Version 1
: Received: 2 November 2017 / Approved: 3 November 2017 / Online: 3 November 2017 (02:17:11 CET)
Version 2
: Received: 3 November 2019 / Approved: 4 November 2019 / Online: 4 November 2019 (04:04:58 CET)
Version 3
: Received: 8 August 2020 / Approved: 9 August 2020 / Online: 9 August 2020 (22:12:13 CEST)
Version 4
: Received: 24 July 2021 / Approved: 26 July 2021 / Online: 26 July 2021 (12:04:41 CEST)
Version 5
: Received: 5 December 2021 / Approved: 6 December 2021 / Online: 6 December 2021 (11:52:36 CET)
Version 6
: Received: 4 September 2022 / Approved: 6 September 2022 / Online: 6 September 2022 (04:24:39 CEST)
Version 7
: Received: 14 May 2023 / Approved: 15 May 2023 / Online: 15 May 2023 (14:37:07 CEST)
Version 8
: Received: 9 January 2024 / Approved: 11 January 2024 / Online: 12 January 2024 (09:54:40 CET)
How to cite:
Beach, R. The Geometrization of Maxwell’s Equations and the Emergence of Gravity. Preprints2017, 2017110022. https://doi.org/10.20944/preprints201711.0022.v7
Beach, R. The Geometrization of Maxwell’s Equations and the Emergence of Gravity. Preprints 2017, 2017110022. https://doi.org/10.20944/preprints201711.0022.v7
Beach, R. The Geometrization of Maxwell’s Equations and the Emergence of Gravity. Preprints2017, 2017110022. https://doi.org/10.20944/preprints201711.0022.v7
APA Style
Beach, R. (2023). The Geometrization of Maxwell’s Equations and the Emergence of Gravity. Preprints. https://doi.org/10.20944/preprints201711.0022.v7
Chicago/Turabian Style
Beach, R. 2023 "The Geometrization of Maxwell’s Equations and the Emergence of Gravity" Preprints. https://doi.org/10.20944/preprints201711.0022.v7
Abstract
Coupling the Maxwell tensor to the Riemann-Christoffel curvature tensor is shown to lead to a geometricized theory of electrodynamics. While this geometricized theory leads directly to the classical Maxwell equations, it also extends their interpretation by giving charge density and mass density, and the four-velocity that describes their motion geometric definitions. These geometric definitions are reminiscent of General Relativity’s interpretation of mass in terms of the scalar curvature R and hint at the emergence of gravity. The gravitational theory that does emerge is shown to be equivalent to Einstein’s General Relativity augmented by an energy-momentum tensor term that mimics the properties of dark matter and/or dark energy. In summary, the proposed geometrization of the Maxwell tensor puts both electromagnetic and gravitational phenomena on an equal footing with both being tied to the curvature of space-time. Using specific solutions to the proposed theory, the unification brought to electromagnetic and gravitational phenomena, as well as the relationship of those solutions to the corresponding solutions of the classical Maxwell and Einstein field equations are compared.
Keywords
Maxwell’s equations; General Relativity; unification of electromagnetism and gravity; dark matter and dark energy; electromagnetic and gravitational radiation; antimatter; antigravity; quantization; superluminal transport
Subject
Physical Sciences, Theoretical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received:
15 May 2023
Commenter:
Raymond Beach
Commenter's Conflict of Interests:
Author
Comment:
The manuscript has been reorganized with much of the technical detail associated with finding the solutions given in the original manuscript now relocated to appendices, this to keep the body of the manuscript more readable. Additionally, a new section comparing and contrasting the classical Lagrangian derivation of the Maxwell equations with the derivation presented in the manuscript in which the manuscript’s equation (1) is taken as foundational, has been added.
Commenter: Raymond Beach
Commenter's Conflict of Interests: Author