Geometric Unity Theory: a Novel Approach to Quantum Gravity Through Four-Dimensional Möbius Strip Geometry

Marcin Mościcki

No zydh7, OSF Preprints from Center for Open Science

Abstract: We present a groundbreaking unified theory of quantum mechanics and gravity based on a fundamental insight: spacetime possesses the geometry of a self-intersecting Möbius strip in four dimensions. This framework, termed Geometric Unity Theory (GUT), offers an elegant, mathematically rigorous resolution to foundational problems in theoretical physics. Quantum phenomena emerge naturally from the self-intersection properties of this structure, while gravitational effects arise from its curvature, preserving Galilean equivalence at all scales. The mathematical framework leverages Clifford algebras and category theory to describe quantum phenomena through the Möbius geometry. This formulation reveals deep connections between quantum measurement, gauge symmetries, and spacetime geometry. By unifying fundamental forces, the theory achieves the goals of traditional grand unification while bridging to string theory. The Möbius geometry's self-intersection properties inherently implement gauge symmetries and higher-dimensional dynamics, maintaining Galilean invariance. This suggests grand unification and string theory may be complementary descriptions of the same geometric reality. GUT makes precise, experimentally testable predictions, including modifications to quantum interference patterns at energies around 10^15 eV, distinctive gravitational wave signatures, and specific corrections to particle physics cross-sections. These predictions can be tested through precision quantum experiments, gravitational wave observations, and high-energy particle collisions. The Möbius geometry's self-intersection property also provides a mechanism for information preservation in the fourth dimension, implementing the holographic principle while preserving Galilean invariance. Two fundamental equations form the core of the framework: the Schrödinger-Möbius equation incorporating gravity through spacetime curvature and the Wheeler-DeWitt-Möbius equation, which unifies quantum mechanics and gravity geometrically. These equations resolve the inconsistency between deterministic quantum evolution and probabilistic measurement. The Möbius strip's self-intersection offers a novel mechanism for quantum measurement without wave function collapse. Its non-orientable nature explains the arrow of time and entropy increase while maintaining Galilean equivalence. GUT addresses several long-standing enigmas in physics. Dark matter emerges as a geometric effect of the fourth dimension, the black hole information paradox is resolved via information preservation in the four-dimensional structure, and quantum entanglement arises from the connectivity of the Möbius geometry. The Heisenberg uncertainty principle is reinterpreted as a natural consequence of this geometry, unifying quantum indeterminacy with gravitational effects. The theory replaces cosmic inflation with geometric expansion, solving the horizon and flatness problems without violating Galilean invariance. By centering on the Wheeler-DeWitt-Möbius equation, GUT provides a unified description of quantum mechanics, gravity, and higher-dimensional dynamics.

Date: 2024-12-25
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Persistent link: https://EconPapers.repec.org/RePEc:osf:osfxxx:zydh7

DOI: 10.31219/osf.io/zydh7

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