Essay Abstract
An uncomputable class of geometric model is described and used as part of a possible framework for drawing together the three great but largely disparate theories of 20th Century physics: general relativity, quantum theory and chaos theory. This class of model derives from the fractal invariant sets of certain nonlinear deterministic dynamical systems. It is shown why such subsets of state-space can be considered formally uncomputable, in the same sense that the Halting Problem is undecidable. In this framework, undecidability is only manifest in propositions about the physical consistency of putative hypothetical states. By contrast, physical processes occurring in space-time continue to be represented computably. This dichotomy provides a non-conspiratorial approach to the violation of Statistical Independence in the Bell Theorem, thereby pointing to a possible causal deterministic description of quantum physics.
Author Bio
Tim Palmer is a Royal Society (350th Anniversary) Research Professor in the Physics Department at the University of Oxford. Tim's PhD (under Dennis Sciama) provided the first quasi-local expression for gravitational energy-momentum in general relativity. Through most of his research career, Tim worked on the chaotic dynamics of the climate system and pioneered the development of ensemble methods for weather and climate prediction, for which he won the Institute of Physics's Dirac Gold Medal. However, Tim has retained an interest in foundations of physics and published a number of papers on non-computability in quantum physics (the first in 1995).