Abstract
A finite non-classical framework for qubit physics is described that challenges the conclusion that the Bell Inequality has been shown to have been violated experimentally, even approximately. This framework postulates the primacy of a fractal-like ‘invariant set’ geometry in cosmological state space, on which the universe evolves deterministically and causally, and from which space-time and the laws of physics in space-time are emergent. Consistent with the assumed primacy of , a non-Euclidean (and hence non-classical) metric is defined in cosmological state space. Here, p is a large but finite integer (whose inverse may reflect the weakness of gravity). Points that do not lie on are necessarily -distant from points that do. is related to the p-adic metric of number theory. Using number-theoretic properties of spherical triangles, the Clauser-Horne-Shimony-Holt (CHSH) inequality, whose violation would rule out local realism, is shown to be undefined in this framework. Moreover, the CHSH-like inequalities violated experimentally are shown to be -distant from the CHSH inequality. This result fails in the singular limit , at which is Euclidean and the corresponding model classical. Although Invariant Set Theory is deterministic and locally causal, it is not conspiratorial and does not compromise experimenter free will. The relationship between Invariant Set Theory, Bohmian Theory, The Cellular Automaton Interpretation of Quantum Theory and p-adic Quantum Theory is discussed.
Highlights
Recent experiments (e.g., [1]) have seemingly put beyond doubt the conclusion that the CHSH version|Corr(0, 0) + Corr(1, 0) + Corr(0, 1) − Corr(1, 1)| ≤ 2 (1)of the Bell Inequality is violated robustly for a range of experimental protocols and measurement settings
Mechanics [20], it is concluded that quantum physics can be described by deterministic causal laws, and where the Bell Theorem is negated through a failure of counterfactual incompleteness [20]
A theoretical framework has been outlined that asserts that no physical experiment has or will demonstrate that the Bell inequality (1) is violated—even approximately
Summary
Recent experiments (e.g., [1]) have seemingly put beyond doubt the conclusion that the CHSH version. The triangle seems impossible because we intuitively assume that any two sides of the triangle necessarily become close at a common vertex Relaxing this metric assumption makes it possible to construct such Penrose Triangles in 3D physical space: it is the projection into 2D of such a 3D structure that provides the illusion (but not the reality) of inconsistency. In conventional quantum theory based on complex Hilbert Space, this assumption is forced on us Motivated by both nonlinear dynamical systems theory and p-adic number theory, we outline in Section 2 a plausible and robust locally causal framework where the metric on state space is explicitly not Euclidean. (1) is necessarily constructed from Hilbert states with irrational descriptors, i.e., non-ontic states not lying on IU and g p distant from the ontic states lying on IU In this sense, (1) is neither satisfied nor violated in Invariant Set Theory: it is undefined.
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