Abstract

Two of the major open questions in particle physics are: (1) Why do the elementary fermionic particles that are so far observed have such low mass-energy compared to the Planck energy scale? (2) What mechanical energy may be counterbalancing the divergent electrostatic and strong force energies of point-like charged fermions in the vicinity of the Planck scale? In this paper, using a hitherto unrecognised mechanism derived from the non-linear amelioration of the Dirac equation known as the Hehl–Datta equation within the Einstein–Cartan–Sciama–Kibble (ECSK) extension of general relativity, we present detailed numerical estimates suggesting that the mechanical energy arising from the gravitationally coupled self-interaction in the ECSK theory can address both of these questions in tandem.

Highlights

  • For over a century, Einstein’s theory of gravity has provided remarkably accurate and precise predictions for the behaviour of macroscopic bodies within our cosmos

  • The ECSK theory of gravity is an extension of general relativity allowing spacetime to have torsion in addition to curvature, where torsion is determined by the density of intrinsic angular momentum, reminiscent of the quantum-mechanical spin [1,2,3,4,5,6,7,8,9,12,13,14,15,16,17,18]

  • We ask: What physical mechanism is responsible for the observed rest mass m x of the elementary charged fermions? To answer this question we express the rest mass energy in CGS units, and assume that it is at least partially1 electromagnetic in nature, so that it satisfies a relation like e2 m x c2 ∼

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Summary

Introduction

Einstein’s theory of gravity has provided remarkably accurate and precise predictions for the behaviour of macroscopic bodies within our cosmos. For the elementary particles in the quantum realm, Einstein–Cartan theory of gravity may be more appropriate, because it incorporates spinors and associated torsion within a covariant description [1,2] For this reason there has been considerable interest in Einstein–Cartan theory, in the light of the field equations proposed by Sciama [3] and Kibble [4]. That torsion contributions within the ECSK theory resolves this difficulty as well, at least numerically, by counterbalancing the divergent electrostatic and strong force energy densities near the Planck scale. As a result of this counterbalancing, our suggestion does not have anything to do with high energy physics The second of these problems can be traced back to the fact that gravity is a considerably weaker “force” compared to the other forces. Our results below lend considerable support to this possibility

Evaluation of the Charged Fermionic Self-Energy within ECSK Theory
S-Matrix Evaluation of the Charged Fermionic Self-Energy within QED
Evaluation of Charged Fermionic Self-Energy by Dimensional Analysis
Particle Masses via Torsion Energy Contribution
Possible Solution of the Hierarchy Problem
Concluding Remarks
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