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American Journal of Modern Physics 2020; X(X): XX-XX doi: 10.11648/j.XXXX.2020XXXX.XX ISSN: 2326-8867 (Print); ISSN: 2326-8891 (Online)

Charge- Equivalence leading to Ilectron from the Electron

D. Venkata Giri1, Ian Leonard Gallon2, Carl Edward Baum3

1Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, NM, USA and Pro-Tech, Wellesley, MA, USA 2Retired, Bridport, Dorset, UK 3Formerly at Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, NM, USA

Email address: [email protected] (D. V. Giri), [email protected] (I. L. ) To cite this article: Doddi Venkata Giri, Ian Leonard Gallon, Carl Edward Baum. Charge-Mass Equivalence leading to Ilectron from the Electron. American Journal of Modern Physics. Vol. x, No. x, 2020, pp. x-x. doi: 10.11648/j.xxx.xxxxxxxx.xx

Received: MM DD, 2020; Accepted: MM DD, 2020; Published: MM DD, 2020

Abstract: Hydrogen atom was considered as the smallest “bit of matter” until the electron was discovered. Nearly all attributes of the electron have been experimentally measured except for its radius. Electron’s radius has been derived in classical mechanics. The angular of the electron has been understood as a purely quantum mechanical effect. In this paper, we have established an equivalence between the charge and mass of a fundamental particle. This leads to a definition of a complex charge or a complex mass, which combine both charge and mass. Every fundamental particle with charge and mass can be defined by a single complex charge. Interaction of two complex charges leads to the familiar Coulomb and Gravitational . It also points out the possibility of a 5th of . By writing the charge and mass of the electron as mass and charge, we come up with a new particle which we have called the ilectron. Some attributes of the ilectron have been derived in this paper and its relation to Planck’s mass and charge are explored. This is a comprehensive paper that has been adapted from material we published in [1-3] for disseminating this information in the Physics community. Keywords: Electron, Ilectron, Complex Mass, Complex Charge, WIMP

by equating the integral of the electric to the 1. Introduction 2 kinetic energy ( mc0 ) as follows. The electron is a negatively charged massive particle  discovered in 1897 by J. J. Thompson [4]. We have listed its 1 qq22 m cdr2  (1) properties in Table 1. All these quantities except for re have 0 2 44 00  r re been determined by . The radius is determined re

Table 1. Attributes of the electro.

Attribute Fundamental “Particle” – the electron rest mass m0 9.10938188  10-31 kg charge (- q) 1.602176462  10-19 C 15 classical radius re 2.81795518 10 m quantum mechanical radius 0 angular momentum Ω = /2 5.27285  10-35 kg m2 /s -24 magnetic moment 1.001159652 B B is the Bohr Magneton, = 9.27400899  10 J/T

2 Doddi Venkata Giri et al.: Charge-Mass Equivalence leading to Ilectron from the Electron

The result is Prior to the development of , the structure of atoms had been determined by experiment and the q2 results conflicted with classical physics. The application of r  (2) e 2 ideas contributed by Planck, de Broglie, Einstein, Schrödinger, 400mc and Heisenberg, culminating in Dirac's equation, laid down −12 with 0 = permittivity of free space = 8.8541878 × 10 F/m. the principles of quantum mechanics. In the next section, we This is the of the of the electron. It is briefly consider classical approach to the Hydrogen atom. seen immediately from equation (1) that if the electron had a This is followed by a discussion of results generated by a zero radius, it would have infinite energy. Quantum physicists complex transformation of the electron leading to speculation now regard the electron both as a point particle and a wave, about a new particle, in Section 3. We introduce the Ilectron but a point particle conflicts with relativity. and consider its properties and implications in Sections 4 and Classically, the electron has to have a nonzero radius, and 5. We look at the electron as a blackhole and show why it is this implies a structure. To develop a model for a fundamental not a blackhole in Section 6. The Ilectronic mass and charge particle, it is necessary to include not only field energy, but are compared to the Planck’s mass and charge respectively in also a mechanical mass (pages 31-32 of [5]). Sections 7 and 8. In Section 9, we investigate the implication suggested (page 84 of [6]), and solutions to Dirac's equation of the equivalence of charge and mass. This leads us to cast (page 116 of [7] and [8) confirmed that the electron has Einstein’s equation in an equivalent form that shows the angular momentum. Let us consider a spinning spherical mass relationship between charge and energy. We conclude the m, radius r spinning about its center, as shown in Figure 1. paper with summarizing remarks in Section 10 followed by a Such a solid body has a moment of inertia I given by list of references. 2 I m r 2 (3) 5 2. Classical Approach to Hydrogen Atom Hydrogen is the simplest atom we have and was originally considered to be the smallest matter until the electron was discovered. Consider the simple Hydrogen atom illustrated in Figure 2.

Figure 1. A solid body of mass m and radius r. its kinetic energy is

1121  EIm rm22222 r (4) 2255 00  Figure 2. The Hydrogen atom with a single orbiting electron. where  is the angular velocity. The angular momentum is The electron experiences a centripetal force and a centripetal . For any object to stay in a circular 2 2  Im r 0 (5) motion, there is a centripetal (center- seeking) force, However, 5 as per ’s laws, there is a reaction force that is The angular momentum vanishes if the radius goes to zero centrifugal. This pseudo-force that is centrifugal is balanced and a point particle is not acceptable classically. Therefore, the by the Coulomb force so that the electron can stay in its electron spin is described as “a purely quantum mechanical circular orbit. effect”. mv2 Zq2 An obvious interpretation of the solution to Dirac's equation o  2 (6) for a stationary electron [9] is that it is moving in a circle of r 4o r radius /2 where is the reduced . Using a classically derived equation of motion that introduces where v is the speed of the electron, r the orbit radius, and Z = the classical stationary state [10] produces a radius some 5% atomic number (= 1 for Hydrogen) and o = permittivity of greater, and a velocity some 5% lower, that is consistent with free space = 8.8541878 × 10−12 F/m. Equation (6) can also be relativity. It is this rotational motion that was termed written so as to relate the speed and orbit radius as, “zitterbewgung” by Schrödinger, the quantum mechanical result being that the velocity was c. American Journal of Modern Physics 2020; X(X): XX-XX 3

2 q q 1 922 v  or r  (7) KxN mC910(/) (15) 2 4 4oomr 4oomv o 1 The result of the orbit radius of equation (7) is consistent G6.670 x 10( N m/Kg)1122 (16) with equation (2) from energy considerations. However, 4πg classically, an accelerating electron radiates energy (E) at a rate given by the Larmor formula [11] In the gravitational force above, the convention is a negative force for attraction. dE We now define two constants  mvJs 2 (/) (8) dt 0 휀 푑 = 0 = 0.861푥10−10(퐶/퐾푔) (17) 1 √ 푔 q2   6.2710 24 (s) (9) 3 6 00mc 푔 10 푑2 = √ = 1.16푥10 (퐾푔/퐶) (18) 휀0 The velocity is ~ c where  is the fine structure constant given by We observe that a dimensionless constant for the electron is given by 2 q 3 1   7.2973525710x (10) 푞 푞 푔 1.6푥10−19퐶 4137 c 0 푑3 = 푑2 = √ = −31 푑2 = 푚표 푚표 휀표 9.1푥10 퐾푔 and the radius is known as the and is given by

2 11 21 Fem 4 1.75푥10 푑2 = 2.03푥10 = (19) a  0 0.52917710 10 (m) (11) F 0 2 G mq0 This approach could be extended to all the elementary Writing Ek for the kinetic energy, the lifetime of the orbiting particles, in particular the and the neutron. It is noted electron is given by that every fundamental particle that has non-zero mass will have an associated constant “d3”. This constant would vanish 1 2 mv 2 for a neutral particle (q = 0) such as a neutron. Ea0 k 2 0 = 4.671011(s) (12) We can now express mass and charge with the same dE vc422 2 dimension by forming a complex Mass (M) or a complex m0 dt r2 charge (Q). There are various ways to form these combinations, as follows. which is hardly long enough to build a ! This problem was overcome by wave mechanics by 푔 푀 = 푚 + 푖푞푑2 = 푚 + 푖푞√ (20) specifying rules for the motion of electrons in atoms. Dirac’s 휀표 development of his relativistic equation incorporated these 휀 rules, but surprisingly produced the result that electrons not 푄 = 푞 + 푖푚푑 = 푞 + 푖푚 표 (21) 1 √ 푔 acted on by any force, move about at the velocity of . 푚 푞 푀 = + 푖 (22) 3. Complex Electron √푔 √휀표 푞 푚 푄 = + 푖 (23) In complex variable theory, it is often to link two variables √휀표 √푔 of same dimension. We can do this for the charge and mass of elementary particles, as follows. Considering the electrostatic For example, if we use the choice of equation (22) and and the gravitational force between two electrons, we have consider complex or combined forces, between two complex ,

q1 qK 21 q 2 q 푚1 푞1 푚2 푞2 fq  (13) 푀1 = + 푖 ; 푀2 = + 푖 (24) 22 √푔 √휀 √푔 √휀 40rr 표 표 we have the complex force given by m m G m m f  1 2  1 2 m 22 (14) 4 gr r MM12 FM  (25) 4 r2 where, in the usual notation Expanding this expression using equation (22), 4 Doddi Venkata Giri et al.: Charge-Mass Equivalence leading to Ilectron from the Electron

푚1푚2 푞1푞2 푚1푞2+푚2푞1 The strength of a force is given by Matt Strassler [12, 13] 퐹푀 = {− 2 + 2} − 푖 { 2 } = 푓푚 + 푖푓푖푚 (26) 4휋푔푟 4휋휀0푟 4휋√푔휀0푟 rf2 Note that the real part gives the well-known gravitational S  (30) c and Coulomb forces. If we now choose M2 to be a neutral particle by setting Comparing the strength of this imaginary force to the electric force, and assuming the neutral particle is a neutron   mq21 q2  0 FfiMm (27) 4gr2 m  0 Sx n 0 ~9.0010 19 (31) ime/ qg Setting The strengths of the four standard forces together with this  new force are given below in Table 2. These strengths are qm 0 (28) 1 im g calculated in the regime where they are effective, the strong force within the nucleus, and the weak force within a nucleon we obtain while the electromagnetic force operates outside the electron.

 mm2 im F f i f fim  (29) Mmim 4 gr2

Table 2. Strengths of the five forces.

Strong Weak Electro Magnetic Imaginary Electro- Mass 0.11 0.020 0.007 (=α) 6.6 1021 2.6  10-35

A force is considered weak if Frc2  () and is “imaginary electron”. considered strong if Frc2    . In the 5. Ilectron Spin and Magnetic Moment electro-mass force would be undetectable, but if the neutral ‘particle’ is a neutron star, this force would be the dominant If we assume the spin of /2is transferred to the new mass force acting on electrons. A typical neutron star contains ~25 we can determine the magnetic moment. The fine structure 56  10 neutrons. constant is given by

q2 4. The Ilectron   (35) 4 c Recognizing that imaginary mass can be interpreted as 0 charge, and imaginary charge as mass, we can consider the Replacing q by qi imaginary electron, where we interchange the mass and charge, but this transformation is not merely an algebraic 2 2 2 82 qqii 7.85 10 43    2.401  10 (36) transform. We must transform the intrinsic mass of the i  2 38 electron to obtain the new charge, the charge transforming as 40 cq 1.602 10 before. The rotational velocity is

푔 휀0 3 푖[푚 ,푞] = [푖푚 , 푖푞] = [ 푞, 푚 ] = [푚 , 푞 ] (32) √1+ −1 푖 푖 √ √ 푖 푖푖 푖 푣 훼 훼 훼 휀0 푔 0 = 휂 = 푖 = √1 + 푖 − √ 푖 = 1 − 2.829 × 10−22 (37) 푐 푒 3 3 3 √ Evaluating the components 훼푖 v  r  0 ii (38) g 9 3/2 mqii e 1.86  10 kg and (33) 2 v0 0 1 2 c

o m00 -41 qmii = 2.17 x 10 C (34) where gg3.2635 2 2 2 푞푖 2 훼푖ℏ 2 푞푖 훼ℏ 2 푞푖 ƛ 휏푖푖 = 3 = 2 = ( ) = ( ) (39) In equation (33), mii is the intrinsic mass equivalent of the 6휋휀0푚푖푐 3 푚푖푖푐 3 푞 푐 3 푞 푐 electron’s charge and qi is the charge equivalent of electron’s intrinsic mass. We are calling this new particle with its mass and is the reduced Compton radius. The radius of rotation is and charge given by equation (34) as the “ilectron” or an then American Journal of Modern Physics 2020; X(X): XX-XX 5

2 2 푞푖 ƛ 푣0 electromagnetic force, yet still fourteen orders greater than 푟 = ( ) 3/2 3 푞 푐 푣2 gravity. Continuing with this idea we constructed a [1 − 0 ] 푐2 hypothetical imaginary electron which turns out to have a substantial mass of ~1.9 10-9 kg and effectively no charge or 2 2.401×10−43 3.861×10−13 = = 6.3 × 10−18푚 (40) magnetic moment. 3 7.297×10−3 13.46×10−33 The ilectron would appear to be a good contender for a The magnitude of the magnetic moment is then given by WIMP (a weakly interacting massive particle), so far undetected hypothetical particle in one explanation of dark 6.3 × 10−18 휇 = 푞 푣 푟 = 1.36 × 10−22푞푐 × 휇 matter. If the ilectron exists, presumably it has an anti-particle 푚 푖 0 9.27 × 10−24 퐵 and an ilectron meeting an anti-ilectron would result in a pair −27 of high energy gamma photons. Assuming a similar imbalance = 1.48 × 10 휇퐵 (41) in the relative numbers as is found for other particle pairs, such The above ideas may be considered as mere speculation, but interactions would be rare. The detection of these gamma rays where would science be if some of us did not occasionally would in all probability require the design of new detectors. break away from what is known. The ilectron has no impact on positron. The anti-particle to the ilectron is the ipositron. 6. Electrons and Black Holes The mass of the ilectron is 1.86 x10-9 kg which converts to ~1021 MeV = 1015 TeV. The maximum energy of the LHC in Briefly, it is worthwhile to look at some analogous CERN is 13TeV. The LHC would have to be upgraded by a relationship between the electron and a . factor of around 8x1013 to produce an ilectron! The classical electron radius is given by the Lorentz Currently the only possibility of confirmation is if the formula [5] (also equations (2) and (7) above), ilectron meets its anti-particle, the ipositron and the resulting gammas pass through our detectors. Gammas above 100 TeV 2 q 15 are classified as ultra-high energy, and so far none have been rxme 2.81710 (42) 0 2 detected. 400mc If they are the elusive WIMP, they would have to provide a Replacing q /  by mg/ in the above, the radius mass of ~90% of the Milky Way. The mass of the sun is e 0 0 ~2x1030 kg and so the number of ilectrons required is of the electron is given by N =[2x1030kg /1.86 x 10-9] ~ 1039 (46) m0 r0  (43) 48 3 4 gc2 With the of the Milky Way being ~10 m the required is A black hole is a region of space and with a strong 83 (47) gravitational pull so that no particle or EM radiation can N  10 m escape from it. The boundary from which no escape is Detection of gammas of this energy would not only support possible is called the “”. The above formula for their existence but would also enable estimates of the density the radius of an electron is similar to the formula for the radius of ilectrons. Scattering of these gammas with electrons may of a Schwarzschild black hole also contribute to an explanation of bursts. mG m 2 From classical theory, the electron has a radius which is r  S 22 (44) larger than its , and hence, is not a black 2 g cc hole. This observation of the similarity of the radius of the electron [equation (38)] and the radius of a black hole Examples of Schwarzschild radii of some common planets [equation (39)] raises an interesting question – if the charges are: sun (3 km), earth (8.7 mm), Moon (0.11 mm) and Jupiter of particles are quantized, are the masses of black holes (2.2m). If the Schwarzschild radius exceeds the physical quantized? That is a question for Astrophysicists and may radius, the object is a black hole. Hence these planets are not already have been addressed. The known properties of the black holes. Alternatively, we estimate the Schwarzschild electron and the derived properties of the ilectron are radius for an electron as considered in Table 3. The classical radius of the electron is given in Table 3. me 58 res   6.76 10 m (45) 4 g c2 In Table 3, we have assumed the angular momentum of the ilectron to be the same as for the electron. The spin velocity whereas the classical radius of the electron is 2.82 x 10-15 m. for the ilectron being so close to c means that the spin radius is With the classical radius of an electron being much larger than remarkably close to the maximum value. its Schwarzschild radius, it is not a black hole.

By forming a complex electron, we have raised the possibility of a new force many orders weaker than the

American Journal of Modern Physics 2020; X(X): XX-XX doi: 10.11648/j.XXXX.2020XXXX.XX ISSN: 2326-8867 (Print); ISSN: 2326-8891 (Online)

Table 3. Comparison of the attributes of the electron and the ilectron.

Attribute Fundamental “Particle” – the electron Hypothesized “Particle” – the ilectron g -31 -9 rest mass moE = 9.10938188  10 kg mqoi E = 1.86 x 10 kg = 1.86 g (Very heavy !) o

000 m E -41 -19 qmIiE = 2.17 x 10 C charge qE = 1.602176462  10 C gg3.2635

with miE as the electron’s intrinsic mass 15 classical radius rE = 2.81795518 10 m Not calculated quantum mechanical radius 0 Assumed zero angular momentum Ω = /2 = 5.27285  10-35 kg m2 /s Ω = /2 = 5.27285  10-35 kg m2 /s (an assumption) 1.48 x 10-27 m based on the assumption above 1.001159652 mB B Magnetic moment -24 -24 mB is the Bohr Magneton, = 9.27400899  10 J/T B is the Bohr Magneton, = 9.27400899  10 J/T 2 2 qE -3 qI -46 Fine structure constant FSC E  = 7.29735x10 ~ (1/137) I  = 1.3387 x 10 40 c 40 c 3 3 11 11 v E v I Spin velocity sE = 0.9518967 sI  . = 1 - 6.68 x 10-24 almost 1, but not quite! c 3 c 3 E I

Designating radius as r it can be shown that  v   sE (49) c r  2.0283810 13 sE 2 Spin of the electron is a quantum mechanical property and is an intrinsic form of angular momentum. Some physicists r 13 rrm~2.1308710sE (48) think of this as the earth rotating on its own axis in 24 hours – sI   2 2 a spinning top. This view, however, is not mathematically where justifiable. In Table 4, we list some fundamental physical constants. Table 4. Some fundamental constants.

Physical Constant Notation Value and Units Planck’s constant h 6.62607 x 10-34 m2 kg /s -18 Planck’s charge qP  2ohc 1.8755 x 10 C 21.764 g hc Or, in energy units Planck’s Mass m  P 2 G 1.220910×1019 G eV -35 Planck’s lP 1.6 x 10 m in c 3 x 108 m/s Permittivity of free space 0 8.85418 x 10-12 F/m G 6.67030 x 10-13 m3 kg-1 s-2 1 Constant related to G g  This is not acceleration of earth’s gravity 1.192 x 109 m-3 kg s2 4 G

length, Planck mass is not a fundamental lower or upper bound; instead, Planck mass is a unit of mass defined using 7. Ilectronic Mass and Its Relation to only what Planck considered fundamental and universal units. Planck’s Mass It is defined as

7.1. Planck’s Mass hc mP  (50) Denoted by mP, is the unit of mass in the system of natural 2 G units known as [14]. It is approximately 0.02 -34 2 milligrams. Unlike some other Planck units, such as Planck where h is the Planck’s constant = 6.6260 x 10 m kg / s and American Journal of Modern Physics 2020; X(X): XX-XX 7

1 m G is the gravitational constant = = 6.670 x 10-11 (Nm2 / qmooEo (59) 4 g iiE gg3.2635 kg2) or m3 kg-1 s-2 with miE is the electron’s intrinsic mass and moE is the rest 9 -3 2 resulting in g = 1.192 x 10 m kg s mass of the electron. We also have the Fine structure constant of the ilectron given by Substituting these physical constants, we get 22 qqii mP = 21.764 g (51)   (60) i 2 4o hc qP Using the mass-energy equivalence E = m c2, Planck mass converts to qi 4623 i 1.3387101.15710xx (61) 19 qP mP = 1.220910×10 GeV (52) In comparison, this value is of the order of 1015 (a We can also get this ratio in another way quadrillion) larger than the highest energy available (13 ilectron charge2.1710Cq x 41 TeV) in the Large Hadron Collider at CERN. i = 1.157 x 10-23 (62) 18 Planck'scharge qP 1.875510Cx 7.2. Ilectron Mass Which is consistent with equation (61) We had earlier derived the ilectron mass as We can write the reciprocal of this ratio as

g Planck'scharge1.875510Cq x 18 P = 8.642 x 1022 (63) mqiiE (53) 41 o ilectroncharge qi 2.1710Cx

Rewriting the Planck’s mass from equation (50) 9. Mass and Energy Equivalence Leading hc m  (54) to Charge and Energy Equivalence P 2 G Sir Isaac Newton believed mass and energy are two distinct Taking the ratio of two masses, we have and unrelatable quantities. In the Newtonian scheme, mass is a measure of inertia or quantity of matter that resists its motion, and mass and energy have distinct and separate identities. mP Planck's mass 2hco 1  = = ~11.706 (55) However, Einstein’s most famous equation mii Ilectron mass qE E E = mc2 (64) We recognize that the ratio of Planck’s mass to ilectron mass is closely related to the fine structure constant of the explicitly states that mass and energy are interconvertible. electron E. Mass does not have to move to have energy. Just need to have In terms of the actual masses, we have mass. This simple equation has enjoyed profound consequences. Now that we have found an “equivalence” g between mass and charge, we can rewrite equation (59) as mq =1.86 x 10-9 kg=1.86 g~1021 MeV=1015 TeV (56) iie  o g E = qc2 = q d2 (65) m Planck's mass 21.764 g o So P  11.70 (57) mgIlectron mass1.86  ii where which is consistent with equation (50). g dc = 1.0777 x 105 c= 3.2333 x 1013 ( Voltage ) (66) 8. Ilectronic Charge and Its Relation to o Planck’s Charge Furthermore, dimensionally speaking, Energy = Charge x Voltage, which suggests, the dimension of the constant Planck’s charge is given by [15] quantity d in equation (60) is the square root of Voltage, and this has been verified. An alternate view is to regard equation q (58) P  4o (hc / 2  )  2ohc (60) as defining charge having an effective mass of Ilectronic charge is given by 8 Doddi Venkata Giri et al.: Charge-Mass Equivalence leading to Ilectron from the Electron

g Ilectron”, Physics Note 23, 9 April 2020, can be downloaded Mqq  (67) from: http://ece-research.unm.edu/summa/notes/index.html 0 [3] D. V. Giri, “Discovery and History of the Electron,” presented Equation (62) indicates that charge and energy are two sides at ASIEM 2017, Bengaluru, India, Slides can be downloaded from: of the same coin. https://www.e-fermat.org/communication/giri-comm-asiaem2 017-2017-vol24-nov-dec-08/ 10. Summarizing Remarks [4] J. J. Thompson, “Carriers of negative electricity,” Nobel Lecture, December 1906; can be downloaded from : We have found that: https://www.nobelprize.org/uploads/2018/06/thomson-lecture. Mass of the ilectron and Planck’s mass are simply related pdf by the fine structure constant of the electron. [5] Jackson, Classical Electrodynamics, John Wiley & Son. m Planck'smass 1 P  = ~ 11.706 (68) [6] Jimenez and Campos, A critical examination of the mii Ilectronmass E Abraham-Lorentz equation for a radiating charged particle, Am J Phys 55(11) Nov 1987. Charge of the ilectron and Planck’s charge are simply [7] J McConnell, Quantum Particle Dynamics, North Holland related by the fine structure constant of the ilectron. Publishing Company, 1958. [8] P. A. M. Dirac, (1928). "The Quantum Theory of the Electron" Planck'scharge qP 1 22  =8.642 x 10 (69) (PDF). Proceedings of the Royal Society A: Mathematical, ilectroncharge q i i Physical and Engineering Sciences. 117 (778): 610–624. Bibcode: 1928RSPSA.117..610D. doi:10.1098/rspa.1928.0023. We have established an equivalence between mass and JSTOR 94981. charge, and this leads us to the following observation. [9] W. Heitler, The Quantum Theory of Radiation, Clarendon Press, Einstein’s equation firmly established the interconvertibility 1954, Chapter 1, p 15. of mass and energy with profound consequences. This leads us to the following [10] I. L. Gallon, Extending Classical Physics into Quantum Domain, Physics Note 21, 3 June 2013. Can be downloaded E = q d2 similar to E = m c2 (70) from: http://ece-research.unm.edu/summa/notes/Physics/physicsNot where E is energy, m is mass, c = speed of light in vacuum, q is e22.pdf charge and d is a simply related to the speed [11] Erber, The Classical Theories of Radiation Reaction, of light, as can be seen in equation (61). The consequences of Fortschritte der Physik 9, 343-392 (1961) the interconvertibility of charge and energy are yet to be determined. [12] M. Strassler, “Of Particular Significance,” May 13, 2013, can be downloaded from: https://profmattstrassler.com/articles-and-posts/particle-physic s-basics/the-known-forces-of-nature/the-strength-of-the-know References n-forces/ [1] I. L. Gallon, D. V. Giri and C. E. Baum (Posthumously), The [13] Dirac, Classical theory of radiating electrons, Proceedings of Electron and the Ilectron, Physics Note 22, December 2016, the Royal Society, 1938. can be downloaded from: http://ece-research.unm.edu/summa/notes/index.html [14] https://en.wikipedia.org/wiki/Planck_mass. [2] D. V. Giri and I. L. Gallon, “Additional Properties of the [15] https://en.wikipedia.org/wiki/Planck_units