Goedel and Physics

Abstract

We introduce some early considerations of physical and mathematical impossibility as preludes to the Goedel incompleteness theorems. We consider some informal aspects of these theorems and their underlying assumptions and discuss some the responses to these theorems by those seeking to draw conclusions from them about the completability of theories of physics. We argue that there is no reason to expect Goedel incompleteness to handicap the search for a description of the laws of Nature, but we do expect it to limit what we can predict about the outcomes of those laws, and examples are given. We discuss the Goedel universe and the role it played in exposing the full spectrum of possibilities that a global understanding of space-time would reveal. Finally,we show how recent studies of supertasks have shown how global space-time structure determines the ultimate capability of computational devices within them.