Incomputability in physics

Abstract

Computability originated from Logic and followed the original path proposed by the founding fathers of the modern foundational analysis of Mathematics (Frege, Hilbert). This theoretical path departed in principle from the contemporary renewed relations between Geometry and Physics. In particular, the key issue of physical measure, as our only access to "reality", is not part of its theoretical frame, in contrast to Physics, since Poincaré, Planck and Einstein. Computability though, by its fine analysis of undecidability, provides a very useful tool for the investigation of "unpredictability" in Physics. Unpredictability coincides with physical randomness, in classical and quantum frames. And an understanding of randomness turns out to be a key component of intelligibility in Physics. © 2010 Springer-Verlag Berlin Heidelberg.