Large Grants
    - Introduction
    - Awardees
    - Introduction
    - Winners
Previous Programs

2019 Intelligence in the Physical World

2019 Information as Fuel

2018 Agency in the Physical World
Awardees; RFP download

2016 Physics of the Observer
Awardees; RFP download

2015 The Physics of What Happens
Awardees; RFP download

2013 Physics of Information
Awardees; RFP download

2010 The Nature of Time
Awardees; RFP download

2008 Foundational Questions in Physics and Cosmology
Awardees; RFP download

2006 Foundational Questions in Physics and Cosmology
Awardees; RFP download

Dr. Christopher J. Isham
Imperial College


Andreas Doering, Imperial College

Project Title

Topos Quantum Theory

Project Summary

In fundamental physics, we are faced with the task of reconciling and uniting two extremely successful, but conceptually very different theories: general relativity, which describes the large-scale structure of the universe in the context of a theory of space and time; and quantum theory, which describes the world of atoms and smaller.

Virtually all approaches to quantum gravity try to change or adapt general relativity; quantum theory is taken more or less for granted. Our research programme aims at a novel reformulation of quantum theory using the concept of a topos - a sophisticated mathematical structure that generalizes set theory. One important feature of topos theory is that a proposition such as "the physical quantity A has a value in a certain range" need not be simply true or false: rather, there are more possibilities that are given by the intrinsic logic that is possessed by a topos. In our programme to reformulate quantum theory in this way, we have already found some deep and beautiful structures. However, much needs to be done before we can express the whole of quantum theory in a topos language. Our long-term goal is to find a topos framework in which all theories of physics can be meaningfully discussed and which will, in particular, allow significant generalizations of quantum theory when applied to quantum cosmology and quantum gravity.

Back to List of Awardees  
Please enter your e-mail address:

Note: Joining the FQXi mailing list does not give you a login account or constitute membership in the organization.