A Topos Foundation for Theories of Physics: IV. Categories of Systems
Abstract
This paper is the fourth in a series whose goal is to develop a fundamentally new way of building theories of physics. The motivation comes from a desire to address certain deep issues that arise in the quantum theory of gravity. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics arises when the topos is the category of sets. Other types of theory employ a different topos. The previous papers in this series are concerned with implementing this programme for a single system. In the present paper, we turn to considering a collection of systems: in particular, we are interested in the relation between the topos representation for a composite system, and the representations for its constituents. We also study this problem for the disjoint sum of two systems. Our approach to these matters is to construct a category of systems and to find a topos representation of the entire category.
Keywords
Cite
@article{arxiv.quant-ph/0703066,
title = {A Topos Foundation for Theories of Physics: IV. Categories of Systems},
author = {A. Doering and C. J. Isham},
journal= {arXiv preprint arXiv:quant-ph/0703066},
year = {2008}
}
Comments
38 pages, no figures