An all-or-nothing flavor to the church-turing hypothesis

Abstract

Landauer’s principle claims that “Information is Physical”. It is not surprising that its conceptual antithesis, Wheeler’s “It from Bit”, has been more popular among computer scientists — in the form of the Church-Turing hypothesis: All natural processes can be computed by a universal Turing machine; physical laws then become descriptions of subsets of observable, as opposed to merely possible, computations. Switching back and forth between the two traditional styles of thought, motivated by quantum-physical Bell correlations and the doubts they raise about fundamental space-time causality, we look for an intrinsic, physical randomness notion and find one around the second law of ther-modynamics. Bell correlations combined with complexity as randomness tell us that beyond-Turing computations are either physically impossible, or they can be carried out by “devices” as simple as individual photons.