Experimental Non-Violation of the Bell Inequality

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 I U 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 I U , a non-Euclidean (and hence non-classical) metric g p 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 I U are necessarily g p -distant from points that do. g p 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 g p -distant from the CHSH inequality. This result fails in the singular limit p = ∞, at which g p 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.

Understanding quantum mechanics: a review and synthesis in precise language

“…More fundamentally, some of those who challenge the appropriateness of mathematical or physical assumptions (as described in Sect. 5.5 above) deny that the inequalities indicate anything significant about either locality or realism [22, § 9.3.2] [166,342,352]. Another fundamental concern is that many definitions of, or assumptions about, realism used in discussing Bell-type inequalities appear to be inconsistent with what are otherwise known to be core features of quantum theory [ .…”

“…Related developments include two similar models: one based on particles, rather than fields [520], and the other deterministic, rather than stochastic [521]. Not directly related but similar approaches include one based on the interaction of a signal wave with a carrier wave [522], and another based on a retrocausal constraining of a classical field [ [342,[527][528][529][530]. Some of these [531,532] stress the importance of the systemapparatus interaction (see Sect.…”

Agent Inaccessibility as a Fundamental Principle in Quantum Mechanics: Objective Unpredictability and Formal Uncomputability

“…In addition to an ontology being contextual or relational, further important questions are (i) whether the ontology is nonlocal [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 ], locally time-symmetric [ 12 , 13 , 14 , 15 , 16 , 29 , 30 , 31 , 32 ], or locally time-asymmetric [ 45 , 46 , 47 ], and (ii) what an experimenter agent can know exactly about a given quantum ontology. For example, in the case of the above-mentioned, time-symmetric ontological model, Leifer and Pusey [ 12 ] have noted that the exact ontic state λ—although it “…may be unknown to the experimenter”—“…is in principle knowable”.…”

“…For critical views arguing against standard interpretations of no-hidden-variables theorems see, for example, Mermin [ 48 ], Maudlin [ 49 , 50 ], Lazarovici et al [ 51 ], Passon [ 52 ], Tumulka [ 8 , 53 ], Norsen [ 6 , 54 ], Palmer [ 47 ], De Gosson [ 55 ], Wharton [ 13 , 32 ], Adlam [ 14 , 15 ], Ghadimi et al [ 26 ], Khrennikov [ 56 , 57 ], Hiley and Van Reeth [ 58 ], Flack and Hiley [ 59 ], and Walleczek [ 60 ]. After performing a careful analysis, Gisin [ 61 ] noted recently that “…Bohmian mechanics is deeply consistent”, and he remarked that “Bohmian mechanics… could inspire brave new ideas that challenge quantum physics.”…”

“…Accordingly, the difference between the effective non-signaling constraint ( Figure 3 B) and the objective non-signaling constraint ( Figure 4 B) is that the latter constraint adopts a fundamental, and not a practical, limit on complete agent access towards an ontic state λ, and towards quantum information transfers, in ontological quantum mechanics in general. For example, this holds true for (SW) quantum ontologies that are locally time-symmetric [ 12 , 13 , 14 , 15 , 16 , 29 , 30 , 31 , 32 ], locally time-asymmetric [ 45 , 46 , 47 ], or strictly nonlocal [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 ]. Finally, the here proposed principle (AIP) is fundamental in the sense that a Turing oracle only could predict the exact value of an individual outcome state as a function of physical systems and computational model evolution.…”