Dualities and Empirical Equivalence

(Philosophy of Science, )

n a series of recent papers, De Haro has presented an argument for the empirical equivalence of duals in physics (i.a. De Bianchi & Keifer (eds.), One Hundred Years of Gauge Theory _2020:91-106_; De Haro, Erkenn _2021_). Our aim in this paper is two-fold: a) we critically evaluate De Haro's argument and b) we introduce a new duality ("the classical double copy") into the philosophy literature. For De Haro, two theories are duals just in case that:

-- there exists an isomorphism between their sets of states; and

-- there exists an isomorphism between their set of quantities;

-- such that the values of the quantities, dynamics, and symmetries are preserved under the isomorphisms.

De Haro argues that any two theories related thus must be empirically equivalent.

After sketching De Haro's proposal, we introduce the classical double copy with the example of the Schwarzschild copy. The Schwarzschild copy is a duality between the Schwarzschild solution in general relativity and the Coulomb solution in electromagnetism such that the metric tensor in general relativity is ``copied'' to the Faraday tensor in electromagnetism. We argue that the Schwarzschild copy is a duality on De Haro's account by showing that the required isomorphisms exists. Thus, De Haro must hold that the duals of the Schwarzschild copy are empirically equivalent. But, physicists reject the claim that these duals are empirically equivalent. This raises a puzzle for De Haro. We argue that this puzzle can be solved by disambiguating the notion of empirical equivalence. We submit that the Schwarzschild copy is a case of "weak empirical equivalence" (WEE) but not of "strong empirical equivalence" (SEE) and that De Haro's construction guarantees only WEE. This, we suggest, explains away the contradictory judgements of the empirical equivalence of the double copy duals. We close by considering two options for De Haro but conclude that neither is attractive.

Chair: Daniela Schuster

Time: 18:10-18:40, 09 September 2021 (Thursday)

Location: SR 1.006

Remark: (Online Talk)

Kabir Bakshi

(University of Oxford, United Kingdom)

I am a first-year BPhil student at Oxford currently interested in philosophy of science and history of early philosophy of science. I currently like vanilla ice-cream and ultimate frisbee.

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