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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 - Equivalence

Bahjat R. J. Muhyedeen Department of Chemistry, College of Science University of Baghdad, Jadriyah, Baghdad, Iraq Contact 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 (v and c) are used to convert the 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 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 -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 0.603797 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 (TKE) of fission fragments of experimental value 29.4- 2 2 37.8 MeV/bc rather than 200 MeV/c given by E=mc . 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, -charged particle constant, b, magnetic constant μb, 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 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) (Espinoza, 2005). 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 ) (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 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 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 and chemistry, including condensed matter physics, solid-state physics, atomic physics, molecular physics, computational chemistry, quantum chemistry, particle 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, , 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 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 . 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 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 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. 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 incited energy. a- The primitive energy: since the Big Bang, the energy was stored mainly in two big reservoirs; 1- binding energies of the 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 2 mathematical equation mi vi 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 this equation. 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 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 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 Δ 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 . It is defined as: γ=1/√ where:

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 , 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 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 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 (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: 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 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 (h = 6.62606957x10-34 J.s), (k = 3.806488x 10-23 J/oK) in addition to the Wien constant to P P 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:

( ) ( ) (1)

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:

E=mbc (2)

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:

( ) ( ) ( ) (3) ( ) The mass-energy equivalence will gets its final value if we substitute for the velocity of light 2.99792458 x108 m/s, as follow:

( ) ( ) (4) ( )

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) Or 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 light1.

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- 2 value for is 34.901 MeV/bc (compared to 173.29 MeV/c ) and the Q- 2 value for is 38.523 MeV/bc (compared to 191.274 MeV/c ). The 2 Q-value for the nuclear fusion is 4.506 MeV/bc (compared to 22.37 MeV/c ) and the 2 Q-value for the nuclear fusion is 1.012 MeV/bc (compared to 5.0 MeV/c ).

1 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

10 11 The Q-value for the nuclear reaction B(d,n) C is 1.3020 MeV/bc (compared to 6.465 MeV/c2).

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. 2 ̅ is equal to 0.0007756 u. The Q-value is 0.7225 MeV/c (based on 931.5 MeV/c2 relativistic) or 0.1455 MeV/bc (based on non-relativistic 187.607MeV/bc). The Q-value for 2 beta decay for , ̅ is 0.11 MeV/bc (compared to 0.54595 MeV/c ). The velocity of beta particle emitted from the nuclear process cannot be calculated from E=mbc directly because of the neutrinos.

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 2 MeV/c ). Another example is that, the Q-value for alpha decay for is 1.29 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, , tau lepton and hadrons as shown below:

The momentum of the fermion The momentum p of the fermion can be given by the following equation: p=mb (1) 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:

(2)

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.

(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: b=λυ (4) 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: E=hb/λ (5) 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:

Bethe formula 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:

[ ( ) ( )]

3 Where N is the number of the atom of the absorber in cm (=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, 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: 2 Ec=1600mec /Z. We can replace c speed with b speed, as the electron cannot move with speed of light, 2 to get the new formula Ec=1600meb /Z. The following Table-2 shows the difference in the calculated values. Table-2: The critical energies for some material

2 2 Material Ec MeV/c Ec MeV/b Cu 24.8 1.005 Pb 9.51 0.385 air (STP) 102 4.132 plastic 100 4.050 water 9 0.365 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 -7 2 to that of light or the electromagnetic ray (the magnetic constant, μo 12.56637061 x 10 N/A and -12 electric constant, εo 8.854187817 x 10 F/m) through Maxwell formula c=1/√(μo εo) as follow:

or , then the new value of μb of the field of √ ( ) ( ) charged particle is equal to 3.265 x 10-6 N/A2. -5 2 So, the ratio of the magnetic constant μb=3.0979 x 10 N/A of the charged particle is larger -6 2 than that of light μo=1.256637061 x 10 N/A 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 hypothesis 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 -6 2 charged field μb was calculated from the Maxwell formula and found to be equal to 3.265 x 10 N/A 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.

Acknowledgement 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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