Weyl-Geometric Unified Field Theory
Weyl-Geometric Unified Field Theory (WGUF) is a grand unified theory (GUT) that attempts to unify the four forces of physics, electromagnetism, the strong force, the weak force, and gravity, by recasting the first three in a geometric framework compatible with the fourth. The theory was proposed by Jussi Lindgren, Andras Kovacs, and Jukka Liukkonen in 2025.[1]
Theory
The fundamental insight is to use differential geometry and Weyl geometry to derive electromagnetism as an intrinsic property of spacetime, similar to gravity in general relativity. The theory employs a Weyl space, in which the metric tensor’s covariant derivative can be non-zero, allowing spacetime geometry to encode electromagnetic properties. Electromagnetic fields, charges, and currents are treated as distortions of spacetime. Electromagnetic potential is considered to be a component of the metric tensor, while light and charge are described as fields, disturbances in spacetime.
The theory adopts a nonlinear generalization of Maxwell’s equations that underlies the theory's geometric representations. The Lorentz force law appears as a geodesic equation in spacetime. Charge density obeys a covariant wave equation, supporting a wave-like view of particles like electrons. The theory can describe quantum phenomena such as the Aharonov-Bohm effect and predicts vacuum fluctuations at the Planck scale, potentially incorporating quantum field theory and offering a geometric interpretation of the Dirac equation.[2]
Unlike string theory, this theory produces testable predictions for the Lorentz force and the impact of electromagnetic fields on spacetime geometry, aligning with general relativity.[3]
Background
Differential geometry
Weyl geometry
Weyl geometry is a generalization of Riemannian geometry. It extends the mathematical framework used in Albert Einstein’s general relativity by introducing additional geometric flexibility, specifically through a non-metricity condition that allows the metric tensor’s scale (or length) to vary across spacetime.
Weyl geometry allows the metric tensor’s covariant derivative to be non-zero, introducing a vector field (related to the electromagnetic potential). This enables the metric to encode both gravitational and electromagnetic fields. The metric tensor can be seen as a grid overlaid on spacetime. The grid’s spacing and orientation (encoded in gμv) describe how to measure distances and angles. In general relativity, mass warps this grid (via gravity), affecting motion. In WGUF, the grid’s flexibility (via Weyl geometry) accounts for electromagnetic activity, making it a universal descriptor of both gravity and electromagnetism.[4]
History
See also
References
- ↑ Lindgren, Jussi. "Einstein's dream of a unified field theory accomplished?". phys.org. Retrieved 2025-04-21.
- ↑ Hanks, Micah (2025-04-16). "Einstein's Unified Field Theory Realized? New Theory Unites Electromagnetism and Gravity Through Geometry". The Debrief. Retrieved 2025-04-21.
- ↑ "Unified Field Theory - an overview | ScienceDirect Topics". www.sciencedirect.com. Retrieved 2025-04-21.
- ↑ Carroll, Sean M. (2019-08-08). "Special Relativity and Flat Spacetime". Spacetime and Geometry. Cambridge University Press. pp. 1–47. doi:10.1017/9781108770385.002. ISBN 978-1-108-48839-6. Retrieved 2025-04-21. Search this book on
External links
- Lindgren, Jussi; Kovacs, Andras; Liukkonen, Jukka (2025-04-01). "Electromagnetism as a purely geometric theory". Journal of Physics: Conference Series. 2987 (1): 012001. Bibcode:2025JPhCS2987a2001L. doi:10.1088/1742-6596/2987/1/012001. ISSN 1742-6588.
- Lindgren, Jussi; Liukkonen, Jukka (2019-12-27). "Quantum Mechanics can be understood through stochastic optimization on spacetimes". Scientific Reports. 9 (1): 19984. Bibcode:2019NatSR...919984L. doi:10.1038/s41598-019-56357-3. ISSN 2045-2322. PMC 6934697 Check
|pmc=value (help). PMID 31882809. - Sanomiya, T. A. T.; Lobo, I. P.; Formiga, J. B.; Dahia, F.; Romero, C. (2020-12-11). "Invariant approach to Weyl's unified field theory". Physical Review D. 102 (12): 124031. arXiv:2002.00285. Bibcode:2020PhRvD.102l4031S. doi:10.1103/PhysRevD.102.124031.
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