Overview
This article studies the structural status of Bell-type factorizability. It argues that the standard Bell factorization assumption need not apply when observable outcomes arise from a non-injective projection of an underlying configuration space.
The central point is not that Bell's theorem is contradicted, nor that quantum mechanics is modified. Rather, Bell inequalities constrain effective descriptions that admit a jointly factorizable completion. Non-injective projection defines a class of effective descriptions in which this condition can fail.
In this setting, Bell-type correlations are traced to information loss under projection: observable outcomes correspond to equivalence classes of underlying configurations, not to independently assignable local variables.
Core contributions
- Non-injective projection: identification of many-to-one effective descriptions as a structural source of non-factorizability.
- Bell factorization: clarification that Bell inequalities constrain descriptions admitting a jointly factorizable completion.
- No dynamical nonlocality: the mechanism does not require superluminal dynamics, retrocausality, or hidden causal influences.
- Toy-model role: the explicit model isolates the structural origin of the violation and is not intended to reproduce quantum correlations quantitatively.
- Classical limit: approximate factorizability is recovered when the effective projection becomes approximately injective.
Conceptual scope
The article does not propose a modification of quantum mechanics, introduce additional physical degrees of freedom, or claim that Bell's theorem is wrong. Its purpose is to isolate a sufficient structural condition under which Bell-type factorizability fails at the effective level.
The analysis preserves operational no-signalling and statistical independence of measurement settings. It also clarifies why non-factorizability does not by itself imply causal nonlocality.
Position within Cosmochrony
Within the broader Cosmochrony programme, non-injectivity is not introduced as an ad hoc modelling device. It is treated as a structural consequence of genuinely emergent effective descriptions: an effective level that is not merely a relabelling of the underlying level cannot remain fully injective.
The Bell paper applies this principle to the probabilistic structure of quantum correlations. It shows how the loss of microstate-level distinguishability induced by projection obstructs the factorized representation assumed in Bell-type arguments.
Relation to quantum mechanics
The article does not derive the full quantitative structure of quantum mechanics. It identifies a structural reason why classical Bell factorizability may fail for projected effective descriptions. The quantitative quantum structure is addressed in companion work on admissibility, phase coherence, SU(2) correlations, and the Born rule.
References
Beau, J. Breakdown of Bell Factorization from Non-Injective Effective Descriptions. Quantum Rep. 2026, 8, 44. https://doi.org/10.3390/quantum8020044