Version 1
: Received: 18 October 2023 / Approved: 19 October 2023 / Online: 19 October 2023 (10:02:29 CEST)
Version 2
: Received: 19 October 2023 / Approved: 20 October 2023 / Online: 20 October 2023 (08:36:13 CEST)
How to cite:
Jean Paul, P.; Wahid, S. Unifying Quantum Mechanics and General Relativity: A Significant Application of Semi-Structured Complex Numbers. Preprints2023, 2023101253. https://doi.org/10.20944/preprints202310.1253.v2
Jean Paul, P.; Wahid, S. Unifying Quantum Mechanics and General Relativity: A Significant Application of Semi-Structured Complex Numbers. Preprints 2023, 2023101253. https://doi.org/10.20944/preprints202310.1253.v2
Jean Paul, P.; Wahid, S. Unifying Quantum Mechanics and General Relativity: A Significant Application of Semi-Structured Complex Numbers. Preprints2023, 2023101253. https://doi.org/10.20944/preprints202310.1253.v2
APA Style
Jean Paul, P., & Wahid, S. (2023). Unifying Quantum Mechanics and General Relativity: A Significant Application of Semi-Structured Complex Numbers. Preprints. https://doi.org/10.20944/preprints202310.1253.v2
Chicago/Turabian Style
Jean Paul, P. and Shanaz Wahid. 2023 "Unifying Quantum Mechanics and General Relativity: A Significant Application of Semi-Structured Complex Numbers" Preprints. https://doi.org/10.20944/preprints202310.1253.v2
Abstract
Recently, a paper was written to establish semi-structured complex numbers ℍ (a new number set invented to enable division by zero) as a useful mathematical tool providing novel results from its application in engineering and science. Whilst the paper was a milestone, the application of this number set to quantum and classical physics had not been fully explored. Consequently, the aim of this research was to use semi-structured complex numbers to develop a new mathematical model for the mass of an object and in course unite classical and quantum physics in a simple yet effective manner. As its major contributions this paper: (1) develops a new mathematical model for the mass of an object called the wave-mass function using De Broglie’s mass and frequency relation and semi-structured complex numbers; (2) uses the new wave-mass function to determine what happens to an object traveling at the speed of light; (3) derives a relation between Schrödinger’s wave function and the new wave-mass function; (4) derives a relation between Einstein’s Field Equation and the new wave-mass function; (5) uses the wave-mass function to combine Einstein’s Field Equation with Schrödinger’s wave function to form a new quantum gravity equation. These results and their applications provide a firm foundation to advance the number set ℍ as a useful mathematical tool.
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:
20 October 2023
Commenter:
Peter Jean Paul
Commenter's Conflict of Interests:
Author
Comment:
Font size for equations have been increases. Please ensure that all equations are clearly shown in the final version. This is the most important part of the manuscript.
Commenter: Peter Jean Paul
Commenter's Conflict of Interests: Author