We present a reconstruction of quantum collapse within the FCF framework, where geometry and temporality are secondary expressions of a substrate of correlations, and where two magnitudes are conserved independently: c(structural-relativistic) and the quantum change q, bound together by τ = c+ q. We hold that collapse is neither an additional postulate nor a fundamental physical process, but rather the geometric re-expression of a correlation, constituted in the receiver frame. The expression / non-expression cycle T₁ → T₂ → T₃ reconstructs, without merely juxtaposing them, the two dynamics that standard quantum mechanics postulates separately —unitary evolution and projection. We show that the Born rule is derived, not postulated, as the only measure compatible with the restriction structure of the receiving Hilbert space (Gleason’s theorem), anchoring the orthomodular lattice in the program’s co-genesis theorem (Document 7); and that the impossibility of non-contextual hidden variables (Kochen–Specker theorem) falls out of that same structure. Probability is ontologically localized in the temporal domain T₂–T₃; the photon (τ = 0, level T₁) appears as the revealing limit that proves the seat of Born is always the receiving Hilbert space. We offer a dual reading —consistent with itself and with observation—between the language of quantum fields and their fluctuations and the language of type-1/2/3 correlations. We then develop the gravitational sector, where asingle commitment—gravity couples to the mean correlational structure (the c-side), not to the quantum branches—performs a fourfold function: it dissolves the conflict between collapse and covariant conservation of energy-momentum (Page–Geilker / DeWitt), predicts the absence of gravity-induced entanglement(falsifiable by Bose–Marletto–Vedral-type experiments), and blocks the superluminal signaling of nonlinear semiclassical theories (Gisin’s no-signaling condition, a ρ̂-fed prescription). The article closes with a register of critical dependencies —DERIVED / MOTIVATED PROPOSAL / OPEN PROBLEM—and with the registered falsifiers, locating the falsifiability of the FCF in its differentiating predictions, not in its internal coherence.
We present a reconstruction of quantum collapse within the FCF framework, where geometry and temporality are secondary expressions of a substrate of correlations, and where two magnitudes are conserved independently: c(structural-relativistic) and the quantum change q, bound together by τ = c+ q. We hold that collapse is neither an additional postulate nor a fundamental physical process, but rather the geometric re-expression of a correlation, constituted in the receiver frame. The expression / non-expression cycle T₁ → T₂ → T₃ reconstructs, without merely juxtaposing them, the two dynamics that standard quantum mechanics postulates separately —unitary evolution and projection. We show that the Born rule is derived, not postulated, as the only measure compatible with the restriction structure of the receiving Hilbert space (Gleason’s theorem), anchoring the orthomodular lattice in the program’s co-genesis theorem (Document 7); and that the impossibility of non-contextual hidden variables (Kochen–Specker theorem) falls out of that same structure. Probability is ontologically localized in the temporal domain T₂–T₃; the photon (τ = 0, level T₁) appears as the revealing limit that proves the seat of Born is always the receiving Hilbert space. We offer a dual reading —consistent with itself and with observation—between the language of quantum fields and their fluctuations and the language of type-1/2/3 correlations. We then develop the gravitational sector, where asingle commitment—gravity couples to the mean correlational structure (the c-side), not to the quantum branches—performs a fourfold function: it dissolves the conflict between collapse and covariant conservation of energy-momentum (Page–Geilker / DeWitt), predicts the absence of gravity-induced entanglement(falsifiable by Bose–Marletto–Vedral-type experiments), and blocks the superluminal signaling of nonlinear semiclassical theories (Gisin’s no-signaling condition, a ρ̂-fed prescription). The article closes with a register of critical dependencies —DERIVED / MOTIVATED PROPOSAL / OPEN PROBLEM—and with the registered falsifiers, locating the falsifiability of the FCF in its differentiating predictions, not in its internal coherence.
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.
Quantum mechanics and quantum field theory (QM/QFT) offer precise mathematical tools for describing microscopic systems, but remain ambiguous with regard to the precise nature of collapse, measurement, and causal structure. This work introduces a structural reinterpretation of quantum evolution grounded in a conserved, Lorentz-compatible coherence substrate. Within this framework, wavefunctions are understood as phase-supported structures that evolve over finite causal intervals bounded by collapse events. We propose that Planck’s constant encodes structural thresholds of the substrate’s capacity to support coherent evolution. These limits define a minimum spatial and temporal envelope—referred to as the coherence tick—during which standard QM/QFT behavior is valid. Collapse is not introduced as a measurement postulate, but emerges as a necessary structural re-lock at the end of each coherence interval. The Collapse Boundary is thus a physically meaningful event horizon, and if energy or configuration offload is required, a Quantum Emission Opportunity (QEO) occurs. This framework preserves all predictive results of QM/QFT while offering a physically causal explanation for collapse timing, wavefunction termination, and entanglement. It resolves the quantum time asymmetry paradox by distinguishing between internal evolution (experienced in +t) and external observation (reconstructed in −t). By reinterpreting Planck constants as causal boundary conditions rather than universal abstractions, this model provides a substrate-based foundation beneath conventional quantum dynamics—one in which measurement, correlation, and irreversibility arise from finite structural support, not observer-induced discontinuity.
Quantum mechanics and quantum field theory (QM/QFT) offer precise mathematical tools for describing microscopic systems, but remain ambiguous with regard to the precise nature of collapse, measurement, and causal structure. This work introduces a structural reinterpretation of quantum evolution grounded in a conserved, Lorentz-compatible coherence substrate. Within this framework, wavefunctions are understood as phase-supported structures that evolve over finite causal intervals bounded by collapse events. We propose that Planck’s constant encodes structural thresholds of the substrate’s capacity to support coherent evolution. These limits define a minimum spatial and temporal envelope—referred to as the coherence tick—during which standard QM/QFT behavior is valid. Collapse is not introduced as a measurement postulate, but emerges as a necessary structural re-lock at the end of each coherence interval. The Collapse Boundary is thus a physically meaningful event horizon, and if energy or configuration offload is required, a Quantum Emission Opportunity (QEO) occurs. This framework preserves all predictive results of QM/QFT while offering a physically causal explanation for collapse timing, wavefunction termination, and entanglement. It resolves the quantum time asymmetry paradox by distinguishing between internal evolution (experienced in +t) and external observation (reconstructed in −t). By reinterpreting Planck constants as causal boundary conditions rather than universal abstractions, this model provides a substrate-based foundation beneath conventional quantum dynamics—one in which measurement, correlation, and irreversibility arise from finite structural support, not observer-induced discontinuity.
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.
This report presents a stand‑alone generative resolution of the long‑standing conflict between quantum theory and general relativity. Instead of treating spacetime or probability as fundamental, the framework introduces possibility—existing in latent and realised modes—as the underlying substrate from which physical behaviour emerges. Quantum evolution, collapse, gravitational curvature, thermodynamic restructuring, and macroscopic identity are shown to be phase‑specific expressions of a single generative process.The central construct is the phase field, which governs transitions between predictive, collapse, geometric, developmental, and identity‑stabilising regimes. Quantum behaviour arises when predictive continuation and collapse dominate; gravitational behaviour emerges when stabilised realisation induces generative curvature; thermodynamic and renormalisation‑group behaviour appear in intermediate developmental regimes.By deriving quantum, gravitational, thermodynamic, and classical limits from the same generative law, the report dissolves the apparent contradictions between unitary evolution, collapse, curvature, locality, and nonlocality. The result is a unified ontology and dynamics in which probability, geometry, and identity are emergent rather than fundamental. The document is fully self‑contained and does not assume familiarity with previous work.
This document establishes the Correlational Co-genesis Theorem (Relativity and Quantum): given a space of exclusivity satisfying axioms A1–A5, the orthomodular lattice of quantum logic and the Bures / quantum Fisher metric on the state space arise as sisters, respectively, the extremal and the infinitesimal limits of a single correlational distinguishability, so that the two structures share a common ancestry rather than being independently postulated. As a reconstruction result it is empirically equivalent to quantum mechanics and predicts no new quantity; its claim is one of explanatory economy, and its component lemmas are labelled throughout under the corpus convention (DERIVED · STANDARD · DESIGN DECISION · MOTIVATED PROPOSAL · OPEN PROBLEM). Within the FCF corpus it belongs to Layer A and sits upstream of the cosmogonic narrative of Document 9, with which it was harmonised in July 2026; version 2 additionally identifies the two branches of the theorem with the two channels of the conservation τ = c + q [MOTIVATED PROPOSAL].