A New Unified Electro-Gravity Theory for the Electron, and the Fundamental Origin of the Fine Structure Constant and the Casimir Effect

Nirod K. Das

doi:10.4236/jhepgc.2021.71003

Abstract

A rigorous model for the electron is presented by generalizing the Coulomb’s Law or Gauss’s Law of electrostatics, using a unified theory of electricity and gravity. The permittivity of the free-space is allowed to be variable, dependent on the energy density associated with the electric field at a given location, employing generalized concepts of gravity and mass/energy density. The electric field becomes a non-linear function of the source charge, where the concept of the energy density needs to be properly defined. Stable solutions are derived for a spherically symmetric, surface-charge distribution of an elementary charge. This is implemented by assuming that the gravitational field and its equivalent permittivity function is proportional to the energy density, as a simple first-order approximation, with the constant of proportionality, referred to as the Unified Electro-Gravity (UEG) constant. The stable solution with the lowest mass/energy is assumed to represent a “static” electron without any spin. Further, assuming that the mass/energy of a static electron is half of the total mass/energy of an electron including its spin contribution, the required UEG constant is estimated. More fundamentally, the lowest stable mass of a static elementary charged particle, its associated classical radius, and the UEG constant are related to each other by a dimensionless constant, independent of any specific value of the charge or mass of the particle. This dimensionless constant is numerologically found to be closely related to the fine structure constant. This possible origin of the fine structure constant is further strengthened by applying the proposed theory to successfully model the Casimir effect, from which approximately the same above relationship between the UEG constant, electron’s mass and classical radius, and the fine structure constant, emerges.

Highlights

The electron is the most fundamental charged particle of nature [1], carrying the smallest mass among all known charged particles, and is classified as a lepton in the standard model of particle physics [2] [3]
A new unified electro-gravity (UEG) theory is presented to self-consistently model a stable structure of an elementary charge particle
A new fundamental physical constant γ, referred to as the Unified Electro-Gravity (UEG) constant, is introduced in order to redefine the energy density around the charge, leading to a new gravitational field which is proportional to the energy density with the γ the constant of the proportionality

Summary

Introduction

The electron is the most fundamental charged particle of nature [1], carrying the smallest mass among all known charged particles, and is classified as a lepton in the standard model of particle physics [2] [3]. The Casimir attractive force between two parallel conducting plates is modeled as a UEG effect due to any non-zero electric field that might escape out of a conductor through any spatial gaps between spherical electrons on the conductor’s surface, which are periodically distributed in the form of square unit cells Equating this force with the expected Casimir force as understood based on quantum mechanics and vacuum zero-point energy [25] [27], approximately the same above relationship between the UEG constant, electron’s mass and classical radius, and the fine structure constant, emerges.

Gravity as Gradient of Free-Space Permittivity

Modeling Energy Density in a Non-Linear Medium around an Electric Charge

The UEG Theory Applied to Model the Casimir Effect

Findings

Discussion and Conclusion