An Introduction to Topos Physics

Abstract

The basic notion of how topoi can be utilized in physics is presented here. Topos and category theory serve as valuable tools which extend our ordinary set-theoretical conceptions, can further the study of quantum logic and give rise to new and 'neo-realistic' descriptions of quantum physics, i.e. make possible the construction of a general scheme for quantum physics, which 'looks like' the classical one. A novel way of writing theories of physics, by representing a formal language of a physical system, into an appropriate topos, is analyzed here. This novel approach is initiated by C.J. Isham and A. Doering and the major part of this paper comes from there; however there has been an effort in simplifying the basic ideas and do this work accessible to 'less experts' of the field. A minor, but not less important, part of this paper is devoted to resuming, in a concise way the background knowledge of logic, quantum logic and category theory, that is necessary for anyone who wishes to follow the whole topos approach.