Instructors: Cecilia Flori, Perimeter Institute
Type: Guelph Waterloo Physics Institute credit course
Dates: January 9 - February 17, 2012, Mondays, Tuesdays and Fridays at 1:30-2:30 pm
Location: Alice Room, Perimeter Institute

This course aims at introducing the students to a novel mathematical way of defining quantum theory. The need of such a reformulation of quantum theory stems from the fact that, as it stands, the canonical formulation of quantum theory leads to an interpretation of the theory which is non realist, in the sense that it is not possible, a priori, to assign values to quantities but this can only be done a posteriori, ie., aftermeasurement.

Such a formulations leads to an instrumentalist interpretation of quantum theory (also known as the Copenhagen interpretation). However, inherent insuch an interpretation are various conceptual problems. A possible way to overcome these problems is to redefine quantum theory in a way that it retains some realism. In this course we will see how this can be done through the mathematical language of topos theory. By re-formulating quantum theory in terms of topos theory we reach a more realist interpretation of quantum theory, in which quantities can be said to have values at all times but the logic that emerges is multivalued. For this reason we call such an interpreatation non-realist. The main idea behindtopos quantum theory is that at the fundamental level lies the logical structure which is seen as fundamental, while probabilities are seen as derived concepts.