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تسجيل مستخدم جديدEquivalence and Duality in Electromagnetism
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تأليف
James Owen Weatherall
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In this paper I bring the recent philosophical literature on theoretical equivalence to bear on dualities in physics. Focusing on electromagnetic duality, which is a simple example of S-duality in string theory, I will show that the duality fits naturally into at least one framework for assessing equivalence---that of categorical equivalence---but that it fails to meet a necessary condition for equivalence on that account. The reason is that the duality does not preserve empirical content in the required sense; instead, it takes models to models with dual empirical content. I conclude by discussing how one might react to this.
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I review the philosophical literature on the question of when two physical theories are equivalent. This includes a discussion of empirical equivalence, which is often taken to be necessary, and sometimes taken to be sufficient, for theoretical equiv
alence; and interpretational equivalence, which is the idea that two theories are equivalent just in case they have the same interpretation. It also includes a discussion of several formal notions of equivalence that have been considered in the recent philosophical literature, including (generalized) definitional equivalence and categorical equivalence. The article concludes with a brief discussion of the relationship between equivalence and duality.
In recent years philosophers of science have explored categorical equivalence as a promising criterion for when two (physical) theories are equivalent. On the one hand, philosophers have presented several examples of theories whose relationships seem
to be clarified using these categorical methods. On the other hand, philosophers and logicians have studied the relationships, particularly in the first order case, between categorical equivalence and other notions of equivalence of theories, including definitional equivalence and generalized definitional (aka Morita) equivalence. In this article, I will express some skepticism about this approach, both on technical grounds and conceptual ones. I will argue that category structure (alone) likely does not capture the structure of a theory, and discuss some recent work in light of this claim.
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