Abstract: The central contribution is the construction of a multisegment, nonorientable geometric framework that treats quantum entanglement and quantum gravity as dual manifestations of a common topological field, with Weyl information providing the proposed conserved bridge between their quantum, gravitational, and thermodynamic descriptions developing a multisegment umbilic theory of quantum entanglement and quantum gravity based on a nonorientable topological manifold and a unified projective geometric algebra framework. The theory interprets quantum states and spacetime geometry as dual projections of a common multivector field, and proposes that their apparent separation arises from the use of local orientable descriptions for globally connected phenomena. Locally two sided segments are globally coupled through a Mobius strip structure, providing a topological interpretation of quantum entanglement as global locality and of gravitational geometry as its macroscopic dual. The theory introduces Weyl information as a globally conserved, scale invariant quantity and formulates a generalized hierarchy in which the unified field equation degenerates into the Einstein field equation, the Dirac equation, and the Schrodinger equation under appropriate limiting conditions. Its multisegment form is further reformulated as a thermodynamic equation of state describing the relationship between quantum information and gravitational energy. Four components are identified: local entanglement, global gravitational geometry, information to energy conversion, and energy to information conversion. A central element is the Higgs-Maxwell demon, interpreted as a thermodynamic and topological interface between local quantum phase space and global gravitational structure. Through a Legendre duality between bundle and co-bundle descriptions, recording and erasing quantum states are associated respectively with the absorption and generation of physical geometric degrees of freedom. The framework therefore proposes an intrinsic connection between quantum mechanics, thermodynamics, entanglement, and gravity. The paper derives terrestrial and weak gravity limits in which the generalized theory reduces to conventional physics and proposes astronomical and laboratory experiments capable of falsifying its predicted information energy transduction and polytropic behavior.
Keywords: Einstein field equation; Higgs mechanism; Legendre duality; information-energy transduction; Majorana neutrinos; Maxwell demon; Möbius strip manifold; multi-segment theory of entanglement and quantum gravity; nonorientable topology; polytropic equation of state; projective geometric algebra (PGA); quantum entanglement; quantum gravity; quantum information spacetime geometry; Schrodinger equation; thermodynamics; topological locality; umbilic theory; Weyl information
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=7394178
