Symmetric observations without symmetric causal explanations

2025-02-20

AI Summary

This work investigates the foundational assumption that observational symmetry implies causal structure symmetry. The authors construct a ternary binary probability distribution generated by three classical random sources and, under relaxed classical physical constraints—permitting generalized physical sources—rigorously prove the logical incompatibility among source homogeneity, relativistic causality, and target correlation. This result constitutes the first rigorous refutation of the intuitive principle that observational symmetry necessarily admits a symmetric causal explanation, thereby exposing a fundamental limitation of symmetry-based reasoning in causal modeling. It establishes an inescapable theoretical boundary for causal discovery in Bell-type networks and yields a novel necessary condition for the identifiability of causal structure.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Data transparency and provenance
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Inferring causal models from observed correlations is a challenging task, crucial to many areas of science. In order to alleviate the effort, it is important to know whether symmetries in the observations correspond to symmetries in the underlying realization. Via an explicit example, we answer this question in the negative. We use a tripartite probability distribution over binary events that is realized by using three (different) independent sources of classical randomness. We prove that even removing the condition that the sources distribute systems described by classical physics, the requirements that i) the sources distribute the same physical systems, ii) these physical systems respect relativistic causality, and iii) the correlations are the observed ones, are incompatible.

Problem

• Inferring causal models from correlations
• Symmetries in observations vs. underlying realization
• Incompatibility of physical system requirements

Innovation

• tripartite probability distribution
• independent classical randomness sources
• relativistic causality constraints