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.v6
Beach, R. The Geometrization of Maxwell’s Equations and the Emergence of Gravity. Preprints 2017, 2017110022. https://doi.org/10.20944/preprints201711.0022.v6
Beach, R. The Geometrization of Maxwell’s Equations and the Emergence of Gravity. Preprints2017, 2017110022. https://doi.org/10.20944/preprints201711.0022.v6
APA Style
Beach, R. (2022). The Geometrization of Maxwell’s Equations and the Emergence of Gravity. Preprints. https://doi.org/10.20944/preprints201711.0022.v6
Chicago/Turabian Style
Beach, R. 2022 "The Geometrization of Maxwell’s Equations and the Emergence of Gravity" Preprints. https://doi.org/10.20944/preprints201711.0022.v6
Abstract
Assuming the geometry of nature is Riemannian with four dimensions, the classical Maxwell equations are shown to be a derivable consequence of a single equation that couples the Maxwell tensor to the Riemann-Christoffel curvature tensor. This geometrization of the Maxwell tensor extends the interpretation of the classical Maxwell equations, for example, giving physical quantities such as charge density a geometric definition. Including a conserved energy-momentum tensor, the entirety of classical electromagnetism is shown to be a derivable consequence of the theory. The coupling of the Riemann-Christoffel curvature tensor to the Maxwell tensor also leads naturally to the emergence of gravity which is consistent with Einstein’s equation of General Relativity augmented by a term that can mimic the properties of dark matter and/or dark energy in the context of General Relativity. 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 with the corresponding solutions of the classical Maxwell and Einstein field equations are examined.
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, Space Science
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:
6 September 2022
Commenter:
Raymond Beach
Commenter's Conflict of Interests:
Author
Comment:
The manuscript’s abstract, introduction, section 2.1 covering the derivation of the equations of electromagnetism, and the conclusion section have all been re written to simplify the discussion. The discussion covering the possibility of superluminal transport has been simplified and clarified. Finally, Section 4.2 covering radiative solutions has been updated and corrected.
Commenter: Raymond Beach
Commenter's Conflict of Interests: Author