The Information-Theoretic Impossibility of Distinguishing Causation from Correlation in Purely Observational Data

Causal reasoning forms the cornerstone of scientific inquiry across disciplines. For the first time, we establish from first principles that observational data inherently lack the information required for definitive causal discovery—a mathematical inevitability that no algorithm can circumvent. This theoretical limit is empirically demonstrated through evaluation of ten state-of-the-art methods, which collectively fail to reliably separate causation from correlation: aggressive algorithms achieve modest accuracy but produce false positives on non-causal data, while conservative methods correctly reject non-causal associations but offer no directional insight. Our findings reposition observational causal discovery: from definitive conclusion to supporting evidence—a paradigm shift grounded in first principles that reframes how causal claims are evaluated across science.