Abstract
I formulate an account of theoretical equivalence for effective quantum field theories. To start, I propose the `Easy Ontology' approach to interpreting what effective theories say about the physical world. Then I show how the Easy Ontology approach can be used to articulate an account of theoretical equivalence. Finally, I discuss the relationship between this account of equivalence and accounts based on formal, mathematical structures. According to the Easy Ontology approach, for each energy level Λ and each effective theory ????Λ at that energy level, the physical propositions described by ????Λ are propositions about quantum fields, particles composed of quanta, physical interactions among fields and particles, transition amplitudes, correlation functions, structures, and so on, all of which interact at Λ. Some effective theories are formulated using terms that denote physical fields rather than physical particles; the contents of those theories include propositions that mention fields only. Other effective theories are formulated in terms that denote physical fields and physical particles both; the contents of those theories include propositions that mention fields and particles. There are further questions, of course, about which of these theories are true, which are more fundamental, which theories' mathematical expressions provide the most perspicuous representation of reality, and so on; and the Easy Ontology approach does not answer questions like these. But with regards to the question of what these theories actually say about the world, there is—according to the Easy Ontology approach—a very straightforward answer: what exists, according to these theories, is whatever these theories say exists. The Easy Ontology approach can be used to formulate an attractive account—call it the `Same Content' account—of theoretical equivalence among effective theories. According the Same Content account, effective theories ????1,Λ and ????2,Λ are equivalent just in case they describe exactly the same class of physical propositions. So ????1,Λ is equivalent to ????2,Λ just in case the physical propositions they describe—as given by the Easy Ontology approach—are the same. The Same Content account preserves certain basic insights of the literature on formal structures, formal symmetries, and theoretical equivalence. According to some effective theories, various formal, mathematical structures correspond to structures in the physical world. And the Same Content Account implies that for two such theories to be equivalent, those physical structures must be identical. But according to the Same Content account, there is more to theoretical equivalence than any one formal criterion captures. (In this way, Same Content respects both a view of equivalence discussed by North (2021) and a pluralist approach to equivalence discussed by Dewar (2019).) In fact, even isomorphism is not sufficient for equivalence: two effective theories may be mathematically isomorphic, and yet be non-equivalent, according to the Same Content account. (In this way, Same Content respects the view—a version of which is discussed by Bradley (this symposium)—that isomorphic theories may be physically distinct.) Theoretical equivalence is, ultimately, a matter of sameness of theoretical meaning; not (solely) a matter of formal correspondence.
