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Universal Quantum Tracking and Infinite Compute: What the Full Wavefunction History Would Let Us Infer About Laws, Causality, and Emergence

Douglas C. Youvan

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.13140/rg.2.2.25020.30086

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What separates quantum computation from classical computation when a classical model may retain every branch history and arbitrary causal memory? We study this question using history-resolved causal stochastic machines (HCSMs), which describe positive causal history laws. Probabilistic Turing machines (PTMs) embed in stochastic-ensemble models (SEnMs), which in turn embed in HCSMs. We prove that HCSM history laws coincide exactly with the fixed-basis, prefix-preserving diagonal sector of ideal quantum processes, denoted by $\mathsf{PTM}_{\rm proc}$ and distinguished here from algorithmic quantum Turing machines (QTMs). Coherent quantum processes extend strictly beyond this sector. The boundary is already visible in reversibility. Born-probability shadows of unitary gates preserve inverse composition exactly for basis permutations with phases. Outside this class, an exact positive stochastic simulation that supports universal quantum continuations must retain predictive information absent from visible probabilities. An inverse-recovery identity quantifies this phase ledger, and universal continuation forces the retained probability law to be tomographically sufficient for the quantum state. Under continuous full-state encoding assumptions, this requirement yields quantum-state dimension lower bounds. The familiar slogan $\mathsf{PTM}\subseteq\mathsf{QTM}$ is thereby sharpened into a precise classical boundary and a no-free-classicalization principle. Complete classical branching does not remove the predictive information needed to represent quantum coherence.

quant-pharXiv:2610.22750•Oct 19, 2026•0 citations

Reality is Singular, Mathematics are Plural: A Principle of Ontological Singularity with a Gap-Gated Instantiation Law for Quantum Foundations

Robert Daniel Kitcey

Physical reality presents itself as a single, causally unified, decohering history, while the mathematical formalism of quantum mechanics is structurally plural: Hilbert space admits superposition, basis freedom, and infinitely many decompositions of any given state. This paper proposes the Principle of Ontological Singularity: formal plurality does not by itself entail ontological plurality. Against Everettian readings that treat decohered sectors of the universal wavefunction as emergent worlds, we argue that Schrödinger evolution supplies unitary dynamics, decoherence supplies approximately autonomous sector structure, and the Born rule supplies statistical weights, but none of these alone supplies worldhood. We formalize this distinction through an ordered pair , where is the plural mathematical map and is a realization selector designating the classically operative sector. We then address the central open question head-on: what determines ? We derive a Spectral-Born Instantiation Law in which the realized sector is selected stochastically from decoherence-stabilized pointer sectors according to Born weights, but only when a Liouvillian classical-instantiation gap exceeds a physical leakage threshold. The parameters of this law are grounded in decoherence timescales rather than left as free metaphysical constants. We introduce the principle of Temporarily Emergent Reality Framework (TERF): the territory is not a permanent feature of an ontological background but a configuration crystallized by conditions and sustained only while those conditions hold. Non-actualized branches are therefore not merely uninstantiated competitors; they are absent from the operative reality set entirely, with no bridge possible because there is nothing on the other end. We further argue that the Everettian ontological extension carries no experimental warrant: no experiment instantiates any additional world we can touch, and the equation’s evidential authority derives entirely from observations made within one causally accessible history. We discuss the law’s relationship to GRW/CSL collapse models, the structure of post-instantiation evolution including recursive refinement, T2 information mechanics at breakdown, and the cosmological scope of the framework—including the primordial kit state, environmentally contingent classical emergence, and the operative irrelevance of multiverse speculation to a framework whose jurisdiction is the territory we occupy. The proposal is presented as a map–territory discipline for quantum foundations: the map may multiply without limit, but the territory remains one—temporarily, contingently, and actually.

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An ontology for causal-set dynamics: Becoming as actualization, the basis as causal past

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The causal-set programme proposes that spacetime is, at bottom, a discrete poset whose Lorentzian geometry emerges, endowed with a covariant sequential growth dynamics. It leaves open, however, two points that an ontology must settle: the status of the "becoming" of growth (a computational procedure or a real process?), and the basis of its quantum version (quantum sequential growth, QSG, does not specify the basis of the histories). We show that the theory Time–Actualization (TA) proposes an ontological answer: becoming is posited as real actualization, while the basis is selected by the couplings carried by the causal past, where that monitoring supplies a sharp basis. This identifies an environment within the ontology; it does not derive its coupling content or construct the full quantum dynamics. We present the interface as a consistency bridge, not a refoundation. The emergent geometry and its Hauptvermutung remain inherited, and the dynamical law of actualization remains open. The proposed unification concerns a common process reading of flashes, system actualizations and causal-set growth; their different rates still require an explicit interface.

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The Causal Interpretation of Quantum Mechanics

Saul T. Epstein

Physical Review•Jan 1, 1953•21 citations
What separates quantum computation from classical computation when a classical model may retain every branch history and arbitrary causal memory? We study this question using history-resolved causal stochastic machines (HCSMs), which describe positive causal history laws. Probabilistic Turing machines (PTMs) embed in stochastic-ensemble models (SEnMs), which in turn embed in HCSMs. We prove that HCSM history laws coincide exactly with the fixed-basis, prefix-preserving diagonal sector of ideal quantum processes, denoted by PTMproc\mathsf{PTM}_{\rm proc}PTMproc​ and distinguished here from algorithmic quantum Turing machines (QTMs). Coherent quantum processes extend strictly beyond this sector. The boundary is already visible in reversibility. Born-probability shadows of unitary gates preserve inverse composition exactly for basis permutations with phases. Outside this class, an exact positive stochastic simulation that supports universal quantum continuations must retain predictive information absent from visible probabilities. An inverse-recovery identity quantifies this phase ledger, and universal continuation forces the retained probability law to be tomographically sufficient for the quantum state. Under continuous full-state encoding assumptions, this requirement yields quantum-state dimension lower bounds. The familiar slogan PTM⊆QTM\mathsf{PTM}\subseteq\mathsf{QTM}PTM⊆QTM is thereby sharpened into a precise classical boundary and a no-free-classicalization principle. Complete classical branching does not remove the predictive information needed to represent quantum coherence.
Physical reality presents itself as a single, causally unified, decohering history, while the mathematical formalism of quantum mechanics is structurally plural: Hilbert space admits superposition, basis freedom, and infinitely many decompositions of any given state. This paper proposes the Principle of Ontological Singularity: formal plurality does not by itself entail ontological plurality. Against Everettian readings that treat decohered sectors of the universal wavefunction as emergent worlds, we argue that Schrödinger evolution supplies unitary dynamics, decoherence supplies approximately autonomous sector structure, and the Born rule supplies statistical weights, but none of these alone supplies worldhood. We formalize this distinction through an ordered pair , where is the plural mathematical map and is a realization selector designating the classically operative sector. We then address the central open question head-on: what determines ? We derive a Spectral-Born Instantiation Law in which the realized sector is selected stochastically from decoherence-stabilized pointer sectors according to Born weights, but only when a Liouvillian classical-instantiation gap exceeds a physical leakage threshold. The parameters of this law are grounded in decoherence timescales rather than left as free metaphysical constants. We introduce the principle of Temporarily Emergent Reality Framework (TERF): the territory is not a permanent feature of an ontological background but a configuration crystallized by conditions and sustained only while those conditions hold. Non-actualized branches are therefore not merely uninstantiated competitors; they are absent from the operative reality set entirely, with no bridge possible because there is nothing on the other end. We further argue that the Everettian ontological extension carries no experimental warrant: no experiment instantiates any additional world we can touch, and the equation’s evidential authority derives entirely from observations made within one causally accessible history. We discuss the law’s relationship to GRW/CSL collapse models, the structure of post-instantiation evolution including recursive refinement, T2 information mechanics at breakdown, and the cosmological scope of the framework—including the primordial kit state, environmentally contingent classical emergence, and the operative irrelevance of multiverse speculation to a framework whose jurisdiction is the territory we occupy. The proposal is presented as a map–territory discipline for quantum foundations: the map may multiply without limit, but the territory remains one—temporarily, contingently, and actually.
The causal-set programme proposes that spacetime is, at bottom, a discrete poset whose Lorentzian geometry emerges, endowed with a covariant sequential growth dynamics. It leaves open, however, two points that an ontology must settle: the status of the "becoming" of growth (a computational procedure or a real process?), and the basis of its quantum version (quantum sequential growth, QSG, does not specify the basis of the histories). We show that the theory Time–Actualization (TA) proposes an ontological answer: becoming is posited as real actualization, while the basis is selected by the couplings carried by the causal past, where that monitoring supplies a sharp basis. This identifies an environment within the ontology; it does not derive its coupling content or construct the full quantum dynamics. We present the interface as a consistency bridge, not a refoundation. The emergent geometry and its Hauptvermutung remain inherited, and the dynamical law of actualization remains open. The proposed unification concerns a common process reading of flashes, system actualizations and causal-set growth; their different rates still require an explicit interface.