Mike Stannett
(University of Sheffield)
Hypercomputation, Physics and Computation

We present an introductory overview of research in hypercomputation theory, especially as it relates to the relationship between physics and computation. On the quantum side, we argue that a computational model of quantum motion exists, showing that if super-Turing computation is possible it must (somewhat paradoxically) derive from uncomputable properties of classical action. On the cosmological side, we review the work of Hogarth, Andréka, Németi et al, showing that realistic models of spacetime permit the solution of formally undecidable problems. Conversely, very simple computational considerations imply that closed timelike curves (CTCs), if they exist, can act as very low capacity information storage systems.

The material, which is based on a recent talk at the BMC 2012, will be presented in easily accessible form, and questions from the audience (especially those we cannot answer) are very welcome.