Quantifying and Interpreting Connection Strength in Macro- and Microscopic Systems: Lessons from Bell’s Approach

Abstract

Bell inequalities were created with the goal of improving the understanding of foundational questions in quantum mechanics. To this end, they are typically applied to measurement results generated from entangled systems of particles. They can, however, also be used as a statistical tool for macroscopic systems, where they can describe the connection strength between two components of a system under a causal model. We show that, in principle, data from macroscopic observations analyzed with Bell’ s approach can invalidate certain causal models. To illustrate this use, we describe a macroscopic game setting, without a quantum mechanical measurement process, and analyze it using the framework of Bell experiments. In the macroscopic game, violations of the inequalities can be created by cheating with classically defined strategies. In the physical context, the meaning of violations is less clear and is still vigorously debated. We discuss two measures for optimal strategies to generate a given statistic that violates the inequalities. We show their mathematical equivalence and how they can be computed from CHSH-quantities alone, if non-signaling applies. As a macroscopic example from the financial world, we show how the unfair use of insider knowledge could be picked up using Bell statistics. Finally, in the discussion of realist interpretations of quantum mechanical Bell experiments, cheating strategies are often expressed through the ideas of free choice and locality. In this regard, violations of free choice and locality can be interpreted as two sides of the same coin, which underscores the view that the meaning these terms are given in Bell’s approach should not be confused with their everyday use. In general, we conclude that Bell’s approach also carries lessons for understanding macroscopic systems of which the connectedness conforms to different causal structures.

On Applicability of Quantum Formalism to Model Decision Making: Can Cognitive Signaling Be Compatible with Quantum Theory?

“…And this paper is not directed to such foundational issues. We mention just the nonlocal interpretation [ 1 , 2 , 3 , 4 , 9 ] (and one must differ Einsteinian and Bell nonlocalities [ 90 , 91 , 92 , 93 ]), the contextual interpretation [ 2 , 8 , 11 , 94 , 95 , 96 , 97 , 98 , 99 , 100 , 101 , 102 , 103 , 104 , 105 , 106 , 107 , 108 , 109 , 110 , 111 , 112 , 113 , 114 ], and the observables incompatibility interpretation [ 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 115 , 116 ].…”

“…He wrote numerous works explaining the violation of the Bell inequalities by contextuality of probabilities (see, e.g., monographs [ 130 , 131 , 132 ]. However, recently, the author became more concentrated on finding the quantum mechanical (QM) explanation of the origin of contextuality and, as was shown in articles [ 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 ] (see also Jaeger [ 115 , 116 ]), the seed of contextuality is in the existence of incompatible observables. From this viewpoint, the violation of the Bell inequalities can be explained by the Bohr complementarity principle —one of the fundamental principles of QM.…”

“…It is impossible to create a representative sample from the colossal ensemble of publications in this area. The author points only to publications that he has read or himself contributed to their writing (see [ 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 ]). See Section 6 for the discussion on the interpretations for the violation of the Bell inequalities.…”

“…Since all interpretational problems of quantum physics are automatically projected on quantum-like theory, the violation of the Bell inequalities for experiments with humans is also characterized by the diversity of interpretations ( Section 6 ). The author advertizes the incompatibility interpretation [ 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 ] (see also [ 83 ]). The latter means that generally outcomes of mental observables, say questions asked to people, cannot be treated as predetermined.…”

Winning a CHSH Game without Entangled Particles in a Finite Number of Biased Rounds: How Much Luck Is Needed?

“…First, the CHSH form can be tested well with current experimental technology. Second, the CHSH form of the Bell inequalities can be symmetrically formulated with expectation values and is so open for applications to macroscopic systems outside physics [19,20]. In such applications, the number of rounds is naturally finite and there is no a priori reason for which measurement settings would occur with equal likelihood.…”