Defining Spacetime

Abstract

It has become apparent that our intuitive notions of space and time are inadequate for developing a theory of quantum gravity. It is perhaps worthwhile to understand where our macroscopically-developed spatial instinct is implicit in the concept of manifold, and to consider alternative methods for defining (vis-a-vis explicating) space and time. A simple example for generating a topos over a fundamental set is provided to illustrate the potential basis of such a definition.

“Many theoretical physicists believe that to progress much further it will be necessary to rethink our understanding of space-time. The 4D manifold structure of general relativity does not seem adequate to describe the kind of processes which are implicated in quantum gravity [1]”