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.

Keywords

• Bell statistic
• CHSH inequality
• free choice
• locality
• propagation of information
• causality