Causal-Relational Closure and the Quantum Paradoxes: One Principle, Four Failure Modes

Oguike Ahaneku

Published Oct 7, 2026• 0 citations

Abstract

Thirty-four quantum and causal paradoxes are shown to arise from four misuses of one distinction: the distinction between a fixed event and a closed relation. The Causal-Relational Closure (CRC) principle, introduced in a companion theory paper, states that a quantum relation remains physically open while an admissible future operation can still complete, distinguish, or reroute it, and that recorded local events never change. Each paradox examined here is traced to one of four failure modes: treating a fixed event as a closed relation; combining context-indexed relations into one classical description that a stated no-go result excludes; assuming a relation closed before any closure; or treating a reversible or coherently controlled measurement interaction as a completed closure. The paradoxes span quantum optics and trajectories (delayed choice, quantum erasure, Afshar, Mott's cloud-chamber track), pre- and post-selection (Hardy, three-box, quantum pigeonhole, quantum Cheshire Cat, the quantum liar, the past of a photon), nonlocality, contextuality and temporal correlations (Einstein--Podolsky--Rosen, Greenberger--Horne--Zeilinger, Kochen--Specker, teleportation, Leggett--Garg, quantum Zeno, Renninger's negative result), observer scenarios (Wigner's friend, Frauchiger--Renner, Local Friendliness, quantum delayed choice), quantum field theory (Fermi's two-atom problem, the Unruh effect), gravity and cosmology (the firewall argument, cosmic delayed choice, the Rietdijk--Putnam argument, the classicality of inflationary perturbations), and statistical and molecular physics (Gibbs, Landauer, Loschmidt, Hund's paradox of optical isomers). Earlier approaches in four domains exhibit structures that CRC seeks to organise: Mott's 1929 analysis of the cloud-chamber track, Hegerfeldt's weak causality, the Harlow--Hayden argument, and Jaynes's resolution of the Gibbs paradox. No new probabilities are predicted; the contribution is a single diagnostic that replaces a family of case-by-case resolutions.

DOI: 10.5281/zenodo.23222479

Related papers

Causal-Relational Closure II: Future Quotients and Causal Depth

Oguike Ahaneku

A formal framework is developed for causal-relational closure (CRC), the principle that a physical relation remains open while an admissible future can still complete, distinguish, or reroute it. At a causal cut, histories are compared only through the probabilities generated by physically admissible future protocols. Two histories are future-equivalent when every admissible continuation gives the same outcome statistics. The resulting future quotient is the coarsest prediction-preserving partition of past histories, and therefore the minimal operational object relative to the declared contract. Several structural results follow. Enlarging the admissible future can only refine the quotient; combining future contracts intersects their equivalence relations; distinctions that have become future-indistinguishable cannot reappear under a fixed complete contract; and exact quotient dynamics exists whenever forward evolution respects future equivalence. For quantum realizations, future equivalence becomes equality modulo the annihilator of the admissible effect space, yielding a contract-dependent distinguishability seminorm. A past-future response matrix provides a finite-dimensional linear representation whose rank defines an operational relational dimension without identifying quotient cardinality with Hilbert-space size. This structure supports quantitative definitions of closure capacity, active causal width, and epsilon-causal depth. Quantum erasure, delayed-choice entanglement swapping, reversible observer records, and complexity-limited black-hole decoding illustrate the same calculus. The mathematics overlaps with causal states, predictive state representations, quantum combs, process tensors, quantum Markov order, and statistical sufficiency; the distinctive claim is the physical inversion that the admissible future helps define the operative relational object rather than merely compress a pre-assumed instantaneous ontology.

Oct 7, 20260 citations

A Causal-Relational Closure Quantum Circuit Laboratory: From Interfering Connections to Future-Programmed Quantum Operations

Oguike Ahaneku

Causal-relational closure (CRC) distinguishes fixed local records from relations that remain open to physically admissible future operations. A sequence of small quantum-circuit laboratories develops this distinction through interfering pairings, target-excluding routes, coherent measurement interactions, and future-programmed quantum gates. The central worked experiment records an informative pointer bit that predicts an input bit with probability 3/4. In one record branch, a later controller measurement distinguishes two prepared phases with conditional probabilities 5/6 and 1/6; in another, the same readout is completely uninformative. More strongly, the phase alternatives in the latter branch produce identical surviving quantum states and therefore cannot be distinguished by any subsequent measurement on the retained apparatus. A no-interaction control shows that phase distinguishability was lost rather than merely revealed by adding another detector. Explicit response matrices illustrate contract refinement, while a second quotient calculation identifies redundant pointer histories under a declared downstream-consumer contract and shows how archive access restores their distinction. State and channel identities, success probabilities, complete instruments, conventional precedents, and dephasing controls are supplied throughout. Established quantum operations provide the implementation language, while CRC supplies the constructive organising principle: fixed events and future-distinguishable relations are treated as different physical questions. The resulting connected circuit family makes that ontological distinction calculable, testable, and accessible without changing standard quantum probabilities.

Oct 31, 20260 citations

Causal-Relational Closure: Future-Determined Quantum Relations Beyond Instantaneous State Descriptions

Oguike Ahaneku

A theory of quantum relations is proposed in which physical meaning is not exhausted by the structure visible on an instantaneous time slice. The central principle is that a quantum relation remains physically open while an admissible future operation can still complete, distinguish, or reroute that relation. Recorded local events remain fixed; relational topology can remain unresolved. The causal-relational closure principle is inspired by conceptual patterns from the Quantum Entanglement Spacetime Theory research programme, but no constructive derivation from Quantum Entanglement Spacetime Theory is assumed. Several established experiments become manifestations of one physical idea. Quantum erasure shows that later access to path information controls which interference relation becomes visible. Delayed-choice entanglement swapping shows that a later measurement can select entangled or separable conditional relations among already registered events. Entanglement swapping between photons that never coexisted shows that a quantum relation need not correspond to simultaneously existing endpoint systems. Localizable entanglement and measurement-based graph-state experiments show that weak pairwise signatures can coexist with strong future-realizable entanglement. These results provide retrospective empirical consistency tests, not exclusive confirmation over standard quantum mechanics. A new composite prediction follows: after endpoint events have been recorded, later Bell measurements on retained mediator systems can program which Bell-correlation graph is realized among those records, including pairings of endpoints that never coexisted. For 2m endpoints, (2m − 1)!! perfect-matching topologies are selectable in the ideal pairwise construction. The state vector remains a valid predictive representation, while instantaneous state structure need not coincide with final physically meaningful relational structure.

Oct 7, 20260 citations

Causal-Relational Closure of Operator Histories: Impurity, Selective Completion, and Information Recovery

Oguike Ahaneku

Operator suppression is interpreted through the causal-relational history of physical events and the admissible futures in which their consequences remain accessible. The Universal Suppression Law (USL), retained in its original symbolic formulation, describes operator observability along compatible histories; independently formulated Causal-Relational Closure (CRC) distinguishes completed event records from relations that later operations can still resolve. The resulting history–future perspective links Heisenberg operator evolution, local impurity, future-response equivalence, and complete quantum instruments without equating their mathematical quantities. Exact Bell-pair witnesses establish that identical subsystem states and impurity can accompany opposite capacities for future discrimination. Identity-fragmented circuits illustrate coherent cancellation around a central computation; coarse relational instruments preserve coherent sectors lost under fine-grained recording; environmental re-engagement recovers locally inaccessible distinctions; and adaptive radiation measurements construct a reference-preserving recovery channel. Each example includes resource or failure controls. A six-part operational taxonomy distinguishes coherent cancellation, coarse recording, fine-grained overmeasurement, environmental leakage, re-engagement, and adaptive recovery. The synthesis offers an operator-centred account of suppression as the observable consequence of relations formed, preserved, transformed, or made inaccessible through causal interaction, while distinguishing exact quantum identities, finite-model evidence, and their ontological interpretation.

Nov 1, 20260 citations

Causal and logical loops from quantum theory

Hippolyte Dourdent

The fundamental nature of causality has been challenged by quantum theory. In particular, recent developments have shown that by relaxing the standard assumption that quantum events are embedded in a fixed background causal structure, a new kind of causal relations, indefinite, can emerge. These indefinite causal structures have been interpreted as causal loops allowing for the violation of a form of causality without paradoxes. On the other hand, quantum contextuality shows that any attempt to extend quantum theory such that classical logic holds in the extended domain fails due to the rise of inconsistent logical loops. There has been increasing evidence that it is a key feature in the understanding quantum paradoxes. This thesis aims at improving our understanding of indefinite causal orders and quantum paradoxes in order to address the question: “Could the non-fundamental nature of causality be related to a form of contextuality ?”The process matrix formalism is a mathematical framework which, in analogy withentanglement and the violation of Bell inequalities (nonlocality), offers new tools - witnesses of causal nonseparability and the violation of causal inequalities with noncausalcorrelations - to study and identify indefinite causal orders. In a bottom-up approach, wehave identified a large class of physically implementable processes, the quantum circuitswith quantum control of causal order (QC-QCs), that includes causally nonseparable processes such as the celebrated “quantum switch”. However these circuits cannot be used to violate causal inequalities. Nevertheless, in another work, I have proposed a significant relaxation of assumptions to certify the causal nonseparability of many processes, showing that it can be done in a semi-device-independent scenario with untrusted local operations and trusted quantum inputs. In particular, I have shown that the quantum switch can generate noncausal correlations in this kind of scenario.In order to refine my understanding of quantum contextuality, I have investigated theorigins of the Kochen-Specker theorem and I have analysed how the Hardy paradox entails a form of logical contextuality. I have identified that the two possible intermediatemeasurements involved in a pre-post-selection version of the paradox differ causally fromeach other. This analysis might be useful to study of the Frauchiger-Renner paradox, a“meta-version” of the Hardy paradox. On a more metaphysical aspect, I have argued fora “Gödelian hunch” from quantum theory, the idea that quantum paradoxes emerge froma lack of distinction between theoretical and metatheoretical objects.Finally, in order to establish a link between indefinite causal orders and contextuality,I have proposed a new causal game, in which the grandfather paradox is formalized interms of a logical inequality. Some process matrices can violate the causal inequalitywithout violating the logical one. I suggest that the emergence of logical inconsistenciesfrom the violation of a logical inequality might be interpreted as a form of contextuality.

Feb 10, 20220 citations

The Frame Structure of Quantum Measurement: How Collapse and Unitarity Coexist

Ahmed Hamid Mahmoud

This paper is a conceptual and interpretive companion to "The Dynamics of Discrete Fact: A Phase-Transition Theory of Wavefunction Collapse" (doi:10.5281/zenodo.18748601), which develops a phase-transition theory of wavefunction collapse in full mathematical detail. The interpretive claims made here rest on the physical model established there. The paper identifies a structural conflation at the root of the quantum measurement problem. The standard formulation treats measurement simultaneously as a physical process and as an experiential event without distinguishing between the two. We formalize this distinction as two complementary descriptive frames — a Reality Frame (F_R) for the continuous dynamics of the system–apparatus field, and an Observer Frame (F_O) for the discrete outcomes recorded by an embedded observer — connected by a calculable critical threshold γ_c derived from the companion paper's phase-transition model. The frame distinction is applied to the three sub-problems of measurement, to five foundational paradoxes (Wigner's friend, Frauchiger–Renner, Schrödinger's cat, delayed choice, and EPR), and to seven major interpretations of quantum mechanics, each shown to privilege one frame while neglecting the other. A Frame Complementarity Principle is conjectured as a testable constraint on the simultaneous accessibility of process information and outcome definiteness.

Feb 26, 20260 citations