The FraMEPhys project will host a workshop on Representation and Equivalence in Physics on Friday 24 February 2023, at the University of Birmingham’s Edgbaston campus in the Arts building, room 439. All are welcome and registration is not required. For queries, please contact m.t.hicks@bham.ac.uk .

**SPEAKERS**

Konner Childers (University of Birmingham)

Lorenzo Cocco (University of Geneva)

Neil Dewar (University of Cambridge)

Michael Townsen Hicks (University of Birmingham)

Niels Martens (Utrecht University)

**SCHEDULE**

*Friday 24 February*

10.00-11.00: Michael Townsen Hicks

Subsystems, Equivalence, and Representation

11.00-12.00: Konner Childers

Duality as Categorical Equivalence

12:00-1:30 Lunch

1:30-2:30: Lorenzo Cocco

Formal Equivalence Is Theoretical Equivalence

2:30-3:30 Niels Martens

Constants of Nature & Theoretical Equivalence

3:30-4:00 Coffee

4:00-5:00 Neil Dewar

Equivalence and Convention

**ABSTRACTS**

Konner Childers

Duality as Categorical Equivalence

It is well known among physicists that many distinct physical theories are equivalent, in that the state space of one can be formally mapped to the other (and vice versa). Yet this introduces a number of problems: what are the formal and conceptual criteria for theoretical equivalence? In other words, when do two distinct yet interchangeable mathematical structures represent the same physical system? To complicate things further, theories can be dual to another theory, sometimes as a feature of holography. Duality is a special yet notably hard-to-define relationship. Although similar to theoretical equivalence, it remains unclear whether dual theories are another case of equivalence or stand as a unique type of theory relation. Indeed, “the complete physical meaning of the duality symmetry is still not clear, but a lot of work has been dedicated in recent years to understand the implications of this type of symmetry” (Alvarez- Gaume et al, “Duality in Quantum Field Theory and String Theory,” CERN). The goal of this talk is to argue the following: at least some dual theories in physics qualify as theoretically equivalent—specifically, they satisfy categorical equivalence uniquely. Moreover, we can see this in a few examples (AdS/CFT, electromagnetic duality, and bosonization) if time permits.

Lorenzo Cocco

Formal Equivalence Is Theoretical Equivalence

Theoretical equivalence between physical theories has been studied in recent years using tools from mathematical logic and category theory. The presupposition of all of this work is that the existence of a suitable mapping or a certain form of intertranslatability is sufficient to ensure a strong identity of physical content. This view is known to its detractors as “formalism” or “quotientism”. The purpose of this talk is to give a systematic defense of formalism. I will give an argument that is roughly similar to some versions of the model-theoretic argument of Hilary Putnam. I will also consider recent objections in the philosophy of physics literature and argue that they are based on an inadequate/antiquated philosophy of language.

Neil Dewar

Equivalence and Convention

The goal of this talk is to analyse the role of convention in interpreting physical theories—and, in particular, how the distinction between the conventional and the non-conventional interacts with judgments of equivalence. We will begin with a discussion of what, if anything, distinguishes those statements of a theory that might be dubbed “conventions”. This will lead us to consider the conventions that are not themselves part of a theory’s content, but are instead applied to the theory in interpreting it. Finally, we will consider the idea that what conventions to adopt might, itself, be regarded as a matter of convention.

Michael Townsen Hicks

Subsystems, Equivalence, and Representation.

I will discuss the view that models of physical theories represent subsystems of the universe rather than the universe as the whole. I begin by explicating these two views about the representational capacity of models. I then present competing considerations in favour of each. Models of physical theories are typically used to represent subsystems of the universe; but they often have features (such as behavior at an infinite boundary) which only make sense if they represent the universe as a whole. I then discuss the specific case of symmetry-related models, which are typically taken to be equivalent. I argue that symmetry variant quantities can only have representational content if models represent subsystems. I then discuss how this view impacts the equivalence of symmetry-related models and our understanding of the relationship between models and their target systems.

Niels Martens

Constants of Nature & Theoretical Equivalence

Are two versions of Newtonian Gravity that have different Newton’s Constants the same theory or are they different theories? This question will be discussed in the context of the debate between realists and anti-realists about absolute Newtonian masses. The crucial issue in that debate is whether an active, uniform scaling of all the masses, ceteris paribus, leads to an empirical difference or not. Should the ceteris paribus clause include (that what is represented by) Newton’s Constant, or should Newton’s Constant be scaled along with the masses as it has non-zero mass dimension? I discuss the senses in which changing Newton’s Constant does and does not generate an inequivalent theory.