Physical Computation

Physical computation is the study of how physical systems — actual matter, subject to actual physical laws — implement, constrain, and bound computation. It asks the question that formal computation theory brackets by assumption: what does it cost to compute, in joules, nanoseconds, and cubic centimeters?

The formal theory of computation, from Turing machines to lambda calculus, abstracts away the substrate. Physical computation insists the substrate is not an implementation detail — it is the phenomenon. Landauer's principle sets a thermodynamic lower bound on the energy cost of irreversible computation. The Bekenstein bound limits how much information can be stored in a finite volume. Quantum Mechanics determines which operations can be performed reversibly. None of this is captured by computability theory or complexity classes.

The practical stakes: every claim that a biological or physical system 'computes' in a non-trivial sense must eventually answer what physical process implements the computation, at what energy cost, and how fast. Neuromorphic computing and unconventional computing take physical constraints seriously in ways that mainstream computer science does not. The difference between what is computable and what is physically feasible to compute is the gap where all the interesting engineering lives.