--- VERSION 3.0 MAJOR REVISION UPDATE (JUNE 2026) --- This manuscript has been comprehensively updated to Version 3.0. This major revision transitions the framework from a static dimensional scaling model into a dynamic, non-linear field theory. Key Additions: The Hambardzumian Substrate Equation: A formalized, non-linear Schrödinger-Newton system that scales gravito-electromagnetic self-attraction by $1/\alpha$ using exclusively fundamental constants. Analytical Soliton Convergence: Direct mathematical derivation showing the collapsed wave substrate naturally stabilizes at the exact spatial radius of the classical electron ($r_e$). Temporal Collapse Constant: Derived an instantaneous wave-to-particle localization timeframe ($\tau \approx 1.76 \times 10^{-19}\text{ s}$) that perfectly matches the intrinsic Zitterbewegung frequency of the electron field. Falsifiable Laboratory Target: Establishes a definitive, low-energy vertical boundary condition for wave function collapse at exactly 3,730 eV (soft X-rays), offering a concrete path for terrestrial experimental verification. [The original Version 1.0 abstract follows below] We propose a reframing of the relationship between quantum mechanics and general relativity,and present a parameter-free analytical expression for the hierarchy problem as a consequenceof that reframing. Rather than treating quantum mechanics and general relativity as twoincompatible theories requiring reconciliation, we argue they are two categorical expressions ofa single underlying field — the same fundamental substrate viewed from opposite sides of athreshold. Wave and particle states are not two behaviors of the same object but two entirelydifferent modes of existence separated by a hard binary boundary. A particle is not a wave thathas been measured — it is a concentration of the wave field that has crossed a critical threshold,analogous to the way sufficient spacetime curvature produces a black hole event horizon. Weshow that both thresholds — the quantum-classical boundary and the event horizon — arestructurally identical: both are the unique dimensionless threshold condition available in theirrespective theories, both produce hard binary phase transitions, and both are expressions of thesame substrate at different scales. From the scale separation between the two thresholds wederive the expression: Hierarchy = alpha x (m_P / m_e)^2, which produces the correctelectromagnetic-to-gravitational force ratio of 10^42 with no free parameters, to within 0.015%precision. This result is consistent with the framework being correct and motivates theexperimental test that would constitute proof: a discrete, reproducible collapse of wave behaviorat approximately 3,730 eV of electromagnetic field energy — derived from existing constantswith no free parameters — which standard quantum mechanics does not predict and thethreshold model specifically does.
--- VERSION 3.0 MAJOR REVISION UPDATE (JUNE 2026) --- This manuscript has been comprehensively updated to Version 3.0. This major revision transitions the framework from a static dimensional scaling model into a dynamic, non-linear field theory. Key Additions: The Hambardzumian Substrate Equation: A formalized, non-linear Schrödinger-Newton system that scales gravito-electromagnetic self-attraction by 1/α using exclusively fundamental constants. Analytical Soliton Convergence: Direct mathematical derivation showing the collapsed wave substrate naturally stabilizes at the exact spatial radius of the classical electron (re). Temporal Collapse Constant: Derived an instantaneous wave-to-particle localization timeframe (τ≈1.76×10−19 s) that perfectly matches the intrinsic Zitterbewegung frequency of the electron field. Falsifiable Laboratory Target: Establishes a definitive, low-energy vertical boundary condition for wave function collapse at exactly 3,730 eV (soft X-rays), offering a concrete path for terrestrial experimental verification. [The original Version 1.0 abstract follows below] We propose a reframing of the relationship between quantum mechanics and general relativity,and present a parameter-free analytical expression for the hierarchy problem as a consequenceof that reframing. Rather than treating quantum mechanics and general relativity as twoincompatible theories requiring reconciliation, we argue they are two categorical expressions ofa single underlying field — the same fundamental substrate viewed from opposite sides of athreshold. Wave and particle states are not two behaviors of the same object but two entirelydifferent modes of existence separated by a hard binary boundary. A particle is not a wave thathas been measured — it is a concentration of the wave field that has crossed a critical threshold,analogous to the way sufficient spacetime curvature produces a black hole event horizon. Weshow that both thresholds — the quantum-classical boundary and the event horizon — arestructurally identical: both are the unique dimensionless threshold condition available in theirrespective theories, both produce hard binary phase transitions, and both are expressions of thesame substrate at different scales. From the scale separation between the two thresholds wederive the expression: Hierarchy = alpha x (m_P / m_e)^2, which produces the correctelectromagnetic-to-gravitational force ratio of 10^42 with no free parameters, to within 0.015%precision. This result is consistent with the framework being correct and motivates theexperimental test that would constitute proof: a discrete, reproducible collapse of wave behaviorat approximately 3,730 eV of electromagnetic field energy — derived from existing constantswith no free parameters — which standard quantum mechanics does not predict and thethreshold model specifically does.
Why does matter possess wave-like properties? Is wave-particle duality an inherent dual nature of matter, or merely a projection of a deeper underlying physical structure under two distinct observational perspectives? This paper presents a rigorous first-principles derivation of matter wave dynamics within the axiomatic framework of Time Field Theory (TFT). The entire derivation relies solely on two core axioms: local intrinsic total velocity conservation and metric self-consistency (flux conservation), without introducing any extra postulates. Following the logical sequence of ontological foundation, phase derivation, wave generation, hierarchical classification, physical correspondence, extreme-case verification, and unified spectrum construction, this paper first establishes the core ontological premise that matter corresponds to localized condensed states of the time field. It then derives the geometric structure of the existence phase angle on the unit circle of the complex plane from the velocity conservation axiom, revealing the fundamental origin of intrinsic material phases. On this basis, the de Broglie relations are strictly derived, eliminating the dualistic contradiction between particle and wave characteristics. This work further distinguishes two distinct wave regimes: intrinsic waves originating from phase evolution within condensed states, and apparent waves arising from the global spatial translation of field distributions, which are respectively mapped onto electromagnetic waves and gravitational waves as two classes of physical reality. Using black hole horizons as an extreme physical testbed, we demonstrate that intrinsic wave phenomena vanish completely at time-freezing surfaces while apparent wave behaviors remain intact, providing a unified explanation for the observational fact that black holes emit no light yet produce gravitational waves. We also clarify the ontological origin of black hole darkness: light is not trapped by gravity, but the physical conditions required for photon generation cease to hold at time-freezing surfaces. Finally, we construct a continuous spectrum of wave behaviors ranging from the vacuum ground state to black hole horizons. This paper proves that wave-like behavior is not a binary ”present/absent” attribute of matter, but a continuous function of the condensation strength of the time field. Quantum mechanics and classical mechanics do not describe two separate physical worlds; instead, they represent two limiting regimes of a single universal time field under different condensation levels.
Abstract For over a century, theoretical physics has treated General Relativity and Quantum Mechanics as fundamentally incompatible: one posits a continuous, deterministic spacetime manifold; the other, a discrete, probabilistic Hilbert space. The Algorithmic Reality Model (ARM) resolves this schism by identifying a single computational mechanism—the Zeno Threshold (Zα)—as the universal bound governing both quantum collapse and spacetime geometry. ARM treats physical reality as the macroscopic projection of a finite-bandwidth computational substrate operating on a timeless, pre-geometric state (the Singleton). By enforcing Landauer's principle of irreversible erasure, ARM derives the entirety of the gravitational sector from seven pre-geometric, quantum informational axioms. Key Derivations & Unifications Emergent Spacetime: Spatial geometry emerges from the Quantum Fisher Information Metric (QFIM) of the observer's state space, while time emerges from the Tomita-Takesaki modular flow. The Lorentzian signature (-,+,+,+) is algebraically forced by the compact/non-compact structure of their isometry generators. The Holographic Scalar (The 3→1 Unification): Applying the Nyquist-Shannon sampling theorem to the holographic boundary yields the exact Bekenstein-Hawking factor of 1/4 as a universal 2D anti-aliasing limit. This simultaneously fixes the area-law coefficient and structurally derives Newton's constant as G = c3ξmin2 / ℏ. Systematic Boundary Deviations: The framework quantitatively resolves macroscopic anomalies as computational resolution limits. Dark energy emerges as the minimum Landauer maintenance cost of the cosmological event horizon, and the MOND acceleration scale (a0) emerges as a thermodynamic noise floor, algebraically locked by the structural identity a02 = (8πG/3)ρΛ. Thermodynamic State Truncation: Wavefunction collapse, the black hole information paradox, and EPR non-locality are rigorously unified as manifestations of the computational substrate's finite Landauer memory budget. Computational Computability Because ARM is built on discrete informational axioms rather than continuous manifolds, the entire framework is natively computable. The structural derivations in this paper—including emergent geodesic lensing, the Bekenstein-Hawking threshold, and the MOND noise floor—have been explicitly verified via sparse Hermitian lattice simulations. The complete open-source computational validation suite is available at: github.com/srdrymn/algorithmic-reality-model-validations This manuscript represents the master synthesis and culmination of the Algorithmic Theory of Reality (ATR) foundational framework.
Abstract: The transition from quantum to classical behavior remains one of the central open problems in fundamental physics. Decoherence theory describes the dynamical process by which quantum superpositions become effectively classical, but does not identify a sharp structural threshold. We present an algebraic criterion for the quantum-classical boundary derived from a single-parameter (N = 3) framework called Trichiral Theory (TT). The framework produces a palindromic degeneracy spectrum whose values — 1, 2, 4, 8, 12, 20, 54 and their mirror — each reduce to closed-form expressions in N (respectively: 1, c, N+1, N2 −1, N(N+1), (N+1)(N+2), 2N3). At the first stable state of this spectrum (degeneracy g = 4 = N+1), the four known forces admit a natural partition into two pairs: the Strong and Weak forces, which are capable of forming new bound states via a three-edge closure mechanism, and the electromagnetic and gravitational forces, which interact with existing states but do not produce new bound configurations. Notably, the gravitational coupling derives as VG = 2VEM 2, linking the hierarchy problem to the quantum-classical boundary through a common algebraic origin. We argue that this 2+2 partition at g = 4 constitutes a precise, falsifiable criterion for the onset of classical behavior, and present three experimentally relevant predictions.
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 general relativity are not fundamental. They emerge from a single substrate: a face-centered cubic quantum supersolid of identical spin-zero bosons called voxels. Four axioms and one empirical anchor (the Rydberg constant) determine the lattice. The microscopic action yields a Gross-Pitaevskii equation for the order parameter and an elastic action for lattice deformations. The Schrödinger equation is the linearized Gross-Pitaevskii equation. The Born rule is the definition of the coherence fraction. Wavefunction collapse occurs when curvature exceeds the coherence energy. The Einstein field equations are the continuum limit of the elastic action. Spacetime curvature is lattice strain. Both theories derive from the same action with no free parameters. The measurement problem is solved. The Hard Problem of consciousness is proposed. Galaxy rotation curves require no dark matter. All fundamental constants are derived. The theory is falsifiable.
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.