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.v1
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.v1
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.v1
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.v1
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.v1
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.
