Version 1
: Received: 27 October 2023 / Approved: 30 October 2023 / Online: 30 October 2023 (10:29:30 CET)
How to cite:
Tawfik, A.N.; Dabash, T. A Quantum Geometric Approach for the Generalization of Spacetime Curvature. Preprints2023, 2023101909. https://doi.org/10.20944/preprints202310.1909.v1
Tawfik, A.N.; Dabash, T. A Quantum Geometric Approach for the Generalization of Spacetime Curvature. Preprints 2023, 2023101909. https://doi.org/10.20944/preprints202310.1909.v1
Tawfik, A.N.; Dabash, T. A Quantum Geometric Approach for the Generalization of Spacetime Curvature. Preprints2023, 2023101909. https://doi.org/10.20944/preprints202310.1909.v1
APA Style
Tawfik, A.N., & Dabash, T. (2023). A Quantum Geometric Approach for the Generalization of Spacetime Curvature. Preprints. https://doi.org/10.20944/preprints202310.1909.v1
Chicago/Turabian Style
Tawfik, A.N. and Tahia Dabash. 2023 "A Quantum Geometric Approach for the Generalization of Spacetime Curvature" Preprints. https://doi.org/10.20944/preprints202310.1909.v1
Abstract
Despite the successful reconciliation of special relativity and quantum mechanics (QM), a good century ago, general relativity (GR) in its current classical formulation still does not compile with QM. While GR gives precise sensical predictions at large scales, QM is obviously dominated at small scales! We think that the everlasting battle for exploring and understanding the Universe and for privileging a consistent perception of reality is therefore awaiting a consolidator rather than a conqueror. This should be capable of either unifying the two different benchmarks or at least bringing one closer to the other! The latter describes the consolidating approach, which is based on extending QM to relativistic energies and gravitational fields and generalizing Riemann to discretized Finsler geometry. Some properties of the additional geometric structures and curvatures which are disclosed by the proposed quantization and apparently overlooked in Einstein's GR, are analytically and numerically characterized. The analytical analyses introduce dynamics with possible nonlinear connections. We conclude that i) additional geometric structures and curvatures are intrinsic essential and ii) the spacetime at the quantum scale is no longer smooth or continuous. A maximal proper force is predicted, which maximally gravitationally accelerates a test particle and importantly manifests the quantum geometric nature of the generalized spacetime curvature.
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.
