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Path–Attractor Compatibility: Reconciling Local Freedom, Collapse, and Deterministic Dynamics

Marriam Naeem

Published Feb 14, 2026• 0 citations
Publisher

Abstract

A longstanding tension in the foundations of physics concerns the coexistence of deterministic(or unitary) dynamics with the apparent reality of choice, causation, collapse, and irreversible destruction. Standard responses either deny the physical significance of freedom, modify dynamicallaws, or relocate the problem to metaphysics. This paper identifies a structural distinction betweenmetastable macroscopic trajectories (paths) and globally constrained end states (attractors) and argues that its absence underlies much of the tension. We show that local degrees of freedom can alter,destabilize, and irreversibly eliminate particular trajectories without modifying the global attractorfixed by deterministic constraints. Collapse is thereby interpreted as loss of metastability ratherthan as a violation of determinism or unitarity. On this basis, we provide a structurally consistentaccount of causal efficacy, historical collapse, and responsibility within fully deterministic dynamics. We further extend this analysis to quantum mechanics, arguing that decoherence generatesmetastable macroscopic sectors within globally unitary evolution and that ontological commitmentattaches to dynamically persistent structure rather than to arbitrary Hilbert-space decomposition.The framework introduces no stochastic postulates and no modifications of physical law, but insteadclarifies the structural level at which freedom, collapse, and irreversibility operate.

DOI
10.5281/zenodo.18641632

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A longstanding tension in the foundations of physics concerns the coexistence of deterministic(or unitary) dynamics with the apparent reality of choice, causation, collapse, and irreversible destruction. Standard responses either deny the physical significance of freedom, modify dynamicallaws, or relocate the problem to metaphysics. This paper identifies a structural distinction betweenmetastable macroscopic trajectories (paths) and globally constrained end states (attractors) and argues that its absence underlies much of the tension. We show that local degrees of freedom can alter,destabilize, and irreversibly eliminate particular trajectories without modifying the global attractorfixed by deterministic constraints. Collapse is thereby interpreted as loss of metastability ratherthan as a violation of determinism or unitarity. On this basis, we provide a structurally consistentaccount of causal efficacy, historical collapse, and responsibility within fully deterministic dynamics. We further extend this analysis to quantum mechanics, arguing that decoherence generatesmetastable macroscopic sectors within globally unitary evolution and that ontological commitmentattaches to dynamically persistent structure rather than to arbitrary Hilbert-space decomposition.The framework introduces no stochastic postulates and no modifications of physical law, but insteadclarifies the structural level at which freedom, collapse, and irreversibility operate.
Deterministic microscopic laws constrain physical systems through conservation laws and boundary conditions, yet macroscopic evolution routinely exhibits irreversible collapse, destruction, and path dependence. We analyze deterministic classical and quantum systems admitting multiple metastable macroscopic trajectories under fixed global constraints and show that deterministic dynamics generally underdetermine macroscopic history. We introduce a distinction between constraint-defined macroscopic equivalence classes, fixed by invariant quantities, and metastable macroscopic trajectories, defined by dynamical stability. Using stability and basin-of-attraction arguments, we characterize collapse as a deterministic loss of metastability in which an entire macroscopic trajectory becomes dynamically inaccessible without violation of microscopic reversibility or conservation laws. Irreversible destruction corresponds to elimination of physically realizable paths rather than loss of information or coarse-grained inaccessibility. We show that explanations based solely on coarse-graining or decoherence are insufficient to account for such trajectory elimination, as they preserve admissibility of erased histories. In contrast, instability-driven trajectory destruction constitutes an ontic dynamical process, directly realized in many-body and condensed matter systems. The framework provides a unified account of irreversible macroscopic change and causal differentiation within deterministic dynamics, without invoking stochasticity, modified laws, or observer-dependent mechanisms. Deterministic laws constrain admissible macroscopic states, while instability and metastability govern the physically realizable histories connecting them.
This preprint presents a foundations-level analysis of physical description based on structural dependency rather than dynamical construction. Quantum mechanics, classical mechanics, and relativistic spacetime are treated as effective regimes arising under different structural conditions, rather than as competing ontologies. The analysis identifies persistence under interaction, irreversible constraint accumulation, stable relational structure, and interaction as minimal requirements for physical behaviour. Collapse is characterised as irreversible loss of compatibility between alternative continuations, without appeal to observers, stochastic dynamics, or additional postulates. Time is treated as structural ordering induced by exclusion, rather than as a primitive background parameter. No new dynamics are proposed and no empirically successful theories are modified. The aim is to clarify explanatory dependencies that underlie familiar physical regimes and to dissolve persistent foundational problems that arise when regime-level descriptions are misidentified as foundations.
The standard formulation of quantum mechanics combines deterministic unitary evolution with non-deterministic measurement postulates. Although operationally successful, this hybrid structure introduces internal tensions between continuity, probability, and physical law. In this work, we examine the standard postulates across five independent formalisms—the Schro¨dinger picture, the Heisenberg picture, the path integral formulation, the density matrix framework, and open-systems measurement theory. By identifying the load-bearing assumptions required to sustain intrinsic randomness, we reveal a deeper consistency condition implicit in all five approaches. When made explicit, this condition enforces a fully deterministic substrate underlying quantum evolution, with apparent stochasticity arising only from coarse-graining over unresolved degrees of freedom. No empirical predictions are altered. Instead, determinism emerges as the minimal completion of the standard formalism.
We introduce the Historical Attractor Theory (HAT), a foundational framework in which physical reality is defined at the level of complete histories rather than instantaneous states. Within this approach, realizability is determined by a global criterion of historical stability, encoded in a scalar functional that orders histories according to their degree of openness. Physical reality corresponds to histories that satisfy a strict closure condition, suppressing incompatible alternatives without invoking fundamental time, dynamical collapse, or observer-dependent postulates. Quantum, classical, thermodynamic, and geometric descriptions emerge as effective regimes operating within historically stabilized narratives. HAT provides a unified structural principle that reorganizes central problems in the foundations of physics by shifting the focus from state-based dynamics to global historical consistency.
Abstract This paper proposes a conservative reinterpretation of quantum phenomena within standard Hilbert space formalism. Rather than treating superposition, decoherence, and measurement as ontologically distinct primitives requiring separate explanatory frameworks, we suggest these phenomena can be coherently understood as dynamical regimes of a single system oscillating between two macrostates: a coherent steady-state regime characterised by constraint-aligned stability, and a transient underconstrained regime characterised by temporarily increased degrees of freedom. Within this framing, decoherence is reinterpreted not as collapse or information loss, but as natural dynamical recovery toward a coherence attractor following environmental perturbation. This interpretive compression introduces no new postulates, no modifications to the quantum formalism, and no claims of empirical novelty. It is offered as a conceptual reorganisation that may reduce interpretive proliferation by unifying apparently disparate phenomena under a common dynamical description. The approach is compatible with standard decoherence theory and maintains neutrality with respect to existing interpretations of quantum mechanics.
This paper is part of the Aetherium Foundations Phase, which develops the formal field equations, emergent geometry, and theoretical structure underlying the Aetherium substrate. The quantum measurement problem arises from the tension between the linear, deterministic evolution of quantum states and the emergence of single, definite outcomes in measurement. Standard formulations introduce collapse postulates or interpretive overlays but provide no physically grounded mechanism for outcome selection within a single world. The Aetherium framework resolves this tension by introducing a pre‑geometric substrate whose intrinsic property is coherence, constrained by the resonant structure of the substrate. Quantum states are coarse‑grained descriptions of coherence patterns, and measurement corresponds to a coherence‑reconfiguration event in which the combined system–apparatus coherence aligns with a resonance‑compatible configuration. Decoherence stabilizes this configuration by redistributing coherence across many degrees of freedom, while probabilities arise from the relative stability of resonant attractor states, yielding the Born rule as a structural consequence of the substrate’s resonance architecture. This coherence‑first ontology provides a single‑world, realist, and local account of measurement that preserves the empirical success of quantum theory while eliminating collapse, branching, and observer‑dependence. The result is a unified and physically meaningful foundation for understanding the quantum‑to‑classical transition.