Quantum Gravity and String Theory

   

The Monopolar Quantum Relativistic Electron an Extension of the Standard Model and Quantum Field Theory

Authors: A Bermanseder

Abstract: Despite the experimental success of the quantum theory and the extension of classical physics in quantum field theory and relativity in special and general application; a synthesis between the classical approach based on Euclidean and Riemann geometries with that of 'modern' theoretical physics based on statistical energy and frequency distributions remains to be a field of active research for the global theoretical and experimental physics community. In this paper a particular attempt for unification shall be indicated in the proposal of a third kind of relativity in a geometric form of quantum relativity, which utilizes the string modular duality of a higher dimensional energy spectrum based on a physics of wormholes directly related to a cosmogony preceding the cosmologies of the thermodynamic universe from inflaton to instanton. In this way, the quantum theory of the microcosm of the outer and inner atom becomes subject to conformal transformations to and from the instanton of a quantum big bang or qbb and therefore enabling a description of the macrocosm of general relativity in terms of the modular T-duality of 11-dimensional supermembrane theory and so incorporating quantum gravity as a geometrical effect of energy transformations at the wormhole scale. Using the linked Feynman lecture at Caltech as a background for the quantum relative approach; this paper shall focus on the way the classical electron with a stipulated electromagnetic mass as a function of its spacial extent exposes the difficulty encountered by quantum field theories to model nature as mathematical point-particles without spacial extent. In particular, a classical size for the proton can be found in an approximation ½Re.X = Rp for a classical electron radius Re and where the factor X represents the symmetry equilibrium for a ß = (v/c} = f(A) velocity ratio distribution for the effective electron rest mass me proportional to the spacial extent of the electron and evolving real solutions for the electron parameters from a quasi-complex space solution for its rest mass meo. Using the ß2 distribution in a unitary interval, then bounded in a function of the electromagnetic fine structure constant alpha; the SI-CODATA value for the rest mass of the electron is derived from first inflaton-based principles in the minimum energy Planck-Oscillator Eo=½hfo in a conformal mapping of the M-Sigma relation applied to the Black Hole Mass to Galactic Bulge ratio for the alpha bound. The M-Sigma ratio so can be considered as a scaling proportion between the interior of a Black Hole mapped holographically and radius-conformally as the internal monopolar volume of the electron as a basic premise of the quantum gravitational approach in quantum relativity and in scaling the Schwarzschild solution onto the electron. A unification condition in a conformal mapping of the alpha fine-structure α onto X described by X ⇔ α in ℵ(Transformation) = {ℵ}3 : X → α{#}3 → # → #3 → (#2)3 → {(#2)3}3 is applied in this context to indicate the relative interaction strengths of the elementary gauge interactions in proportionality: SNI:EMI:WNI:GI = SEWG = #:#3:#18:#54. For the symmetry equilibrium, the electric potential energy and the magnetic action energy are related for an electron velocity of veX = 0.78615138.c and an effective mass energy of mef = γme = mecf = 1.503238892x10-30 kg*. This mass-velocity relationship is supplemented by the Compton constant as: meRe = Compton constant = αh/2πc = lplanck.α.mplanck = mecrec , which proportionalises the quantum relativistic size of the electron with its mass. The Compton constant ensures Lorentz invariance across all reference frames in cancelling the length contraction with the relativistic mass increase in the product of the proper length lo and the proper rest mass mo as lo.mo=loγ.mo/γ in special relativity (SR) in the self-relative reference frame of the monopolar electron. Subsequently then for an electron speed veX and for rec = αh/2πcmecf = 1.71676104x10-15 m* as a decreased self-relative classical electron radius given by the Compton constant, we calculate a relatively negligible monopolar velocity component in (vps/c)2 = 1/{1+rec4/([2πα]2rps4)} = 1.55261006x10-35 and characteristic for any substantial velocity for the electron. The analysis then defines a maximum velocity for the electron with a corresponding quantum relative minimum mass in the form of the electron (anti)neutrino in ve|max = (1 - 3.282806345x10-17) c and m(νe)=m(ντ)2 = 0.00297104794 eV* (0.002963740541 eV) respectively. At this energy then, no coupling between the electron and its anti-neutrino would be possible and the W- weakon could not exist. Subsequently, we shall indicate the effect of the Compton constant and of the quantum relativistic monopolar electron to calculate all of the neutrino masses from first principles in setting mν = mneutrino = me.(rneutrino)/Re and where rv naturally applies at the limit of the electron's dynamical self-interaction as indicated, that is the electron's quantum relativistic mass approaches that of the instanton of the qbb. This leads to: mνElectronc2 = mv(νTauon2)c2 = mν(νMuon2+νHiggs2)c2 = μo{Monopole GUT masses ec}2rps/4πRe2 and where vHiggs is a scalar (anti)neutrino for the mass induction of the (anti)neutrinos in tandem with the mass induction of the scalar Higgs boson in the weak Goldstone interaction. For the electrostatic electron the ß distribution at A=½, the Compton constant gives mecrec = meRe for ß2 = 0 and at A=1, the Compton constant gives mecrec = ½me.2Re for ß2 = X and as the mean for a unitary interval is ½, the electron radius transforms into the protonic radius containing monopolar charge as internal charge distribution in Rp = ½XRe and proportional to the effective electron rest mass me proportional to the spacial extent of the electron. For the proton then, its 'charge distribution' radius becomes averaged as Rproton = 0.85838052x10-15 m* as a reduced classical electron radius and for a speed of the self-interactive or quantum relativistic electron of vps = 1.576125021x10-17 c. This monopolar quantum relativistic speed reaches its quantum relativistic {v/c = 1-} limit and its maximum QR monopolar speed of 0.0458 c at the instanton boundary and defines a minimum quantum monopolar relativistic speed for the electron at vpse = 1.50506548x10-18 c for its electrostatic potential, where Ue=∫{q²/8πεor²}dr = q²/8πεoRe = ½mec2 for a classical velocity of ve=0 in a non-interacting magnetic field B=0. 2Ue = mec2 so implies a halving of the classical electron radius to obtain the electron mass me = 2Ue/c2 and infers an oscillating nature for the electron size to allow a synergy between classical physics and that of quantum mechanics. A reduced classical electron size is equivalent to a decrease of the Compton wavelength of the electron, rendering the electron more ‘muon like’ and indicates the various discrepancies in the measurements of the proton’s charge radius using Rydberg quantum transitions using electron and muon energies. The calibration for the classical electron radius from the electron mass from SI units to star units is (2.81794032x10-15).[1.00167136 m*] = 2.82265011x10-15 m* and differing from Re = 2.777777778x10-15 m* in a factor of (2.82265011/2.777777…) = 1.01615404. A reduction of the classical electron radius from Re = 2.777777778x10-15 m* to (2.777777778x10-15).[0.998331431 m] = 2.77314286x10-15 m, then gives the same factor of (2.81794032/2.77314286) = 1.01615404, when calibrating from star units. The units for the Rydberg constant are 1/m for a Star Unit* – SI calibration [m*/m] = 0.998331431… for a ratio [Re/SI ]/[Re/*] = (2.77314286/2.777777) = (2.81794032/2.82265011) Reducing the classical electron radius Re from 2.81794032 fermi to 2.77314286 fermi in a factor of 1.01615404 then calibrates the effective electron mass me to Re in the Compton constant Re.me = ke2/c2 = (2.77777778x10-15).(9.29052716x10-31) = 2.58070198x10-45 [mkg]* with Re.me = ke2/c2 = (2.81794033x10-15).(9.1093826x10-31) = 2.56696966x10-45 [mkg] with [mkg]* = (1.00167136)(1.00375313)[mkg] = 1.00543076 [mkg]. Using this reduced size of the electron then increases the Rydberg constant by a factor of 1.01615404 Using the Rydberg Constant as a function of Alpha {and including the Alpha variation Alpha|mod = 60πe2/h = 60π(1.6021119x10-19)2/(6.62607004x10-34) = 1/137.047072} as Ry∞ = Alpha3/4πRe = Alpha2.mec/2h = mee4/8εo2h3c = 11.1296973x106 [1/m]* or 11.14829901x106 [1/m] defines variation in the measured CODATA Rydberg constant in a factor 10,973,731.6x(1.01615404).(137.036/137.047072)3 = 11,148,299.0 Subsequently, using the Rydberg energy levels for the electron-muon quantum energy transitions, will result in a discrepancy for the proton's charge radius in a factor of 10,973,731.6/11,148,299.0 = 0.98434134… and reducing a protonic charge radius from 0.8768 fermi to 0.8631 fermi as a mean value between 0.8768 fermi and 0.8494 fermi to mirror the unitary interval from A=½ to A=1 for the electron’s relativistic ß distribution. The local geometry related to the Compton radius h/2πm is shown to manifest in a linearization of the Weyl wormhole wavelength λps = λweyl of the qbb in the photon-mass interaction as a quantum gravitational limit proportional to the mass of the electron in rweyl = λweyl/2π = 2GoMc/c2 = h/2πcmps for a curvature mass Mc = hc/4πGomps conformally transforming Mc = 6445.79 kg* into 2.22..x10-20 kg* quantum gravitationally and in a corresponding increase of a sub Planck length linearization of rcplanck = 2Gomps/c2 = 5.4860785x10-47 m* (star units calibrated to the SI mensuration system) to the wormhole scale of the quantum big bang as a quantum geometric curvature effect. The qbb results from a Planck scale conformal transformation of fundamental parameters in the inflaton, descriptive of energy transformations between five classes of superstrings culminating in the Weyl-Eps wormhole as the final superstring class of heterotic symmetry 8x8 to manifest the supermembrane EpsEss as the wormhole of the 'singularity creation', which is a derivative from a monopolar Planck-Stoney cosmogenesis. Recircularizing the Compton radius into a Compton wavelength in a {photon - gauge photon} interaction labeled as electromagnetic monopolar radiation or {emr - emmr}, then is shown to define the quantum energy of the vacuum per unit volume as a horn toroidal space-time volumar in Vortex-PE = VPEps = ZPEweyl = 4πEps/λps3 and completing the encompassing energy spectrum in integrating the electric-, magnetic- and monopolar field properties in {½melectric + ½mmagnetic(v/c)2 + δmmonopolic}c2 = mc2. The self-interaction of the electron in energy, so crystallizes its monopolar super brane origin in the addition of a quantum self-relative magnetic energy acting as a 'hidden' electromagnetic monopolar field in the volume of spacetime occupied by the electron as a conformal transformation from the inflaton epoch. A Planck-Stoney 'bounce' of the electronic charge quantum established the interaction potential between charge and mass energy to break an inherent supersymmetry to transform string class I into string class IIB in modular conformal self-duality of the monopole supermembrane. Following this initial transformation relating displacement to electric charge in the magneto charge of the monopole; a heterosis between string classes HO(32) and HE(64) enabled the bosonic superstring to bifurcate into fermionic parts in a quark-lepton hierarchy from the HO(32) superstring to the HE(64) superstring of the instanton of the qbb and who is called the Weyl or wormhole boson Eps in this paper. We shall also indicate the reason for the measured variation of the fine structure constant by Webb, Carswell and associates; who have measured a variation in alpha dependent on direction. This variation in alpha is found in the birth of the universe as a 'bounce' or oscillation of the Planck length as a minimum physical displacement and becomes related to the presence of the factor γ3 in the manifestation of relativistic force as the time rate of change of relativistic momentum prel. Furthermore, the mass-charge ratio {e/meo} relation of the electron implies that a precision measurement in either the rest mass moe or the charge quantum e, would affect this ratio and this paper shall show how the electromagnetic mass distribution of the electron crystallizes an effective mass me from its rest mass resulting in meoγ = me'γ2 related to the coupling ratio between the electromagnetic (EMI) and the strong nuclear interaction (SNI), both as a function of alpha and for an asymptotic (not running) SNI constant defined from first principles in an interaction transformation between all of the four fundamental interactions. Since {1-ß2} describes the ß2 distribution of relativistic velocity in the unitary interval from A=0 to A=1, setting the quantum relativistic mass ratio [moe/me]2 = {1-ß2} equal to a cosmological MSigma ratio conformally transformed from the Planck scale, naturally defines a potential oscillatory upper boundary for any displacement in the unit interval of A. An increase or decrease in the 'bare' electron mass, here denoted as moe can then result in a directional measurement variation due to the fluctuating uncertainty in the position of the electron in the unitary interval mirroring the natural absence or presence of an external magnetic field to either decrease or increase the monopolar part of the electron mass in its partitioning: melectric + mmagnetic + δmmonopolar = mec{½+½[v/c]²} + δpsmec = mec with mec2√{1 + v2γ2/c2} = mec2γ = mecc2 for m = mec from the energy-momentum relation E2 = Eo2 + p2c2 of classical and quantum theory. The cosmic or universal value of alpha so remains constant in all cosmological time frames; with the fluctuation found to depend on a constant #= α in a strong interaction constant as a function of alpha. At the core of physical consciousness lies quantum consciousness; but there it is called selfinteraction of a particle or dynamical system in motion relative to its charge distribution. We shall indicate, that it is indeed the charge distribution within such a system and quantized in the fundamental nature of the electron and the proton as the base constituent of atomic hydrogen and so matter; that defines an internal monopolar charge distribution as a quantum geometric formation minimized in the classical size of the electron and the energy scale explored at that displacement scale. Finally we describe the particles of the Standard Model and including a quantum geometric explanation for the CP violation of the weak interaction, from their genesis in the inflaton and a grand unification symmetry in a transformation of supermembranes and cosmic strings appearing today in a spectrum of cosmic rays: SEWG------------------------SEWg--------SEW.G---------SeW.G--------S.EW.G------------S.E.W.G Planck Unification I----------IIB----------HO32------------IIA-----------HE64---------Bosonic Unification

Comments: 121 Pages. ISSN: 2153-8301

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[v1] 2019-05-13 06:03:25

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