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

Area of Science:

• Foundational physics
• Statistical analysis
• Causal inference

Background:

• Bell inequalities are crucial for understanding quantum mechanics and entanglement.
• Their application to macroscopic systems and causal models is less explored.
• Classical systems can exhibit behaviors analogous to quantum phenomena.

Purpose of the Study:

• To demonstrate the utility of Bell inequalities as a statistical tool for macroscopic systems.
• To show how Bell's approach can invalidate certain causal models in macroscopic settings.
• To explore the implications of Bell inequality violations in classical and financial contexts.

Main Methods:

• Applying Bell's inequality framework to a macroscopic game setting without quantum measurements.
• Analyzing data from macroscopic observations to test causal models.
• Investigating optimal strategies for violating inequalities and their mathematical equivalence.
• Examining the connection between violations, cheating strategies, free choice, and locality.

Main Results:

• Macroscopic observations analyzed with Bell's approach can invalidate specific causal models.
• Violations of Bell inequalities can be achieved through classical cheating strategies in macroscopic games.
• Two measures for optimal violation strategies are mathematically equivalent and computable from CHSH-quantities under non-signaling conditions.
• Insider trading in finance can be detected using Bell statistics.

Conclusions:

• Bell's approach offers valuable insights into the causal structures of macroscopic systems.
• The concepts of free choice and locality in Bell's framework have distinct meanings compared to their everyday usage.
• Bell inequalities provide a powerful statistical tool for analyzing correlations and causality beyond quantum mechanics.