Tone Theory and Real Number Quantum Mechanics
Anthony SANTANA
Published Sep 1, 2026• 0 citations
Abstract
Abstract Standard complex quantum mechanics relies on the abstract field of complex numbers to formu-late wave interference and phase variations across multipartite systems. This paper systematicallyre-evaluates the mathematical necessity of complex vector spaces by mapping the real-number quan-tum mechanics framework of Pedro Barrios Hita et al. (2026) directly onto the Tension-OptimizedNewtonian Entropy (TONE) Grand Unified Theory. We substitute the abstract phase structures ofcomplex Hilbert spaces with physical, geometric transformations tracking real-wave fluid volumestraversing a 10D tripartite manifold surface substrate. By analyzing the quotient space structureand the local flag equivalence relations, we prove that the unobservable global phase ambiguitymatches the tangible mechanical orientation of continuous wave packets vibrating against a discretesurface Planckian mesh. This real-number derivation eliminates the necessity for complex coordi-nate dependencies, regularizes multi-particle state representations without non-local tensor productconstraints, and establishes a completely deterministic, scale-dependent hydrodynamic alternativegoverned by strict macro-fluid Hamiltonian conservation rules. Keywords: TONE Theory, Real Number Quantum Mechanics, Quotient Space, Phase Ambiguity,Surface Planckian Mesh, Fluid Manifold Substrate.PACS: 03.65.Ta, 03.65.Ud, 02.10.De, 47.10.adCopyright: Copyright Pending © 2026DOI: 10.5281/zenodo.22238469
- DOI
- 10.5281/zenodo.22238468
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