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Quantum Mechanics as Tension Pathfinding: Wavefunction Collapse from Accessibility Minimization

Henrik Lehn

Published Dec 31, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.18105028

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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.
This paper develops a relational framework that reinterprets quantum mechanics as the behavior of a continuous generative field governed by the propagation and resolution of orientation under constraint. In this account, superposition reflects unresolved constraint geometry, collapse arises when constraint stabilizes and forces coherence to resolve, tunneling emerges from the propagation of constrained orientation through regions of elevated constraint density, and entanglement results from shared constraint boundaries that enforce joint coherence resolution across separation. Probability is reframed as coherence‑weighting across unresolved resolution paths, and the classical limit appears when constraint geometry becomes sufficiently stable to produce deterministic updates. The wavefunction is interpreted as a mathematical encoding of coherence across constraint geometry rather than a physical object or epistemic state. This unified mechanism dissolves the conceptual divides between classical, quantum, electromagnetic, and energetic behavior, situating all physical phenomena within a single operator framework grounded in the continuous structure of the relational field. The result is a coherent, mechanism‑level redefinition of quantum mechanics that integrates its core phenomena without invoking discontinuities, intrinsic randomness, or dual ontologies.
This paper presents a variational framework for deriving classical mechanics without presupposing time as fundamental. Motion emerges from extremal principles on configuration-space paths, with time appearing as a derived parameter describing ordered structural change. The framework extends naturally to quantum phenomena: quantum teleportation, double-slit interference, wavefunction collapse, and delayed-choice quantum eraser all emerge as geometric consequences of configuration-space structure and recordability constraints on mutual information. No wavefunction collapse, measurement postulate, or retrocausality required - four major quantum “mysteries” reduce to a single mechanism. The work was developed using AI-assisted methodology (ChatGPT for formalization, Claude for review) and represents a novel approach to foundational physics research
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.
Background The measurement problem in quantum mechanics originates from the coexistence of two incompatible rules: continuous Schrödinger evolution and discontinuous wavefunction collapse during measurement. Collapse is not derived from physical necessity but introduced as an exception, creating unresolved interpretational ambiguity. Core Framework Kearon Conditional Unlocking Fields (K-CUF) models all systems as recursive update processes governed solely by necessity and constraint. States persist only if they remain viable under recursive stabilization. No particles, observers, or measurement axioms are assumed as primitives. Within this framework, the quantum wavefunction represents a conditional update field a structured set of allowable but unrealized outcomes. Prior to measurement, no specific outcome is required to persist. Measurement as Constraint Escalation Measurement is defined as the physical coupling of a system to an apparatus or environment that introduces unavoidable constraints. This coupling increases necessity density such that recursive ambiguity can no longer be maintained. Only states capable of persistence under the new constraint regime survive stabilization. The resulting discrete outcome is not a collapse but a conditional unlocking driven by constraint viability. Resolution of the Measurement Problem No wavefunction collapse occurs. No observer-dependent dynamics are required. No branching universes or hidden variables are introduced. The quantum-to-classical transition is continuous, not categorical. Discrete measurement outcomes arise as persistence artifacts under constraint amplification, not as fundamental entities. Relation to Decoherence Decoherence explains the suppression of interference terms but does not account for outcome singularity. K-CUF subsumes decoherence while providing a generative explanation for why one outcome stabilizes rather than many. Implications This framework reframes measurement as a physical, necessity-driven process and resolves the measurement problem without metaphysical additions. It offers a unified constraint-based interpretation applicable to quantum, classical, and abstract systems.
Abstract:The quantum measurement problemthe fundamental conict between the deterministic, unitary evolution described by the Schrödinger equation and the stochastic, irreversible outcomes observed in experimentshas remained unresolved since the inception of quantum mechanics nearly a century ago. Here we demonstrate that the Chrono-Singularity Unication (CSU) framework provides a complete, rst-principles resolution of all ve components of the measurement problem with zero adjustable parameters. From a minimal informational substrate ΨI characterized by three internally-calibrated constants (α = ln 2, β = ln 2, w = −1), we derive: (i) the Born rule P = |ψ| 2 as a mathematical necessity via the GNS construction and spectral theorem; (ii) the emergence of the preferred (position) basis through Dobrushin concentration bounds on redundant environmental records; (iii) single denite outcomes from the sampled-history ontology without dynamical collapse; (iv) full compatibility with special relativity through topological linking that preserves no-signaling while permitting Bell-inequality violation; and (v) unique, falsi- able experimental predictions including a mass-dependent gravitational decoherence oor testable in near-future molecular interferometry experiments. Significance:This framework provides the exact geometric scaling required to resolve the Hubble tension and derives the Diósi-Penrose gravitational decoherence floor (τ=ℏ/ΔEG) strictly as a low-energy macroscopic limit. This paper serves as the theoretical foundation for a fully deterministic, parameter-free unification of quantum mechanics and general relativity.
The quantum measurement problem — the question of what physically occurs when a quantum system yields a definite outcome upon measurement — has remained unresolved since von Neumann's formalization of quantum mechanics in 1932. Existing interpretational frameworks each address aspects of this problem while leaving a specific mechanistic gap unfilled. The Copenhagen interpretation declares collapse without explaining it. The many-worlds interpretation removes collapse but cannot specify the preferred measurement basis. Pilot wave theory identifies a guiding field without identifying what it is. Relational quantum mechanics correctly describes the relational structure of measurement outcomes without specifying the physical process by which relational facts are established. Decoherence theory specifies which outcomes are available through environmental selection without explaining which outcome actually occurs. In each case the effect of measurement is described with precision while the mechanism remains absent. This paper proposes that the Dimensional Evolution geometric framework provides that mechanism. Wavefunction collapse is resonant selection — the stabilization of a specific harmonic configuration when an observer's resonance structure synchronizes with a quantum system's scan traversal through a completed entropic pathway. This is not a metaphysical claim. It is a physically grounded geometric process from which the measurement postulates of standard quantum mechanics emerge as derived consequences rather than foundational axioms. The Born rule reflects the fractal exponential geometry of the coherence manifold. The preferred basis is geometrically specified by observer-system resonance compatibility. The measurement cut dissolves into a continuous spectrum of resonance stability requiring no quantum-classical boundary. The definite outcome problem is resolved by resonant synchronization completing — a deterministic geometric event whose apparent randomness reflects incomplete knowledge of resonance conditions rather than fundamental indeterminacy. The paper maps DE's resonant selection mechanism against each major interpretation, identifying precisely where DE does explanatory work each interpretation cannot. Three testable experimental predictions are proposed — geometry-dependent collapse timing, resonance-bandwidth-dependent outcome distributions, and a geometric memory effect in measurement apparatus — each grounded in physical principles confirmed at other scales and each distinguishable from standard quantum mechanical and decoherence predictions. The implications of this account for the Heisenberg uncertainty relation are identified as a priority for subsequent formal development.