On a Physical Theory of Causation in Multiscale Analysis of Biological Systems

Causal analysis of multiscale systems is crucial for understanding how biological networks are organized and function across scales, including the origin of life itself. This article introduces an axiomatic theory of causation based on the physical concept of cause. Its rigorous derivation from first principles allows us to formulate the law of conservation of causation, expressed in terms of the continuity equation in fluid dynamics. This law states that the flow of causation in dynamical, endogenously coarse-grained systems is conserved across scales. This means that these systems are causally renormalizable across scales; both upward and downward causation are forbidden. The theory also introduces a tool for calculating (i) the minimal linear chain necessary for a biological system to causally connect its two components at a distance, and (ii) the spatial span of the system, defined not as a metric volume of space occupied by the system but as the number of scales causally spanned by its dynamics. Finally, it raises age-old questions about reductionism and emergence, determinism and agency in living systems.