On Dualities and Equivalences Between Physical Theories

TL;DR

This paper explores the distinction between dualities and equivalences in physical theories, emphasizing that dual theories can disagree about the world despite being considered the same in physics, impacting how we understand theoretical equivalence.

Contribution

It clarifies the conceptual difference between dualities and equivalences in physics, highlighting that dual theories may not be logically or philosophically equivalent, with examples from string theory.

Findings

Dual theories can disagree about the world.

Duality does not imply logical equivalence.

Implications for understanding theoretical equivalence.

Abstract

The main aim of this paper is to make a remark about the relation between (i) dualities between theories, as `duality' is understood in physics and (ii) equivalence of theories, as `equivalence' is understood in logic and philosophy. The remark is that in physics, two theories can be dual, and accordingly get called `the same theory', though we interpret them as disagreeing---so that they are certainly not equivalent, as `equivalent' is normally understood. So the remark is simple: but, I shall argue, worth stressing---since often neglected. My argument for this is based on the account of duality developed by De Haro: which is illustrated here with several examples, from both elementary physics and string theory. Thus I argue that in some examples, including in string theory, two dual theories disagree in their claims about the world. I also spell out how this remark implies a limitation of proposals (both traditional and recent) to understand theoretical equivalence as either logical equivalence or a weakening of it.