Abstract

YouTube link: https://youtu.be/YiBXqfTzwEA

Registration form to attend Q&A session on Zoom: https://forms.gle/tTRQreym7s6pR2rW6

In physics, a duality is, roughly speaking, a translation scheme between two apparently different theories. Much of physicists’ interest in dualities is due to there being cases where the translation scheme carries one from a formulation, or regime, of a theory where solving problems (i.e. calculations) are hard to a formulation or regime where they are easier. So one can solve a hard problem by doing a calculation in an easier setting, and translating the result back.

This talk will discuss the less practical question (as you might expect from a philosopher!) about how to make the idea of duality precise. I will argue that a duality is an isomorphism. This means in the simpler cases: a map between the theories’ state spaces, and quantities, that preserves values of quantities and also respects the dynamics. I will illustrate with some examples. In some, the word ‘translation’ is very appropriate since the two theories, despite their apparent differences, make the same claims about the world. In other examples, they make different claims.

This talk is based on joint work with Sebastian De Haro (Trinity College, and University of Amsterdam). The two corresponding papers are on the arxiv at: https://arxiv.org/abs/1707.06681 https://arxiv.org/abs/1806.01505