Symmetric observations without symmetric causal explanations
This addresses a foundational issue in causal inference for scientific fields, but it is incremental as it builds on existing frameworks with a specific counterexample.
The paper tackled the problem of whether symmetries in observed correlations imply symmetries in the underlying causal models, showing via a tripartite binary distribution that this is not the case, even when relaxing classical physics constraints.
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.