One proposes a scale-invariant, non-orientable topological model of the universe, called the umbilic totality, which unifies quantum mechanical dualities (bra/ket, state/apparatus, or derivatively, entanglement) and pseudo-Riemannian general relativity within a single mathematical (claiming to be ontomathematical) framework. By replacing standard 2 complex phase trigonometry via a 4 non-orientable Möbius strip (MS) topology, one shows that quantum entanglement and covariant metric curvature emerge as grade-dual projections of a single projective geometric algebra (PGA) multivector field. One generalizes Gromov non-squeezing, Birkhoff ergodicity, and Noether’s theorem to non-orientable phase spaces, demonstrating that local metric energy fluctuations are balanced by a globally conserved topological action. One demonstrates that Occam’s razor strictly favors Majorana neutrinos over Dirac neutrinos under umbilic Fermi transformations, offering a clear empirical test for the model. The ontomathematical framework is designed to resolve the long-standing incompatibility between quantum mechanics and general relativity and argues that this incompatibility stems from a fundamental topological misconception: using orientable, locally Euclidean structures rather than a global, scale-invariant, non-orientable topology. Using conformal projective geometric algebra (PGA), the framework replaces the conventional complex phase with a Möbius topology. Within this single multivector structure, physical concepts traditionally treated as distinct (such as particle versus field, metric curvature versus quantum state, bra versus ket vectors, and spacetime geometry versus phase space) are reinterpreted as complementary local projections of a single underlying geometric totality. The proposed generalized PGA-Einstein field equation establishes a mathematical hierarchy whose limiting cases naturally degenerate into the core equations of established physics: general relativity, the Dirac equation, and the Schrödinger equation. Crucially, a multi-segment degeneration simultaneously accounts for spacetime connectivity and non-local quantum correlations. Quantum entanglement is thus reinterpreted not as instantaneous action at a distance, but as continuous global locality across a non-orientable manifold, providing a topological explanation for Bell inequality violations. Beyond postdictions such as CPT-invariance and cosmological flatness, the model offers a series of experimentally or observably falsifiable predictions, providing concrete empirical criteria to validate or falsify the proposed framework.
Keywords: 4 non-orientable holonomy and topology; Bell - Tsirelson bound; bra-ket unification; chiral parity inversion (P-flip); conformal projective geometric algebra (PGA); contravariant-covariant duality; generalized PGA-Einstein field equation(s); Majorana neutrinos; Möbius strip topology; non-orientable phase space; ontomathematics; quantum gravity and entanglement correspondence; quantum mechanics foundations; real projective geometry (RP2); scale-invariant Weyl information conservation; spacetime Clifford algebra (Cl3,1); spinor-torsion coupling; topological entanglement; umbilic Fermi transformation; Umbilic Totality
https://dx.doi.org/10.2139/ssrn.7280720 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=7280720
