Chemical Physics Seminar: Liquid and Solid State NMR Investigations of Electrolytes for Beyond Lithium Ion Applications

Prof. Jean Maruani, The Honorary Director of Research, Pierre and Marie Curie University, Paris

04 July 2017, 15:00 
Kaplun Building, Room 118 
Chemical Physics Seminar

Abstract:

The Dirac gyromagnetic factor, fine-structure constant and gravitational invariant: deviations from whole numbers
The Dirac equation [1], which was derived by combining the relativistic invariance condition with the quantum probability principle, explained the half-integer spin of fermions and predicted antiparticles. In previous papers [2a-c], we have conjectured that the electron is a massless charge spinning at light velocity in the positron field, this internal motion being responsible for the rest mass. The wave beat between the electron and the positron [3] has been shown to be the reason for the gyromagnetic factor being ge = 2. Very accurate measurements and quantum electrodynamics computations have shown that actually ge departs from 2 by: g ≡ (ge - 2) / 2 ≈ 0.001159652181 ≈ 1/ 2a + P/ 2(a)2 + A/ 2(a)3 + … (within 1 ppb) [4], a being the fine-structure constant inverse: a ≡ -1 = hc / kee2.

The fine-structure constant  was first introduced by Sommerfeld to express line splittings in atomic spectra. But its inverse was given its current significance by Eddington [5], who proposed the full integer value of 137 on theoretical grounds. The primeval prime number 137 is endowed with a number of special properties [2d]. However, the measured value of a departs from 137 by ~ 0.3 ppt: a ≡ (a - 137) / 137 ≈ 0.0002627664234. In this paper, we propose an expansion of this increment similar to that derived for ge: a ≈ (1/2) ( /137)2 - (9/16) ( /137)4 … (within 0.4 ppb). A theoretical explanation is in progress.
Among the mathematical properties of 137 [2d] is a relation to the Mersenne Catalan series, Mn = 2n - 1. The sequence of these numbers is: M2 = 3, M3 = 7, M7 = 127, M127 ≈ 1.7014118 x 1038. The sum of the first three terms is 137, which approximates the strength of the electromagnetic force [6]. In previous papers [2], we have proposed equivalents of  to express the gravitational force, e.g.: p = Gmp2 / hc. The inverse of this invariant: dp ≡ p-1 ≈ 1.69328 x 1038 (within 15 ppm due to the inaccuracy in G), appears very close to M127 ! The relative deviation: d ≡ (M127 - dp) / M127 ≈ 0.00478021, can be expanded in terms of 137 (as was a) or of a (as g): d ≈ (1/3) (2/137) - (2/5) (2/137)2 ... (within 0.7 ppm) ≈ (2/ a) + (5/ a)2 … (within 0.3 ppm).

The gravitational force Fg is related to the electromagnetic force Fe also in that Fg is to Fe as Fe is to the Planck force FP [2b-d]: Fg / aFe = aFe / FP = 1 / dp, a and dp being defined above. This is due to the fact that Fe is proportional to the square of the particle rest energy E0 = m0c2 expressed in terms of the much larger Planck energy: (hc/G)1/2c, while Fg is proportional to the fourth power of this ratio [7]. All this comforts the Pythagorean view [4-6] that physical constants are not due to chance, but determined by mathematical properties.

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[1] Dirac, P. A. M. The Principles of Quantum Mechanics; Clarendon Press: Oxford, 1st edition 1930, 4th edition 1958; chaps 11-12.

[2] Maruani, J. (a) Prog. Theor. Chem. Phys. B 2012, 26, 23-46; (b) ibid. B 2013, 27, 53-74; (c) J. Quantum Matter 2015, 4, 3-11; (d) J. Chin. Chem. Soc. 2016, 63, 33-48; and references therein.

[3] de Broglie, L. L’Electron Magnétique: Théorie de Dirac; Hermann: Paris, 1934; chaps 9-22.

[4] Todorov, I. Hyperlogarithms and periods in Feynman amplitudes; Opening Lecture at QSCP XX (Varna, 2015); published as CERN-TH-2016-042; and private communication.

[5] Eddington, A. New Pathways in Science; Cambridge U. P., 1935; chap. 11.

[6] Sanchez, F. A coherent resonant cosmology approach and its implications in microphysics and biophysics; to be published in Proceedings of QSCP XX (Varna, 2015); and private communication.

[7] Macken, J. Prog. Theor. Chem. Phys. B 2015, 29, 219-245; and private communication.

 

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