We propose Coordinate Slicing Theory (CST), an interpretive framework for quantum mechanics that maintains a single realized reality without hidden variables, branching worlds, or observer-dependent collapse. CST posits that physical systems extend not only through spacetime but also through an ontic probability manifold P — a real, observer-independent structure encoding unresolved potential for definiteness, rather than a catalogue of pre-existing outcomes or mere epistemic uncertainty. Definite facts are created through interaction via "slicing": a localized interaction that produces stable relational records by localizing a system's extension in P. Which outcome a slicing event creates is irreducibly chancy: CST relocates and reframes the selection problem rather than solving it, contributing an ontology of the pre-outcome situation and a covariant account of when and where facts are created. Classical definiteness arises from continual environmental slicing, while quantum phenomena appear when extension in P persists until interaction. Entanglement is reinterpreted geometrically as shared probability structure: entangled systems occupy a common structure in P, so a single slicing event jointly creates correlated outcomes without signaling, temporal ordering, or pre-existing values. CST is an interpretation, not a modification of quantum dynamics, and is empirically equivalent to standard quantum mechanics. We construct explicit toy models in which quantum states arise as projections of densities on probability manifolds (S² for qubits, CP³ for qubit pairs), with unitary dynamics lifted to a flow on the manifold. A no-go lemma shows that deterministic responses cannot reproduce the Born rule for pure states; the models therefore employ stochastic likelihood responses, which reproduce Born statistics exactly for all preparations, recover projective collapse and repeatability, satisfy no-signaling, reproduce Bell correlations, and yield a foliation-independent update scheme for spacelike-separated interactions.
We propose Coordinate Slicing Theory (CST), an interpretive framework for quantum mechanics that maintains a single realized reality without hidden variables, branching worlds, or observer-dependent collapse. CST posits that physical systems extend not only through spacetime but also through an ontic probability manifold P — a real, observer-independent structure encoding unresolved potential for definiteness, rather than a catalogue of pre-existing outcomes or mere epistemic uncertainty. Definite facts are created through interaction via "slicing": a localized interaction that produces stable relational records by localizing a system's extension in P. Which outcome a slicing event creates is irreducibly chancy: CST relocates and reframes the selection problem rather than solving it, contributing an ontology of the pre-outcome situation and a covariant account of when and where facts are created. Classical definiteness arises from continual environmental slicing, while quantum phenomena appear when extension in P persists until interaction. Entanglement is reinterpreted geometrically as shared probability structure: entangled systems occupy a common structure in P, so a single slicing event jointly creates correlated outcomes without signaling, temporal ordering, or pre-existing values. CST is an interpretation, not a modification of quantum dynamics, and is empirically equivalent to standard quantum mechanics. We construct explicit toy models in which quantum states arise as projections of densities on probability manifolds (S² for qubits, CP³ for qubit pairs), with unitary dynamics lifted to a flow on the manifold. A no-go lemma shows that deterministic responses cannot reproduce the Born rule for pure states; the models therefore employ stochastic likelihood responses, which reproduce Born statistics exactly for all preparations, recover projective collapse and repeatability, satisfy no-signaling, reproduce Bell correlations, and yield a foliation-independent update scheme for spacelike-separated interactions.
Decades of work in geometric quantum mechanics and decoherence theory have clarified how quantum behaviour arises from underlying symplectic and dynamical structures, yet both leave unresolved why measurements yield definite outcomes with |ψ|² frequencies. This paper proposes a deterministic geometric account that retains the strengths of those approaches while eliminating the need for stochastic collapse or multiple-world postulates. The result is a unified description in which observed statistics follow from conserved geometry rather than from probabilistic axioms. Physical reality is represented by a single trajectory ω(t) evolving under Hamiltonian flow on a compact symplectic manifold Σ. Interaction with an environment imposes new constraints that dynamically partition Σ into isolated outcome regions {Ωᵢ}, whose invariant volume ratios μ(Ωᵢ)/μ(Ω₀) reproduce Born weights. Outcome definiteness arises from trajectory confinement within an isolated region, and the framework predicts a quantitative correspondence between interference visibility V and the dynamical separation I of outcome regions. In the macroscopic limit, V ≈ 1 − I, so high separation (I → 1) corresponds to classical definiteness and negligible remaining visibility. The exact functional form, together with parameter-free calculations and proposed experimental tests, is developed in the forthcoming Paper C and a companion note (2025–2026). The paper establishes a complete ontological basis for deterministic quantum measurement, defines how isolation and re-isolation govern the appearance of classicality, and clarifies compliance with Bell, Kochen–Specker, Fine, and PBR constraints. It shows that a finite, measure-preserving geometry can reproduce the statistical structure of quantum theory while remaining open to empirical refutation. This framework, termed Constraint-Surface Dynamics, thus offers a deterministic and falsifiable alternative foundation for quantum mechanics.
The standard measurement postulate of quantum mechanics stipulates an instantaneous, non-local update of the global wavefunction upon measurement of an entangled subsystem. This postulate has been a persistent source of foundational tension, both with the locality structure of relativistic physics and with the dynamical character of the decoherence program. We separate the measurement postulate into three logically independent claims: definite outcome realization, Born-rule probability assignment, and instantaneous projection for the global wavefunction. We argue that the third claim can be eliminated at the axiomatic level and propose a modified measurement postulate, Postulate M, that replaces it. Under Postulate M, a single pointer outcome is realized locally when environmental decoherence has einselected a pointer basis at the measurement site; the corresponding selection acts on the global wavefunction as a conditional restriction to a branch rather than as a physical operation on spacelike-separated regions. We show that Postulate M recovers the standard measurement postulate as a limiting idealization for vanishing decoherence time, derives Lüders’ rule for sequential measurements, and yields no-signaling as an automatic structural consequence — not only at the level of measurement statistics but at the level of physical states themselves. Two explicit illustrations in the EPR scenario — with one and with both particles coupled to local spin environments — demonstrate the framework concretely and exhibit its frame-independent, manifestly local character. The framework is built on standard decoherence theory, compatible with multiple candidate mechanisms for single-outcome realization including gravitationally-induced collapse proposals, and naturally situated within a ψ-ontic reading of the quantum state. It represents, we argue, a reformulation of quantum mechanics as a local, state-realist theory — preserving Einstein’s aspiration for an objective physical world in the only form consistent with the empirical content of quantum mechanics, namely realism about the wavefunction rather than about pre-measurement observable values.
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.
We demonstrate that quantum and classical physics are not contradictory theories requiring reconciliation. They are different projections of the same relational structure onto incompatible bases. The Translation Principle formalizes this as precise mathematical structure with a two-layer ontology. Layer 0 (Fundamental): The coherence manifold M — coherence-rich, pre-geometric, non-local, fully specified, unitarily evolving. Contains more information than any classical description can represent. Layer 1 (Emergent): Classical projections extracting partial structure — geometric, local by construction, necessarily incomplete. Each projection operator Pi_i maps M onto a reduced representation, selecting a basis and discarding relational degrees of freedom that do not fit the frame. Core results: - Non-commutativity as projection geometry. Two classical views appear incompatible when their projection operators do not commute: [Pi_i, Pi_j] != 0. The order of observation determines the classical reality obtained. Neither projection is wrong — each is partial and order-dependent. - Translation law: mapping between classical descriptions requires manifold reference. Pi_j(M) = T_{i->j}(Pi_i(M)). Direct translation between classical projections is impossible without accessing M — proven formally. This explains why quantum foundations remains puzzling when approached classically. - Loss and surplus maps: every projection trades classical definiteness for discarded relational structure. Loss maps describe which coherence is destroyed; surplus maps describe what becomes measurable. - Measurement problem resolved: measurement does not collapse the manifold. It couples the system to an external channel that enforces a specific projection operator. The manifold evolves unitarily throughout. Definite outcomes emerge from projection stabilization, not collapse. - Wave-particle duality dissolved: one relational structure, two incompatible projections. Pi_wave discards localization, preserves phase. Pi_particle discards phase, preserves localization. Complementarity becomes projection non-commutativity. - Entanglement resolved: entangled systems share a single coherence manifold. Spatial separation appears only after projection into classical coordinates. No signal propagates — shared relational structure persists. Non-locality is projection artifact. - Preferred basis explained: position dominates classical reality because it minimizes correction cost under environmental coupling. Not fundamental — cheapest to maintain. Systems that actively protect coherence (superconductors, lasers, BEC) temporarily flip the preferred basis. - Pointer states explained: not selected by environment as special rule. They survive because everything else is too expensive to maintain. Formation attractors with lowest D:C ratio. - Four testable predictions: projection reversibility (confirmed by quantum eraser experiments), basis cost hierarchy (consistent with decoherence measurements), manifold coherence detection in macroscopic systems, and translation operator universality across physical domains. - Relationship to quantum interpretations: Copenhagen partially correct (measurement matters, but no collapse needed), Many-worlds unnecessary (single manifold with multiple projections, no branching), Bohmian mechanics replaced (explicit manifold structure operating non-classically), QBism grounded (quantum states as projection operators, not pure subjectivity). Provides ontological foundation for the entire coherence framework: Coherence-Gated Formation describes when projections stabilize, Coherence Propagation Constant governs how long they persist, and the RMAxt gradient equation provides the mathematical backbone connecting all three. Part of the Coherence Institute publication sequence (Track B9). This paper answers the foundational question: what is being projected? The answer — coherence manifolds containing full relational structure — grounds all subsequent physics in the framework.
Quantum entanglement is usually formulated as a nonseparable state in Hilbert space whose measurement statistics violate Bell-type inequalities. This paper proposes a speculative geometric framework intended not as a replacement for quantum mechanics, but as a candidate interpretive and model-building language for entanglement correlations. The central idea is that an apparently separated pair of three-dimensional measurement events may be regarded as low-dimensional projections of a single higher-dimensional object. In a lower-dimensional analogy, an observer represented by a point in a one-dimensional observational domain probes a two-dimensional circular object by emitting a ray. Entanglement preparation is modeled as the generation of concentric layers inside the higher-dimensional object. A measurement operation selects a layer, while the time of measurement fixes a common ray direction. The observed result is the intersection point between the time-ray and the selected concentric layer. Correlation arises because distinct layer-intersection points share a common ray and belong to a common higher-dimensional object. The framework is then generalized into a mathematical model in which measurement settings correspond to layer coordinates, time fixes a common phase variable, and correlations are determined by a layer-distance function. Because the model treats measurement settings as constrained by a common higher-dimensional/time-phase structure, it explicitly relaxes measurement independence, placing it near the family of superdeterministic or measurement-dependent hidden-variable approaches. The paper derives the minimal structural requirements for such a framework to reproduce the singlet-state correlation E(a,b)=−cos(a−b) and discusses its relationship to Bell's theorem, contextuality, nonlocality, invariant-set ideas, and deterministic approaches to quantum foundations. The proposal remains a conceptual and mathematical scaffold; its physical value depends on whether it can yield testable deviations, a principled dynamics for the time-ray, and a non-ad-hoc account of layer selection.
We propose an interpretation of quantum mechanics in which the wavefunction represents unresolved potential relative to an observer, measurement is deterministic resonance stabilisation, and Born-rule probability quantifies the observer’s incomplete access to the full entropic and phase-geometric state of the observer–system interaction. An observer is defined operationally as any bounded system capable of converting external entropy into internal coherence. On this view,superposition is not a set of co-existing realities but an unresolved field of possible coherence resolutions; collapse is not a stochastic discontinuity but a deterministic phase-lock between observer and system; and the classical world is the high-coherence limit in which environmental observation is dense enough to continuously stabilise macroscopic facts.The interpretation preserves the full predictive machinery of quantum mechanics while providing a unified account of the measurement problem, the Born rule, decoherence, entanglement, delayed choice, Wigner’s friend, and the quantum-to-classical transition. We formalise the framework through a resonance-selection rule, an observer equation of collapse, and a prime-modal state-space structure, and identify five classes of empirically accessible predictions.