This paper presents ToCA Quantum Phase Regulation (QPR), the quantum-mechanical application of the Theory of Cosmic Architecture (ToCA). It demonstrates that fundamental quantum phenomena—such as superposition, entanglement, and wavefunction collapse—are not primitive features of nature, but emergent mechanical consequences of the universal tension minimization law: ∂ₜD(t) ≤ 0 where D(t) represents the deviation from local equilibrium in high-dimensional amplitude space. Key Theoretical Advances: Emergent Quantum Mechanics: Shows that Schrödinger-type dynamics arise naturally as the most efficient path for reducing tension in a complex amplitude landscape. "Superposition" is reinterpreted as parallel tension minimization, and "Entanglement" as correlated geometric tension (D_corr > 0) across subsystems. Resolution of the Measurement Problem: The framework dissolves the measurement problem by defining "collapse" as a rapid tension lock-in event triggered by strong macroscopic gradients. This eliminates the need for observer-dependent postulates. The Universal Residual Floor: A central, falsifiable prediction is that no quantum system can reach zero tension (D(t) ≥ D_floor > 0). The paper identifies this predicted floor in data from seven independent high-precision experiments (2023–2025), including deviations in Bell tests, double-slit visibility, and superconducting qubit coherence. Physical Interpretation of Complex Action Theory (CAT): Aligning with the Nielsen-Ninomiya framework, QPR suggests that the "imaginary action" (S_I) corresponds to the integrated tension over a system's history: S_I ≡ ∫ D(t) dt This provides a tangible physical mechanism for the suppression of high-S_I histories. Role in the ToCA Framework: This document focuses on the microscopic and quantum-information aspects of the theory. It is part of a series outlining the complete architecture: Main Theory: ToCA v2.4: The Theoretical Foundation for Tension Minimization (The axiomatic core). Gravity: ToCA Quantum Gravity Integration (QGI) (The application to spacetime and cosmology).
This paper presents ToCA Quantum Phase Regulation (QPR), the quantum-mechanical application of the Theory of Cosmic Architecture (ToCA). It demonstrates that fundamental quantum phenomena—such as superposition, entanglement, and wavefunction collapse—are not primitive features of nature, but emergent mechanical consequences of the universal tension minimization law: ∂ₜD(t) ≤ 0 where D(t) represents the deviation from local equilibrium in high-dimensional amplitude space. Key Theoretical Advances: Emergent Quantum Mechanics: Shows that Schrödinger-type dynamics arise naturally as the most efficient path for reducing tension in a complex amplitude landscape. "Superposition" is reinterpreted as parallel tension minimization, and "Entanglement" as correlated geometric tension (D_corr > 0) across subsystems. Resolution of the Measurement Problem: The framework dissolves the measurement problem by defining "collapse" as a rapid tension lock-in event triggered by strong macroscopic gradients. This eliminates the need for observer-dependent postulates. The Universal Residual Floor: A central, falsifiable prediction is that no quantum system can reach zero tension (D(t) ≥ D_floor > 0). The paper identifies this predicted floor in data from seven independent high-precision experiments (2023–2025), including deviations in Bell tests, double-slit visibility, and superconducting qubit coherence. Physical Interpretation of Complex Action Theory (CAT): Aligning with the Nielsen-Ninomiya framework, QPR suggests that the "imaginary action" (S_I) corresponds to the integrated tension over a system's history: S_I ≡ ∫ D(t) dt This provides a tangible physical mechanism for the suppression of high-S_I histories. Role in the ToCA Framework: This document focuses on the microscopic and quantum-information aspects of the theory. It is part of a series outlining the complete architecture: Main Theory: ToCA v2.4: The Theoretical Foundation for Tension Minimization (The axiomatic core). Gravity: ToCA Quantum Gravity Integration (QGI) (The application to spacetime and cosmology).
We demonstrate that quantum mechanics emerges naturally from universal tension minimization, resolving the measurement problem and unifying quantum and classical physics. The wavefunction represents a map of accessible tension pathways, with its squared magnitude quantifying the relative tension of each path. Wavefunction collapse is not mysterious — it is the system committing to the minimum accessible tension path when measurement forces path selection. The Schrödinger equation derives from dD/dt ≤ 0 with quantum constraints. Heisenberg uncertainty emerges from quantum tension floors (Third Law). Entanglement reflects shared tension fields, not "spooky action." The double-slit experiment shows interference of tension pathways, resolved upon measurement. This framework unifies quantum mechanics with general relativity and thermodynamics under the Theory of Cosmic Architecture (TOCA), eliminating probabilistic interpretation in favor of deterministic tension minimization with accessibility constraints. Quantum mechanics is not fundamentally different from classical physics — it is tension dynamics at scales where quantum floors dominate.
Quantum mechanics remains one of the most empirically successful theories in the history of science, yet persistent conceptual and interpretive challenges continue to accompany its application across measurement, decoherence, representation, and observer-dependent inference. This work introduces a structured application of the Cosmic Algorithm Theory-12 (CAT-12) framework to quantum mechanics, demonstrating how functional constraints—rather than new dynamics—clarify these long-standing issues. The paper formalizes four functional harmonic laws as structural constraints on quantum systems: the Law of Dynamic Precision, the Law of Harmonic Equilibrium, the Law of Harmonic Phase Translation, and the Law of Harmonic Phase-Lag Integration. Together, these laws delimit the conditions under which quantum descriptions remain physically meaningful with respect to resolution, stability, representation, and temporality. Complementing these structural constraints is the Law of Non-Coercive Alignment, a relational principle governing how theoretical interpretations may lawfully align with observational data without forcing premature interpretive closure. Importantly, this work does not modify quantum dynamics, introduce new physical entities, or propose alternative measurement postulates. All standard predictions of quantum mechanics are preserved. The contribution instead lies in clarifying why increased resolution can amplify degeneracy, why decoherence reflects regulated redistribution rather than collapse, why multiple mathematical representations remain conditionally equivalent, and why measurement outcomes emerge through temporally integrated interactions rather than instantaneous events. Through physics-first figures, formal constraint expressions, and worked examples drawn from canonical quantum scenarios, the paper demonstrates that many quantum “paradoxes” function as boundary indicators—signaling violations of admissible resolution, translation, or inference—rather than as failures of the theory itself. Interpretive plurality is reframed as a lawful consequence of structural underdetermination rather than a defect requiring resolution. This work positions CAT-12 as a cross-scale constraint architecture, applicable not only to quantum mechanics but also to atomic, chemical, biological, and cosmological systems where resolution, stability, representation, and temporal integration interact under finite physical limits. The framework is intended as a conceptual and methodological tool for researchers working in quantum foundations, measurement theory, open systems, and the philosophy of physics.
This preprint presents a foundational theory that reinterprets quantum mechanics not as a description of fundamental physical reality, but as the emergent statistical signature of a universal information-processing architecture. We introduce and formally define the Ze (Zero-point entropy) system—an active predictive engine that operates through a mandatory cycle of forward prediction and retrograde inference. The system's core axiom is that the retrograde encoding process, essential for reconciling past models with present evidence, necessitates a complete cessation of the forward information flow. From this single architectural constraint, we mathematically derive phenomena isomorphic to quantum superposition, interference, and wavefunction collapse. Superposition corresponds to a dynamical equilibrium of multiple predictive hypotheses; collapse is a structured, non-fundamental process triggered when hypothesis divergence exceeds a system-specific stability threshold; and interference arises from the coherent blending of compatible hypotheses. The framework positions quantum behavior as an epistemic property of any system performing active inference under this architectural constraint, bridging domains from particle physics to cognitive neuroscience. We present novel, falsifiable predictions and propose that quantum theory describes the dynamics of a universal class of predictive engines, not a microscopic realm of reality.
Abstract Wavefunctions are central to quantum mechanics, yet their ontological status remains one of the most debated questions in physics. This volume, within the Informational Constraints Quantum Event Realism (ICQER) framework, proposes a novel reinterpretation of wavefunctions as superpositions of informational constraint patterns distributed across quantum event networks. Moving beyond traditional views of the wavefunction as a mere probability amplitude or abstract mathematical tool, we develop a rigorous framework in which quantum states emerge from the coherent overlap and interplay of constraints that govern allowable event configurations. We establish the mathematical formalism for representing constraints as vectors in an event Hilbert space, constructing wavefunctions as linear combinations of constraint patterns with complex amplitude coefficients. Within this framework, measurement corresponds to the selective enforcement of constraints through projection operators, providing a natural, physical mechanism for wavefunction collapse that does not require observer intervention. Quantum dynamics, governed by the Schrödinger equation, is reinterpreted as the unitary propagation of constraint patterns through the event network, preserving coherence and enabling interference, entanglement, and other hallmark quantum phenomena. The constraint-based perspective resolves foundational puzzles including wave-particle duality, the measurement problem, and quantum nonlocality, while grounding the wavefunction in an objective, realist informational structure. We further explore the connection between quantum constraints and gravitational constraints within the Universal Constraint Gravity (UGC) framework, advancing a unified constraint-based foundation for physics across scales. This volume establishes wavefunctions as distributed informational structures that define quantum reality at its most fundamental level, opening new avenues for foundational research, quantum computation, and the unification of quantum mechanics with gravity.
The Relative Cosmic Equilibrium (RCE) framework is a unified physical model that redefines all fundamental phenomena—mass, time, charge, forces, and spacetime— as emergent consequences of a single scalar energy deviation field ∆E(x, t) seek- ing equilibrium. In this paper, we extend the RCE framework to the foundations of quantum mechanics. Using a slow-envelope approximation, we show that the Schrödinger equation emerges naturally from the linear dynamics of ∆E near equi- librium, with Planck’s constant ℏ appearing as the minimal topological action unit, not an ad hoc input. Quantum superposition is reinterpreted as a multimodal dy- namical equilibrium, in which the field oscillates coherently between degenerate energy minima. Measurement is identified as the introduction of an external energy gradient that breaks this degeneracy, leading to exponential relaxation toward a single outcome. This mechanism yields a characteristic, calculable collapse time: τ ≈ ℏ ∆Emeas where ∆Emeas is the energy exchanged during measurement. In conventional measurements (∆E ∼ eV), this time is ∼ 10−16 s, well below detection. However, in weak measurements with extremely low exchanged energy (∆E ∼ neV), RCE predicts an observable collapse time of ≈ 0.66 μs (for ∆Emeas = 1 neV). We present an explicit comparison with standard quantum mechanics, which offers no defined collapse timescale, and propose a feasible table-top optical experiment to test this prediction. This renders RCE a falsifiable framework and transforms the quantum measurement problem from a philosophical issue into a testable physical question.
Title: Quantum Mechanics: The Interpretation of Barcelona Description: For a century, the Copenhagen interpretation has taught us that quantum mechanics is fundamentally probabilistic, that the wavefunction collapses upon measurement, and that there is no reality independent of observation. Einstein rejected this: "God does not play dice." This preprint presents a concrete, testable alternative: the Cosmic Mesh — a discrete, elastic, fractal tetrahedral lattice that constitutes spacetime itself. From this single physical substrate we recover all quantum phenomena without probability, without collapse, and without action at a distance: The wavefunction is a real vibration in the Mesh. Entanglement is the same vibration extended across space. Measurement is a local interaction that does not create reality; it only reveals it. Particles are standing waves trapped in topological knots; light is free vibration. We derive a single deterministic rule that governs all motion: At each discrete time step, a vibration migrates to the neighboring tetrahedron that maximizes the local entanglement gradient (Sk−Si). The fine-structure constant emerges geometrically as: α−1=135+2πϕ5≈137.034 where 135 is the ideal torsional-to-volumetric ratio emerging from the geometry of the tetrahedral lattice (90° + 45°), and 2πϕ/5 is the residual torsional stress from 120º cracks and fractal inheritance (golden ratio ϕ). The Mesh is local, deterministic, and testable. We predict that quantum entanglement decays with distance beyond a fundamental coherence length — a direct, falsifiable test of the Copenhagen interpretation. This concise summary is based on the full framework developed in "THE BREATHING UNIVERSE: A Torsional Solid Machine" (Zenodo, 2026). For complete mathematical derivations, including the mechanical origin of lepton masses and the emergence of general relativity, see that work. Keywords: quantum foundations, emergent quantum mechanics, discrete spacetime, topological defects, entanglement, Bell inequalities, Copenhagen interpretation, deterministic quantum theory, elastic lattice, tetrahedral mesh, Weyl curvature imprints, dark matter, cosmological constant, fine-structure constant, golden ratio License: Creative Commons Attribution 4.0 International (CC BY 4.0) Related works: Bertran, A. (2026). THE BREATHING UNIVERSE: A Torsional Solid Machine. Zenodo. Bertran, A., Jussà, E., Vila, M. (2025). The Universe's Geometric Inertia – The Jussà-Vila Ansatz. Zenodo.