secret of the universe. In 1804 John Dalton stated his simple Atomic Theory.
In the early 20th century the scientists started investigation the atom structure after the discovery
of the electron, theorized by G. Johnstone Stoney (1874) and discovered by J. J. Thomson (1897), the
proton theorized by William Prout (1815) and discovered by Ernest Rutherford (1919) and the neutron
discovered by James Chadwick (1932). The theoretical and experimental researches on the energy,
atom, 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, 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 theoretical and experimental works in nuclear physics resulted in formation of Standard
Model (1970 to 1973) (Agrawal et al, 1998; Bromley, 2000; Kane, 1987). Although the Standard
Model well describes the elementary particles and composite particles, but it is still considered as a
provisional theory rather than a truly fundamental one.
Therefore, some new speculative theories beyond the Standard Model extruded attempts to
remedy these deficiencies. According to Preon Theory -coined by Jogesh Pati and Abdus Salam in
1974- (Pati and Salam, 1974; Dugne et al, 2002), there are one or more orders of particles more
fundamental than those found in the Standard Model called preons, which are derived from "prequarks" which look like “particle zoo model” that came before it. The interest in preons has vanished
since the simplest models were experimentally ruled out in the 1980s.
The Grand unification Theory attempts to combine the electroweak interaction (through
Bosons W ± , Z o ) with the strong interaction (through Gluon) into a single 'grand unified theory' (GUT)
(Encyclopedia Britannica, 2008). GUT predicts that at extremely high energies (above 1014 GeV), the
electromagnetic, weak nuclear, and strong nuclear forces are fused into a single unified field (Parker, B
1993; Hawking S., 1988). Such a force would be spontaneously broken into the three forces by a
Higgs-like mechanism. However, the non-observation of proton decay made it less important.
The Supersymmetry tried to extend the Standard Model by adding an additional class of
symmetries to the Lagrangian. These symmetries exchange fermionic particles with bosonic ones. In
other words, in a supersymmetric theory, for every type of boson there exists a corresponding type of
fermion, and vice-versa. Such symmetry predicts the existence of supersymmetric particles,
abbreviated as sparticles, which include the sleptons, squarks, neutralinos and charginos. But these
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Bahjat R. J. Muhyedeen
particles are so heavy that they need more experiments to be verified, (Baer and Xerxes, 2006). As of
2008 there is no direct evidence that supersymmetry is a symmetry of nature (Martin, 1999; Lykken,
1996; Drees, 1996; Bilal, 2001; Arygres, 2001).
String Theory is an incomplete mathematical approach to theoretical physics, whose building
blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point
particles that form the basis for the standard model of particle physics, (Arygres, 2001; Cooper et al,
1995; Junker, 1996).
The string theory, mainly M-theory out of five string theories, suggest that all "particles" that
make up matter and energy are comprised of strings, measuring at the Planck length
(
meter), that 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, (Schwartz, 1998;
Troost, 2005; Witten, 2005). String theory is formulated in terms of an action principle, either the
Nambu-Goto action (using the principles of Lagrangian mechanics) or the Polyakov action (using
conformal field theory), which describes how strings move through space and time. These strings
vibrate at different frequencies which determine mass, electric charge, color charge, and spin. A string
can be open (a line) or closed in a loop. As a string moves through space it sweeps out a twodimensional surfaces f(τ,σ) called a world sheet. One particularly interesting prediction of string theory
is the existence of extremely massive counterparts of ordinary particles due to vibrational excitations of
the fundamental string. Another important prediction is the existence of a massless spin-2 particle
behaving like the graviton. The main aim of this theory is to treat the universe through the quantum
mechanic and classical mechanic.
In my previous article I have discussed the idea of conversion of mass to energy and vice versa
and I showed it is incorrect neither in the chemical nor in nuclear reactions. The annihilation reactions
of electron-positron are pseudo processes in addition to that if they occur they will break the laws of
conservations. These reactions are misinterpreted by workers. These reactions represent elastic
scattering and they could not happen at very low energies otherwise the emitted positron from nucleus
will annihilate immediately with outer electrons of the same atom. Billions of positrons released by
nuclear reaction P-P chain in the Sun and some of them reach our earth without noticing such
annihilation (Muhyedeen, 2008).
I also proposed a primitive new nuclear model (still not mature model) to explain the nuclear
reactions to pass the virtual mass defect mechanism and to fix proton and neutron mass inside and
outside of the nucleus. This model proposes new elementary particles called conservons and magnetic
sub-quarks called magnetons. 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. The sixth state represents the black hole structure in which there are no nuclei identities but
only elementary particles that combined with very strong nuclear forces. This state represents the basic
building blocks of matter. 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 maintained that moving charged particles are dual in nature due to their charge and its
inherent electromagnetic field. I as well maintained 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 0.624942362 x
New Concept of Mass-Energy Equivalence
164
108 m/s. This b constant is equal to 0.2085 of speed of light. In my opinion, that this b constant
represents the optimum speed to be reached by the moving charged particles.
In present paper I would like to correct some ideas on mass-energy relationship such as kinetic
and potential energy. In addition to explain the correct meaning of E=mc2 which deeply treated by
Einstein.
2. The Mass-Energy Relationship in E=mv2 Equation
The coupled behavior of mass and energy is 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 how motion can be converted to heat. 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 were also another theory in mechanic which was
called the theory of the conservation of momentum suggested 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 of 1940. For example, 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.
The E=mc2 equation is also still not confirmed in the chemical reaction and reason cited for this
is that equipments are not enough sensitive (Arthor, 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 investigation of the
Big Bang theory because the creation of mass or energy in 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 is far less than the theoretical value predicted by E=mc2. Robert Serber (member of
first American team entered 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 DsJ* (2317)+ having mass 2,317 mega-electron volts (or 2.32
GeV/c2). But this mass is far less than current estimates based upon E=mc2.
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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
convertible; secondly, the radiation has mass. In my perception, that these ideas are utterly incorrect
and the mass and the energy are inconvertible.
I may classify the energy in universe into two types of energy. These are primitive and incited
energy.
a. The primitive energy: since the Big Bang, the energy was stored mainly in two big
reservoirs; 1- binding energies of quantized levels of atomic orbital and 2- binding energies
of quantized levels of 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 this 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 any body or
particle. For example an earthquake roll down a rock from a mountain, researcher
accelerates particle or 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 had published in the literature for 330 years since Leibniz
mathematical equation ∑ mi vi2 in 1676-1689 up to present time.
The scientists do understand the equation as they read and write it that means they believe the
kinetic energy just come from multiplication of mass of the moving particle (or body) by its velocity
square v2. In 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 this
equation.
Actually, this is unclear concept. In addition to that the scientists look at the concept of energy
2
(E=mv ) calculated from the mass of particle nature in similar way to that energy (E=hν) calculated
from electromagnetic spectrum of wave nature. This misunderstanding is obscure and misleading
which resulted in creation of deceptive ideas that the scientists to the same historical serious errors
about E=mc2.
In my opinion, the kinetic energy calculated from the moving mass is just a mathematical
equivalent function which indicate to the equivalent amount of energy that correspond to any reaction
resulted by 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 type of
energy from any moving mass.
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Normally, the anticipated energy from a wave or particle can not calculated directly unless
there is a conversion factor. For example, the energy calculated from the electromagnetic wave is used
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. Coriolis-Poncelet calibration factor idea might come from
the incorrect understating of kinetic energy equation as just come 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 as E=mv2.
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 calibration factor to be E=Kx2 (William Rankine in 1953
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 α ∆
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 great disaster to
science since 20th century 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 (∆m=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 spit of the
great work that submitted by those scientist but all of them never focused on the real meaning of the
energy which is 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 think 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 to 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, 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 universal constant which can
be used to convert the mass to energy in simple equation E=mc2. The incorrect interpretation of E=mc2
through accepting c2 can be used as 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:
γ=1/ 1 − β 2 where:
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Bahjat R. J. Muhyedeen
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.
Originally, in 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 1 − β 2 which 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 to use 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 what ever is? But I can not accept 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 an 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 its
speed). I think, the arbitrary mathematical factor should not 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 so called rest and relativistic mass as chemist.
Of these three delusive concepts is the mass increment (relativistic mass). This concept, for me
as chemist, is a big disaster in science since there is no way to any moving mass to increase with
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 is 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 the mass of the moving
particle is increased? Is that through creation of atoms or increase 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 this?
All these labyrinths came from the misunderstanding of the equation E=mc2 since Einstein said
2
c 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:
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168
E=pc (should be understood so)
E=mcc (should be read so) (although there is no mass can move with speed of light)
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 become 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:
89.9 terajoules
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 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 depend on the velocity of the
moving particle and the second velocity as 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 would like to suggest a new conversion factor based on experimental principles, first, it
is based on semi-empirical formula, second, it is based on wave quantized character and third, it is
based on universal constants which reflect quanta characters which called by Max Planck energy
resonators.
Starting from black body treatment of Max Planck (Planck, 1901), we realize that the emission
of electromagnetic radiation from the black body is depending on the temperature which also
determines the frequency of the emitted radiation.
If we used the two universal experimnetal constants of Max Planck (hPlanck= 6.62606896*10-34
J.sec), (kPlanck= 1.429*10-23 J/deg) (in oK) we can see that the energy can be given from these two
constants; E=hPlanckν and E=kPlanckT. Please note that this constant is also wrongly known as
Boltzmann since the Boltzmann constant theoretically comes from R/NA (Boltzmann, 1877). The
success of Max Planck treatment which results in finding the two constants hPlanck and kPlanck was based
on three assumptions that the energy is composed of oscillators; the temperature is in Kelvin and the
wavelength at its max value. These assumptions and in addition to some theorem and some
experimental values led him to a historical success of black body radiation.
Now, we have to use the same three assumptions to find the new converting factor (massenergy equivalence formula). If we start from the relation between the temperature of the black body
radiation and the energy through the second constant KPlanck we will get the following equation:
E = 0.624942362 x10 8 * mc
(1)
The detailed derivation is explained in my previous article (Muhyedeen, 2008)
This equation may be rewritten as a general formula as E=(mb)c or as follow:
E=mbc
(2)
b is new universal constant and equals to 0.624942362 x 108 m/s which may represent the
optimum speed for electrons or any light charged particle.
Now, we can write the mass-energy equivalent as follow:
E
= 0.624942362 x108 * c
m
(3)
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Bahjat R. J. Muhyedeen
The mass-energy equivalence will gets its final value if we substitute for the velocity of light
2.99792*108 m/s, as follow:
E
= 1.87354 x1016 J / Kg
m
(4)
For one atomic unit, amu, the mass-energy equivalent is calculated as follow:
(5)
1amu = (1.66054 *10-27 kg)* 1.87354*1016 J/kg
(6)
1amu = 3.111*10-11 J
The equivalent energy to one amu in MeV is calculated as follow:
(7)
1 amu (in MeV) = 3.111*10-11 J * MeV/ 1.60218*10-13 J
Or
1 amu = (194.177) MeV
(8)
If If we relate our value of the mass-energy equivalence in MeV with that of Einstein then we
get the following; the ratio of mbc/mc2 is equal to (194.177 MeV/ 931.49 MeV) = 0.20846
Let us now test our mass-energy equivalent of (E/m) from our equation E=mbc in relation to
the speculative equation of Einstein E=mc2 in the calculation of the energy released from nuclear
fission where the Einstein equation E=mc2 overestimated the Q-value. In laboratory it is confirmed
(Hambsch,1989; Thiereus, 1981) that using thermal neutrons the Total Kinetic Energy (TKE) of fission
fragments (of the mass=3.55x10-28Kg) 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). These observations
are more than three decades old (Bakhoum, 2002). Some alternate suggestions have been made to
explain the total kinetic energy of fission fragments by extending the successful Liquid-Drop Model of
Bohr and Wheeler (Straede, 1987; Wilkins, 1976). Bakhoum has attempted to explain the same with
Wave Mechanical equation E=mv2 (Bakhoum, 2002). He estimated the TKE of fission fragments from
Gaussian graph in the range of 175MeV (as experimentally it is observed less), instead of expected
200MeV. 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=0.625 x 108 m/s)(Bakhoum, 2002).
The new equation E=mbc gave 41.7 MeV which is in good agreement with experimental value.
(E=3.55x10-28Kg x 0.624942362 x 108 m/s x 2.99792*108 m/s)/ 1.60218*10-13 J/MeV=41.7 MeV)
The Experimental Value
(Hambsch, 1989; Thiereus, 1981)
scaled-values 29.4-37.8 MeV
From Our
Equation E=mbc
41.7 MeV
From E=mc2 (Einstein,1905)
200 MeV
From E=mv2 From Gaussian
graph (Bakhoum,2002)
175 MeV
7. Some Derived Equations for Non-Relativistic Particles
As I expect, that the B constant is a universal value which represents the integrated or optimum
velocity of all elemental charged particles (like leptons) can be emitted through all nuclear reactions or
processes and no charged 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 shown below:
Since E=mbc, then the momentum, P can be derived by division by velocity of light:
(E/c)=[(mbc)/c]
then the momentum will be given as below;
p=mb
(1)
We can now write a similar equation to De Broglie for non-relativistic equation as follow
λ=
h
Bm
(2)
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 elementary particles as below:
b=λυ
(3)
New Concept of Mass-Energy Equivalence
170
This equation can be used for particles moving with velocities less than velocity of light and the
energy can be calculated as follow:
E=hb/λ
(4)
or
(5)
E=mb2
Which can be applied for heavy hadrons but less than alpha, and;
(6)
E=mv2
which can be applied for heavy hadrons
E=mvb
(7)
which can be applied for heavy hadrons but equal or more than alpha
E=mbc
(8)
which can be applied for light particles such as electron, muon and neutrino and others produced from
nuclear fission reactions.
E=mvc
(9)
which can be applied for any accelerated particles with velocity v should 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.
These equations are written based on the new concepts of E=mv2 and E=mc2 which used
different conversion factor (v, b and c) depend on the velocity of the measured particles. If the
velocity of the particle is less than 0.05c then we can use v as conversion factor, if the velocity of the
particle is less than 0.5c then we can use b constant as conversion factor and if the velocity of the
particle exceed 0.5c then we can use c as conversion factor.
The philosophy of choosing the conversion factor (v, b and c) for mixed beam of particles
(especially those produced through fission or nuclear reactions) should be studied more by the
scientists to get an international approval while for heavy single particle with known velocity less
than 0.05c we may depend on the formula E=mv2.
Beta Rays-Calculation
Consequently, for the momentum, P, value for electron in excited atomic orbital or in Beta decay from
nucleus can be calculated from the following:
P=bme, me=9.109x10-31 Kg
P=0.624942362 x 108 m/s x 9.109x10-31 Kg
P=5.692599975458x 10-23 Kg m/s
The wavelength of the electron of excited atomic orbital or Beta decay can be calculated from b
constant.
λ=
h
= 1.164x10-11m
Bm
The frequency of the electron is given by:
E MBC
=
=25.7736 x 10-18 Hz
h
h
The energy of beta decay may be calculated from E=mbc directly as follow:
E=mbc = 1.704375 x10-14 J or E= 0.107 MeV
The remainder of the beta energy will appear as excess energy of the neutrino. The energy
equation E=hυ=hb/λ can be used in particles physics for heavy particles more than alpha based on its
speed. The speed should be near the b-value.
υ=
Alpa Rays-Calculation
For the heavy charged particles the formula E=mvb can be used in estimation of its velocity if it is
accompanied with some light ray but we can use E=mvv to pure alpha rays. For example, the energy of
171
Bahjat R. J. Muhyedeen
alpha particle emitted from the source can be calculated as follow: mass of alph=4 amu, the
velocity=15000km/s, 1amu=1.66054x10-27kg then;
E=mvb= 4x 1.66054x10-27kg *15x 106 m/s *0.624942362 x 108 m/s=38.8 MeV (for non pure
alpha rays).
E=mvv= 4x 1.66054x10-27kg *15x 106 m/s *15x 106 m/s = 9.32 MeV (for pure alpha rays).
This figure (9.32 MeV x2 = 18.64 MeV) is near to Cockcroft and Walton calculation for bombardment
of 7Li by proton in 1932 where they got two alpha products of 17.2 MeV.
One important note should be mentioned that the dependence on mass defect (∆m) in the
calculation of nuclear reaction can be used at present time due to lack of the fact about the nucleus
components. The nuclear calculations still pledged with the details data of the nucleus. These data may
be improved due to the promising forthcoming high-energy physics accelerators and hadron colliders
like CERN, SLAC and others provided that they do not use c2 as a conversion factor.
b -Constant Components
Since the two components of the light or the electromagnetic ray, the magnetic constant, µo and electric
constant, εo are related to the speed of light due to Maxwell formula as follow:
c=
1
µ oε o
, εo= 8.854187817 x 10-12 F/m, µo= 1.256637061 x 10-6 N/A2
Then we can write the same equation for the constant b, and calculate the magnetic component
for the charged particle field. But here we can suppose that the value of electric constant, εo is fixed
due to the fixed electronic charge but the value of the magnetic constant, µo will change and increase
for these charged particles that result in strong interaction more than the electromagnetic spectrum.
Thus, we get the new magnetic constant, µoB as follow:
B=
1
µ B x8.85418781710 −12
, then the new value of µoB of the field of charged particle is
equal to 3.265 x 10-6 N/A2.
So, the ratio of the magnetic constant µoB=3.265 x 10-6 N/A2 of the charged particle is larger
than that of light µo=1.256637061 x 10-6 N/A2 by 2.56 and this give 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 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
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 give a clear vision about the moving mass. The speculative Lorentz factor has also
discussed to be 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
hypothesis.
New Concept of Mass-Energy Equivalence
172
Finally, 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 0.624942362 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 µoB 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 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=194.177 MeV from E=mbc rather than 1 amu=931.49 MeV from
2
E=mc because this equation overestimate 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.
Acknowledgement
The author is highly indebted to Professor Dr. G. A. W. Derwish for his valuable and fruitful
discussions, suggestion and comments.
173
Bahjat R. J. Muhyedeen
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