International Journal of Scientific Reports Oakley WS. Int J Sci Rep. 2017 Apr;3(4):95-99 http://www.sci-rep.com pISSN 2454-2156 | eISSN 2454-2164
DOI: http://dx.doi.org/10.18203/issn.2454-2156.IntJSciRep20171472
Original Research Article
Validating internal electron and proton energy configurations via a
theoretical derivation of the mass ratio mp/me
William S. Oakley*
San Jose, California, USA Received: 10 February 2017 Accepted: 16 March 2017 *Correspondence: William S. Oakley E-mail: willoakley@earthlink.net Copyright: © the author(s), publisher and licensee Medip Academy. This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT Background: There are no particle models giving theoretical rest mass energy values for the electron or proton, and their internal energy configurations are unknown. Consequently there is no theoretical basis for the proton/electron rest mass ratio mp/me. Previous articles established both electrons and protons consist of quantum loops of the same 6.8MeV base quantum energy, albeit in different relativistic states. Methods: Prior work is extended by considering internal particle energy cross coupling factors to derive detailed theoretical expressions for the internal energy distributions of electrons and protons. These expressions consist of the base quantum energy modified by terms containing only relativistic factors of the fine structure constant, α ~ 1/137. For mp/me the base quantum energy cancels and the derived mass ratio is given by the particle‟s internal quantum loop relativistic states. The derived mass ratio is compared to the empirical value. Newton‟s gravitational constant, G, is calculated from the electron internal energy configuration. Results: Derived particle energy configurations give proton mass and proton/electron mass ratio values fully consistent with empirical data. The common base quantum loop energy is obtained to 6ppm. Combining particle mass energy expressions gives mp/me to ten digits and consistent with the 2014 CODATA value via an expression containing only the fine structure constant. A theoretical value for Newton‟s gravitational constant is obtained to an uncertainty of 6ppb. The Hierarchy problem is resolved, and the Planck scale of matter is adjusted. Conclusions: The particle energy configurations are validated by providing particle mass energy values and a proton/electron mass ratio consistent with empirical data. Newton‟s G is shown not a natural constant, and misunderstanding its nature gave rise to the Hierarchy problem and an erroneous value for the Planck scale of matter, both now resolved. . Keywords: Proton-electron mass ratio, Proton mass energy expression, Electron mass energy expression, Gravitational constant, G. Planck scale, Hierarchy problem
INTRODUCTION
The ratio of the mass of the proton to that of the electron has long been theoretically unsupported by physical particle models, the lack of which is a long standing problem. Both particles exhibit exactly the same, although opposite, electric charge values but their 2014
CODATA rest mass energies differ greatly; for the electron mec2 = 0.5109989461(31)MeV and for the proton mpc2 = 938.2720813(58)MeV. The CODATA value for the proton - electron rest mass ratio is: 1,836.15267389(17). [In concise form the two digits in parentheses indicate the standard uncertainty in the prior two digits].
International Journal of Scientific Reports | April 2017 | Vol 3 | Issue 4 Page 95
Oakley WS. Int J Sci Rep. 2017 Apr;3(4):95-99
Recently published articles describe particle models wherein both electrons and protons are composed of the same energy quantum of about 6.8MeV in the form of relativistic quantum loops of about 35MeV.1,2 Each quantum loop consists of an energy quantum of nominally 6.8MeV relativistic by α-1/3, i.e. 5.15559 x 6.8MeV = 35MeV. On formation both particles undergo relativistic volume changes of α with loop energies relativistic by α±1/3 in each dimension.
Given the above proton empirical rest mass energy, a three dimensional model with the base quantum energy relativistic by α-1 provides a nominal initial value for the base quantum energy as in (1), where the fine structure constant is α ~1/137.035999139(31).
mpc2 = 938.2720813MeV ~ α-16.84MeV = 937MeV (1)
From the referenced helical-toroid electron model,1 with the nominal base quantum energy mqc2 = 6.8MeV, the nominal electron rest mass energy in (2) is close to, but somewhat greater than, the empirical value of 0.510998946MeV,
mec2 ~ 2α2/36.8MeV = 0.51166MeV (2)
It is clear the 6.8MeV base energy value is insufficiently precise and both expressions (1) and (2) require adjustment by considering possible internal particle dynamics, such as energy cross coupling between quantum loops. Initial internal energy adjustment values can be obtained by analyzing the sparse set of cross- coupling values available from simple relativistic expressions containing α. The empirical particle mass ratio mp/me places an additional constraint on the values within the expressions.
Particle Models: The above nominal expressions for the proton and electron mass energies are both based on conceptual models describing the energy distribution within the particles. The electron is described as two circulating electromagnetic (EM) components each of spin-½ and energy mqc2 propagating rectilinearly in an involute helical toroidal curved space-time path close to and just outside an event horizon as in Figure 1a. The nominal internal electron relativistic energy distribution of 2mqc2(α2/3.α2/3.α-1/3) about the x, y, z, axes was previously given,1 where the Newtonian gravitating mass derives from the space-time curvature about the x and y axes, and the rotational energy about the z axis , (i.e. 2α-
1/3mqc2 ~70MeV), is reduced by the coupling factor α, to energy about the x and y axes.
The proton is described as a single spin-½ component of energy mqc2 propagating rectilinearly just inside an event horizon in an evolute toroidal curved space-time path as in Figure 1b. Due to the toroidal propagation paths each particle evidences a magnetic dipole to the observer.
Figure 1: (a) Electron energy involute space-time
path.
Figure 1: (b) Proton energy evolute space-time path.
The proton is considered a single spin-½ wave of mqc2 with two passes about the z axis overlapped to form a spin-1 wave in a quantum loop in the x, z plane, tangential to and rotating about the z axis into the y, z plane so the x and y axes energy is symmetric. As described in a previous article,2 the proton‟s relativistic energy distribution about the x, y, z, axes relative to the observer domain is consistent with (1), the inverse of that for the electron, and resembles the quark partial charge notion,
mpc2 = mqc2(α-2/3.α-2/3.α1/3) (3)
This observer domain energy distribution derives from the inversion of the distribution in an internal particle domain very similar to that of the spin-1 electron, at 2mqc2(α2/3.α2/3.α-1/3), but with the single spin-½ loop wavelength passing twice around the z axis per quantum
International Journal of Scientific Reports | April 2017 | Vol 3 | Issue 4 Page 96
Oakley WS. Int J Sci Rep. 2017 Apr;3(4):95-99
cycle to achieve particle stability via energy phase match to mimic a spin-1 EM wave and provide unit charge.
The two particles exhibit equal but opposite charge values as energy localization in the observer domain causes the particles to undergo opposite volume changes by adopting different relativistic states. On localizing the volume the two component electron circulation expands by α, whereas on localizing the volume of the proton‟s single component contracts by α. This results in the space-time metric surrounding the particles having oppositely directed radial strains, producing opposite charge effects. Via space-time curvature, the observed particle gravitational rest mass depends on the propagation radius of curvature of the particle‟s quantum loops in their relativistic states. Reference 1 describes the electron internal mass energy of 2mqc2 reduced by about α2/3 due to loop expansion, whereas the proton single internal loop mass energy of mqc2 is increased by α-1 via loop contraction. Both particles have been previously described as in dynamic equilibrium between radial (electric) and circumferential (mass) metric strains.1,3
As noted in the introduction both electron and proton consist only of components with the same base quantum energy mqc2, so the empirical mass ratio mp/me depends only on the relativistic state of each particle’s circulating loop energy. To a first approximation this ratio is nominally given by;
mp/me ~ α-1/2α2/3 = 1821.2 (4)
The ratio (4) differs somewhat from the empirical 2014 CODATA rest mass ratio of 1,836.15267389(36), but essentially confirms the base energy mqc2 is likely the same for both particles. It also indicates the particle‟s basic quantum loop energy configurations are probably valid, but are only approximate as the individual particle mass energy expressions are nominal, each requiring minor but different, adjustments.
The electron energy distribution 2mqc2(α2/3.α2/3.α-1/3) shows the primary energy circulation of 2α-1/3mqc2 about the z axis couples about the x and y axes via the coupling constant α, and forms relativistic energy 2mqc2α2/3 about the x and y axes. The coupled energy thereby oscillates along the z axis to form a three dimensional particle as in Figure 1a. But subsequent smaller cross axis recoupling factors are not included. The nominal proton mass energy expression (1) does not include the particle‟s rotation energy about the toroid z axis. For these reasons mqc2 must differ slightly from the 6.84MeV in (1).
METHODS
The precise value of mqc2, the base quantum energy for both electrons and protons, is not a factor in the proton/electron mass ratio as evident from (4). Possible cross axis energy coupling factors for the electron and proton mass energies are deduced as follows.
The electron
As above, the first coupling by α reduces the z axis energy and forms energy about the x, y axes of 2α2/3mqc2. A second order coupling must exist with energy recoupling back from about the x, y axes to about the z axis, postulated as occurring via a second coupling factor α2/3, reduced by half due to a π/2 phase change. This energy then recouples again about the x and y axes by α and is thus α5/3/2 of the initial energy about the x, and y axes). The energy about the x, and y axes is thereby 2α2/3mqc2/(1 + α5/3/2). This coupling-recoupling cycle repeats with the coupling reduced by α5/3/2 at each cycle giving (5). The sign of the coupling is reversed on alternate coupling cycles due to phase effects, giving the electron rest mass energy expression,
mec2 = 2mqc2α2/3/[1 + α5/3/2 - (α5/3/2)2 + (α5/3/2)3 -..] MeV (5)
Where [1 + α5/3/2 - α10/3/4 + α15/3/8 ….] = 1.0001372521822646 = K (say), and 2α2/3 = 0.0752442900019.
From (5), mec2 = (2α2/3mqc2/K).MeV; 2mqc2 = 13.58426213MeV; and mqc2 = 6.792131067MeV.
Thus 2mqc2 = α-2/3Kmec2, and the CODATA value me = 9.10938356(11) x 10-31kg, gives 2mq = 2.421614665 x 10-29kg. The value mqc2 is uncertain by 6ppb as it derives from the empirical value mec2.
The Gravitational constant G
As previously determined in reference [1] a theoretical value for Newton‟s gravitational constant GN, is given by;
GT = (ħc/c4)/4mq
2 (6)
With c the numerical value of c in cgs units, (for reasons explained briefly in the note below), and where c4 = (2.99792458 x 1010)4, we obtain;
ħc/c4 = 3.913938931 x 10-68 J/m (7)
From above (2mq)2 = 5.864217632 x 10-58kg2, and we obtain a theoretical value GT for Newton‟s constant;
GT = (ħc/c4)/4mq
2 = (3.913938931 x 10-68) /5.864217588 x 10-58, SI units
= 6.674273033 x 10-11, SI units (8)
This is within the standard uncertainty of the empirical value GN, at GN = 6.67408(31) x 10-11 (SI units). The uncertainty in GT is limited by (5) to about 6ppb via the uncertainty in the derived value of mqc2, following the uncertainty in the empirical value of mec2.
International Journal of Scientific Reports | April 2017 | Vol 3 | Issue 4 Page 97
Oakley WS. Int J Sci Rep. 2017 Apr;3(4):95-99
Note: Reference 1 shows the historical assumption that gravity acts via force between masses in the observer domain is incorrect and inadvertently introduced a numerical factor equal to c4 into G. Hence the dimensions of GN, Newton‟s classical constant, are in error by c4. The real force of gravity acts on quantum energies mqc2 circulating within particles, wherein each energy propagates rectilinearly in a relativistic state close to a toroidal event horizon and is thereby dimensionally remote by c2 from the observer domain in which mass is measured, i.e. m = E/c2.
The proton
As shown previously,1, 2 the proton energy circulation is very similar to the electron, but with the relativistic factors “inverted”, i.e. mpc2 = mqc2(α-2/3.α-2/3.α1/3).
Using the value of mqc2 derived from (5) above we obtain
α-1mqc2 = 930.7664668MeV (9)
This differs from the empirical value mpc2 by;
mpc2/α-1mqc2 = 938.2720813 / 930.7664668 = 1.008063907 (10)
The proton energy circulation as shown in Figure 1b and described by mpc2 = mqc2(α-2/3.α-2/3.α1/3) is primarily rotationally relativistic about the x, y axes with the energy coupled about the z axis by α and the x, y circulation normally reduced by (1-α). However, as in reference [3], the proton energy propagates in a domain just inside a toroidal event horizon and the local space- time curvature is reversed by transiting the event horizon into the observer domain. Thus the internal energy distribution (α2/3.α2/3.α-1/3) is evident to the observer as (α-
2/3.α-2/3.α1/3) and the energy about the x, y axis is effectively increased by (1 + α), giving;
α-1(1 + α)mqc2 = 937.5585983MeV (11)
This is less than the proton rest mass energy by 1.000761001. As noted above, the rotation energy about the z axis is α that about the x, y axes, and is postulated to recouple back about those axes again reduced by α, for a recoupling of α2 , (= 0.00005325135448). This coupling factor likely repeats on subsequent cycles resulting in a recoupling of (1 + α2 – α4) at 1.000053248587732, increasing (11) to give (12);
α-1(1 + α)(1 + α2 – α4)mqc2 = 937.6085214MeV (12)
This energy value differs from the empirical proton rest mass energy by;
938.2720813 / 937.6085214 = 1.000707715 (13)
If, similar to as in the electron, the proton internal loop energy cross couples, and considering the uncertainty in
mqc2, this factor is likely (1 + α4/3/2) = 1.000707713. Increasing (12) by this factor gives mpc2 = 938.2720791MeV. This can be considered as the two halves of each loop energy of α2/3mqc2 interacting with each other for a total of (α2/3mqc2)2/2 = α4/3mqc2/2. If so, presumably there would be no subsequent re-coupling.
It is therefore postulated;
mpc2 = α-1(1 + α)(1 + α4/3/2)(1 + α2 - α4
)mqc2 = 938.2720791MeV (14)
The above calculation gives essentially the same value as the proton empirical rest mass, both having an uncertainty of about 6ppb. These calculations employed ten digit numbers so rounding off during multiple calculation steps may significantly affect the last two digits.
Proton / electron mass ratio: In calculating the electron / proton mass ratio from (5) and (14), the mqc2 terms cancel and we obtain (15), a mass ratio containing only terms of α and thus independent of individual particle masses. The standard uncertainty in the empirical value of α is only 0.32ppb, which requires a calculation to 15 significant digits to minimize computational round-off errors. Thus,
mp/me = α-5/3(1 + α)(1 + α4/3/2)(1 + α2 - α4
)[1 + α5/3/2 - (α5/3/2)2 + (α5/3/2)3 -..] / 2 = 1836.15267772749. (15)
RESULTS
This mass ratio result closely matches the empirical mass ratio (1836.152 673 89(17), over nine orders of magnitude, differing by only 2.09ppb. Much if not all of this difference may be due to the small uncertainty in the value of α.
The electron and proton internal energy distributions described above via relativistic quantum loop concepts give the particle masses to a few parts per billion, fully consistent with empirical data.
The base quantum loop energy common to both particles is; mqc2 = 6.792131067MeV, and is derived via the electron rest mass energy with an uncertainty of 6ppb. Note α-1/3mqc2 = 35.0174MeV.
A theoretical value for Newton‟s classical gravitational constant GN is obtained matching and surpassing empirical data with increased precision, providing an uncertainty of 6ppb due to the uncertainty in mqc2.
DISCUSSION
The impact of this analysis is far reaching with one major consequence being resolution of the Hierarchy problem. This problem is the lack of an explanation for the dearth of particles with masses much greater than the proton at
International Journal of Scientific Reports | April 2017 | Vol 3 | Issue 4 Page 98
Oakley WS. Int J Sci Rep. 2017 Apr;3(4):95-99
about 1 GeV, but less than the traditional Planck mass at about 1.22×1019GeV, a huge gap of about 19 orders of magnitude!
The Planck mass has been historically obtained by equating the strong force with the gravitational force due to an assumed mass M, i.e. ħc/r2 = GNM2/r2, leading to M = (ħc/GN)1/2. However, as shown herein Newton‟s GN contains a hereto unrecognized factor of c4, essentially a numerical value of about (3 x 1010)4, which places the historical Planck mass too high by about 1020.
The Planck scale has been described as where the strong force, the electromagnetic force, and gravity are all equal. But the described electron model shows these are all equal in the frame in which the electron energy rotates. This equality is clearly necessary for particle stability. Replacing GN in the Planck mass derivation with GT as in (6) shows the “Planck mass” is 2mq
2, thereby resolving the Hierarchy problem.
CONCLUSION
The conceptual particle models provide a basic energy configuration by which the localization of electromagnetic energy as quantum loops gives rise to the observed attributes of mass and charge. A detailed mathematical description of the particles is not intended, but the above analysis strongly supports the conceptual electron and proton models as composed of similar quantum loops by producing the proton rest mass and the proton / electron rest mass ratio with uncertainties essentially matching the CODATA 2014 empirical data. Obtaining a theoretical value for the proton - electron mass ration to within 2.1ppb of the empirical value substantiates the particle concepts.
The base quantum loop energy mqc2 is the same for both particles, but the basis for this particular value remains unknown. The derivation of GN via the electromagnetic quantum loop electron model emphasizes Newton‟s original concept that “mass is a notion enabling quantification of the gravitational effect”, and is not a particle attribute at a fundamental level. The gravitational „constant‟ G is the same for both electron and proton and the long standing Hierarchy problem is resolved.
With the introduction of mqc2, the electron and proton rest mass energies and the gravitational constant G are now given via mqc2, and the number of basic unknown parameters in the Universe is reduced by two.
Funding: No funding sources Conflict of interest: None declared Ethical approval: The study was approved by the institutional ethics committee
REFERENCES
1. Oakley, W. S. Analyzing the large number problem and Newton‟s G via a relativistic quantum loop model of the electron. Int J Sci Rep. 2015;1(4):201- 5. 2. Oakley WS. Deducing the proton energy configuration. Int J Sci Rep. 2016: 284-7. 3. Oakley WS. Resolving the Electron - Positron mass annihilation mystery. Int J Sci Rep. 2015;1(6):250- 2.
Cite this article as: Oakley WS. validating internal electron and proton energy configurations via a theoretical derivation of the mass ratio mp/me. Int J Sci Rep 2017;3(4):95-9.
International Journal of Scientific Reports | April 2017 | Vol 3 | Issue 4 Page 99