Quantum theory, gauge fields, and general relativity traditionally rest on independent foundations. This paper argues that they can be understood within a unified logical framework when the Self-Consistent Reference Frame Principle (RCC) and causality are applied to a local Hilbert-space framework. The unifying object is the comparator U_{ij}, which translates states between sites. In gauge theory it becomes the parallel transporter yielding the Yang-Mills action; in quantum mechanics it forces the Born rule through a functional equation without Gleason's theorem; in gravity it becomes the Levi-Civita connection giving the Einstein-Hilbert action via Lovelock's theorem. Among the nine theorems and two lemmas, the Phase Unity Theorem establishes that the comparator Schur phase, the gauge transformation parameter, and the quantum global phase are structural correspondences of a single U(1) symmetry. The Coleman-Mandula separation of internal and spacetime symmetries follows from RCC as a consequence of distinct encoding schemes. The Higgs mechanism emerges as a corollary: RCC prohibits bare mass terms for gauge fields. The framework yields one parameter-free falsifiable prediction: a pattern of SMEFT Wilson coefficients that can be tested at colliders, albeit with current precision limitations.
Quantum theory, gauge fields, and general relativity traditionally rest on independent foundations. This paper argues that they can be understood within a unified logical framework when the Self-Consistent Reference Frame Principle (RCC) and causality are applied to a local Hilbert-space framework. The unifying object is the comparator U_{ij}, which translates states between sites. In gauge theory it becomes the parallel transporter yielding the Yang-Mills action; in quantum mechanics it forces the Born rule through a functional equation without Gleason's theorem; in gravity it becomes the Levi-Civita connection giving the Einstein-Hilbert action via Lovelock's theorem. Among the nine theorems and two lemmas, the Phase Unity Theorem establishes that the comparator Schur phase, the gauge transformation parameter, and the quantum global phase are structural correspondences of a single U(1) symmetry. The Coleman-Mandula separation of internal and spacetime symmetries follows from RCC as a consequence of distinct encoding schemes. The Higgs mechanism emerges as a corollary: RCC prohibits bare mass terms for gauge fields. The framework yields one parameter-free falsifiable prediction: a pattern of SMEFT Wilson coefficients that can be tested at colliders, albeit with current precision limitations.
Quantum theory, gauge fields, and general relativity traditionally rest on independent foundations. This paper argues that they share a single structural origin when the Self-Consistent Reference Frame Principle (RCC) and causality are applied to a local Hilbert-space framework. The unifying object is the comparator U_{ij}, which translates states between sites. In gauge theory it becomes the parallel transporter yielding the Yang-Mills action; in quantum mechanics it forces the Born rule through a functional equation without Gleason's theorem; in gravity it becomes the Levi-Civita connection giving the Einstein-Hilbert action via Lovelock's theorem. Among the ten theorems and two lemmas, the Phase Unity Theorem establishes that the comparator Schur phase, the gauge transformation parameter, and the quantum global phase are structural correspondences of a single U(1) symmetry. The Coleman-Mandula separation of internal and spacetime symmetries follows from RCC as a consequence of distinct encoding schemes. The Higgs mechanism emerges as a corollary: RCC prohibits bare mass terms for gauge fields. The framework yields one parameter-free falsifiable prediction: a pattern of SMEFT Wilson coefficients testable at colliders.
The companion paper (Tang, 2026) showed that the Self-Consistent Reference Frame Principle (RCC), applied to local Hilbert-space fibres, yields the Born rule, the Yang--Mills action, and the Einstein--Hilbert action as consequences of reference-frame self-consistency and causality. (In that derivation, "quantum foundations" refers to the Born rule and the emergence of Hilbert-space structure; unitary dynamics, the tensor-product rule for composite systems, and the measurement postulate lie outside its scope.) The present paper removes the linearity assumption. It reformulates RCC on nonlinear state manifolds---smooth manifolds without a preferred linear or metric structure, on which symmetry groups act by diffeomorphisms. The core object is the nonlinear comparator, a G-equivariant diffeomorphism between fibres that translates reference frames. Each result of the linear paper---the Born-rule probability formula, the gauge connection, the gravitational metric, and the phase unity identity---is reconstructed in this more general setting and reduces to its linear counterpart precisely when the state manifold carries a Kähler structure, the geometric condition under which P=|⟨φ|ψ⟩|² is recovered. (Unitary dynamics, the tensor-product rule, the observable algebra, and the measurement postulate remain external inputs.) The nonlinear framework reveals structures inaccessible in the linear case: the Born rule generalises to a family of G-invariant transition functions; gauge theory arises as a special case of fibre-bundle geometry with a nonlinear G-action; nonlinear comparator corrections---torsion and anholonomy effects from the curvature of the fibre---generate additional SMEFT operators, most notably O₃B with C₃B≠0; and the gravitational sector receives subleading corrections from fibre-valued geometric invariants. The nonlinear framework yields a strictly larger set of falsifiable predictions: the linear results are recovered in the Kähler limit, while the deviations constitute a new experimental window into the geometry of state space.
This work derives the fundamental framework of quantum mechanics intrinsically from the first-principle axioms of UD duality theory. Starting from the inherent binary expansive–condensative attributes of the UD ontology, four fundamental physical fields are naturally decomposed by spontaneous symmetry breaking across spatial and material existential domains. A two-component complex spinor structure is uniquely constructed, and the imaginary unit i is proven to be not merely a mathematical convention but a structurally necessary ingredient required by both the compact SU(2) symmetry and the orthogonal inter-containment of U and D attributes. Within the flat spacetime limit of the UD gravitational action, a system of coupled Klein–Gordon field equations is established, governed by a single self-consistent fundamental mass scale m₀=1/(2πe^π) with no adjustable free parameters. The coupling constant is determined analytically from the UD vacuum equilibrium background values and the U↔D duality symmetry. Through explicit construction of four-component Dirac spinors and auxiliary field decomposition, the on-shell equivalence between the UD coupled field equations and the free Dirac equation is rigorously demonstrated. The non-relativistic limit further recovers the Pauli equation and the Schrödinger equation sequentially, reconstructing the core dynamical equations of quantum mechanics from a unified foundational origin. Global U(1) phase invariance of the UD action is verified via total-derivative decomposition, yielding the standard Noether conserved current. The Born probability interpretation is deduced directly from the global normalization axiom by isolating localized laboratory-scale excitations from the cosmic background, eliminating the need for independent quantum postulates. Based on the intrinsic properties of the UD field components, a self-consistent ontological interpretation is provided for wave–particle duality, double-slit interference, and the quantum measurement problem. In this framework, the measurement problem is dissolved rather than solved: no collapse postulate is required, and determinism is restored at the ontological level. The theory naturally implies that the continuous D_U field permits quantum superposition, while condensed D_D intrinsic entities possess definite classicality without physical particle-state superposition. Three testable theoretical predictions are presented, establishing falsifiable physical consequences of the UD quantum formulation. This paper completes the intrinsic derivation of the foundational structure of quantum mechanics from UD theory. Together with the previously derived general relativity framework, it realizes the homologous unification of gravity and quantum mechanics within a single self-contained axiomatic system.
Important status notice: This version has been superseded by v2.0. Subsequent work shows that the single-domain three-diagonal construction used here produces an experimentally excluded common-mode photon-speed anisotropy. Readers should consult the revised version and 10.5281/zenodo.21464971. We propose that conservation of probability — the single axiom A=1 — is sufficient to derive the principal results of quantum mechanics without additional postulates. On a bipartite three-dimensional causal lattice T³_diamond, each particle is represented as a causal session: an independent phase oscillator that propagates amplitude across the lattice subject to |ψ_R|² + |ψ_L|² = 1 at every tick. No Hamiltonian and no measurement postulate are assumed; a Hilbert-space structure with unitary evolution emerges from the U(1) oscillator and the per-session amplitude constraint rather than being postulated a priori. From this single constraint, the paper derives: (i) the Dirac equation in the continuum limit a→0, with the gamma matrices identified as geometric encodings of the bipartite RGB/CMY sublattice geometry; (ii) wave-particle duality and the Born rule as consequences of amplitude redistribution under A=1, with Gleason's theorem securing the |ψ|² uniqueness from the framework's emergent Hilbert space; (iii) quantization of atomic orbitals as Arnold tongue attractors of the two-body phase dynamics, recovering the hydrogen Bohr radius to four significant figures (k_min = 0.0970 vs k_Bohr = 0.0971) without fitting; (iv) gravity as a clock-density gradient rather than spacetime curvature — a refraction of causal paths through regions of higher session density, reproducing the 1/r² force law with an explicit weak-field metric tensor g_μν as a functional of the clock-density field; (v) photon emission as a structural consequence of A=1: the Coulomb interaction is a probability source that a single session cannot accommodate, mandating creation of a new photon session at orbit lock-in; (vi) the structural form of the induced gauge action (Sakharov / Zeldovich), whose leading-order term has the Maxwell form on O_h-averaged observables, with a closed-form gauge-sector birefringence sharing the same optical axis (1,1,−1) as the kinematic-sector prediction. Energy and momentum conservation are not independent inputs — they are consequences of A=1 applied to closed session sets. The numerically tractable results are verified or partially verified by a suite of more than fifteen experiments with no free parameters beyond the Planck-scale calibration of the lattice spacing; an audit table records the status of every claim. The paper conjectures that the Standard Model gauge group SU(3) × SU(2) × U(1), together with Lorentz SO(3,1), is the automorphism group of the framework's extended per-site amplitude — a precise 18-dimensional Lie-algebra equality. The existing framework is shown to carry SO(3,1) × U(1) (dim 7) on the per-site (ψ_R, ψ_L) amplitude; the remaining factors require structural extensions (per-site C² isospin and C³ colour indices) that are the subject of a companion paper. Six computational scaffolding scripts establish the conjecture's components. This is Paper I of the A=1 Discrete Causal Lattice series. Companion papers in preparation address the Standard Model gauge derivation, the Farey-sequence mass spectrum (and its Veneziano-amplitude limiting case), plasma and gradient-ionization phenomenology, the proton-interior structure, quantum measurement theory, and a Hilbert-6th-style combinatorial foundation for continuum physics. What changed in v1.0 (since v0.98-RC): * Three new audit-table rows: long-horizon escape mechanism (PART), lock-in resonance grid-independence across {65, 81, 97, 113}³ grids (PART), and the Standard Model gauge-group conjecture as a precise 18-dimensional Lie-algebra equality (STUB).* A Gleason-uniqueness subsubsection in the Born-rule discussion, addressing the necessity question for the |ψ|² measure.* An explicit metric-tensor formula in the gravity section, identifying g_μν as a functional of ρ_clock in the weak-field limit.* Refined automorphism conjecture with explicit decomposition into established and structural-extension factors.* New Acknowledgments section. Source code, paper sources, and data files: https://github.com/JackDMenendez/discrete-causal-latticeLicense: Paper text and figures CC BY 4.0; source code MIT.
We propose that the quantum measurement problem is a frame problem, resolved by recognizing that coherence is relative to a choice of coherence frame—analogous to the relativity of simultaneity in special relativity. We introduce coherence relativity, a geometric framework in which physical reality is described on a joint manifold M×Σ, where M is emergent spacetime and Σ is a coherence manifold whose points represent distinct observational perspectives. In this framework, wave function collapse is not a dynamical process but a transformation between coherence frames induced by measurement interactions. We present a derivation of the Born rule—that measurement probabilities equal squared amplitudes—as the unique probability measure invariant under coherence-frame relabelings and splittings, given additivity and continuity. This derivation unifies insights from Gleason's theorem, Zurek's envariance, and operational reconstruction programs within a single geometric structure. We demonstrate the framework with the double-slit experiment in two coherence frames and identify six experimentally testable signatures distinguishing Coherence Relativity from standard quantum mechanics: non-linear visibility scaling, frame-transformation hysteresis, coherence-space curvature effects, modified gravitational decoherence, measurable transformation timescales, and coherence revival. The most accessible predictions—erasure hysteresis and transformation timescales—are testable with current superconducting qubit and trapped ion platforms. v4 (April 2026): Adds three new paradox resolutions (Quantum Zeno with D_f completion interpretation, Sleeping Beauty via CR-internal derivation from axioms A1+A3, and a unifying meta-theorem characterizing all quantum paradoxes as non-Born-compliant frame transport). Introduces Prediction 7 (Zeno/anti-Zeno crossover at τ_meas ≈ τ_transform with pointer-basis dependence). Total experimentally testable signatures increased from six to seven. 21 pages.
We propose a fully local realist unified physical framework derived entirely from a single minimal underlying rule: space is filled with discrete ground-state field quanta, whose sole dynamical property is nearest-neighbor attraction proportional to the product of their excitation levels, with strictly conserved total excitation across all space. This rule is not an ad hoc postulate, but a distillation of a universal physical tendency observed across all scales—spontaneous attraction between adjacent entities, structurally isomorphic to van der Waals forces, nuclear binding, the Casimir effect, and Bose–Einstein condensation. From this single rule, we derive the following core consequences forward, with no reverse-engineering: Excitations spontaneously form stable self-bound topological structures with a “hard core + extended ripple” profile, naturally accounting for wave-particle duality without separate postulates; Newtonian gravity (F∝r2M1M2) emerges directly as the macroscopic sum of all nearest-neighbor attractions, with the inverse-square law following purely from 3D geometry and flux conservation; An all-or-nothing threshold mechanism for quantum measurement, explaining the photoelectric effect and Born rule without wavefunction collapse; A paradox-free local realist account of double-slit interference, quantum erasure, and delayed-choice experiments; Gravitational time dilation, motion time dilation, and Lorentz invariance as emergent phenomena, with no additional assumptions about spacetime structure. This framework is fully compatible with all existing experimental observations of standard quantum mechanics and general relativity, while making three falsifiable, qualitatively distinct predictions. The central prediction—a sharp threshold step in interference visibility versus path-marking coupling—is testable with existing quantum optics equipment. We do not claim to replace established theories, but offer a minimal, self-consistent, falsifiable alternative local realist picture.