Equivalence, Duality, and the Interpretation of Physical Theories

Thomas Barrett (University of California, Santa Barbara)
My aim in this talk is to demonstrate that the following two questions are closely related. The question of content: What is the content of a physical theory? The question of equivalence: When should we consider two theories to be equivalent? I will argue that we can approach the former question by way of the latter. In slogan form, one might put this suggestion as follows: We go a long way towards pinning down what the theory "says about the world" by pinning down which other theories "say the same thing."

Laurenz Hudetz (London School of Economics)
This talk addresses the question what it is to interpret a formalism. First, I explicate the notion of an uninterpreted formalism and explain how uninterpreted formalisms can be extended to pre-interpreted formalisms. Second, I show how pre-interpreted formalisms can be connected to data. For this purpose, I draw on the theory of relational databases to clarify what data collections and data schemas are. This leads to an explication of the notion of empirically interpreted formalisms. Third, I introduce the notion of an ontological conceptual schema in order to explain how empirically interpreted frameworks can be extended to ontologically interpreted frameworks.

James Weatherall (University of California, Irvine)
I will connect recent discussions of the (in)equivalence of different formulations of electromagnetism in philosophy of science with the large literature in physics on "electromagnetic duality", a special case of "S duality". I will argue that the electromagnetic duality indicates a sense in which the mathematical formalism of electromagnetism may be understood to be (non-trivially) equivalent to itself, by the lights of the criteria philosophers have introduced. But I will also argue that this simple example shows that a condition philosophers of science have taken to be necessary for theoretical equivalence is not realized by (all) dualities in physics.

Sebastian De Haro (University of Amsterdam), Jeremy Butterfield (University of Cambridge)
We have elsewhere advocated a schema for understanding dualities, both in string theory and other fields of physics. In this talk, we use it to address how duality relates to logical equivalence, intertranslatability, of theories. We argue that not all dualities lead to what we call physical equivalence. Indeed, physical equivalence can only obtain, under appropriate conditions, for 'internal interpretations'. These are interpretations that starts from what our schema calls the 'bare theory' i.e. what is common to the two dual theories, ignoring their specific structures.