A loophole of all `loophole-free' Bell-type theorems

Abstract

Bell's theorem cannot be proved if complementary measurements have to be represented by random variables which cannot be added or multiplied. One such case occurs if their domains are not identical. The case more directly related to the Einstein-Rosen-Podolsky argument occurs if there exists an `element of reality' but nevertheless addition of complementary results is impossible because they are represented by elements from different arithmetics. A naive mixing of arithmetics leads to contradictions at a much more elementary level than the Clauser-Horne-Shimony-Holt inequality.

v2 is completely rewritten and extedned by new sections on non-Diophantine arithmetic

References in corpus (12)

• Waves along fractal coastlines: From fractal arithmetic to wave equations
• Is Einsteinian no-signalling violated in Bell Tests?
• Tensor-product vs. geometric-product coding
• Cartoon Computation: Quantum-like computing without quantum mechanics
• Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus
• Nonclassical joint distributions and Bell measurements
• Teleportation seen from space-time
• Non-Newtonian mathematics instead of non-Newtonian physics: Dark matter and dark energy from a mismatch of arithmetics
• Elementary gates for cartoon computation
• Simple fractal calculus from fractal arithmetic
• Dark energy as a manifestation of nontrivial arithmetic
• Violation of the Bell's type inequalities as a local expression of incompatibility

Cited by in corpus (6)

• A Note on Bell's Theorem Logical Consistency
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• Bell inequalities, Counterfactual Definiteness and Falsifiability
• Imitating quantum probabilities: Beyond Bell's theorem and Tsirelson bounds
• Consequences of the single-pair measurement of the Bell parameter
• Comment on "A Loophole of All "Loophole-Free" Bell-Type Theorems"