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Equivalence and Duality in Electromagnetism

Published online by Cambridge University Press:  01 January 2022

James Owen Weatherall
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Abstract

In this article 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 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.

Type
Physical Sciences
Information
Philosophy of Science , Volume 87 , Issue 5: PSA 2018 - Proceedings of the 2018 biennial meeting of the Philosophy of Science Association. Part II Symposia Papers , December 2020 , pp. 1172 - 1183
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

I am grateful to Seb de Haro, for organizing the session in which this article was presented, and to my cosymposiasts, Thomas Barrett, Seb de Haro, and Laurenz Hudetz, for a lively and interesting session. I am also grateful to Sean Carroll, Ben Feintzeig, Nick Huggett, and Sarita Rosenstock, for very helpful comments on the talk, and to Seb de Haro for detailed comments on a draft. This article was made possible in part through the support of grant 61048 from the John Templeton Foundation. The opinions expressed in this publication are those of the author and do not necessarily reflect the views of the John Templeton Foundation.

References

Alvarez, Enrique, Alvarez-Gaumé, Luis, and Lozano, Yolanda. 1995. “An Introduction to T-Duality in String Theory.” Nuclear Physics B 41(1–3): 1–20.Google Scholar
Alvarez-Gaumé, Luis, and Hassan, S. F.. 1997. “Introduction to S-Duality in N = 2 Supersymmetric Gauge Theories: A Pedagogical Review of the Work of Seiberg and Witten.” Fortschritte der Physik 45 (3–4): 159–236.CrossRefGoogle Scholar
Barrett, Thomas William. 2019. “Equivalent and Inequivalent Formulations of Classical Mechanics.” British Journal for Philosophy of Science 70 (4): 1167–99.CrossRefGoogle Scholar
Barrett, Thomas William, and Halvorson, Hans. 2016. “Morita Equivalence.” Review of Symbolic Logic 9 (3): 556–82.CrossRefGoogle Scholar
Butterfield, Jeremy. Forthcoming. “On Dualities and Equivalences between Physical Theories.” In Spacetime after Quantum Gravity, ed. Huggett, Nick and Wüthrich, Christian. Oxford: Oxford University Press.Google Scholar
Coffey, Kevin. 2014. “Theoretical Equivalence as Interpretive Equivalence.” British Journal for the Philosophy of Science 65 (4): 821–44.CrossRefGoogle Scholar
Dawid, Richard. 2017. “String Dualities and Empirical Equivalence.” Studies in History and Philosophy of Science B 59:21–29.CrossRefGoogle Scholar
De Haro, Sebastian. 2017. “Dualities and Emergent Gravity: Gauge/Gravity Duality.” Studies in History and Philosophy of Science B 59:109–25.Google Scholar
De Haro, Sebastian. Forthcoming. “Spacetime and Physical Equivalence.” In Spacetime after Quantum Gravity, ed. Huggett, Nick and Wüthrich, Christian. Oxford: Oxford University Press.Google Scholar
De Haro, Sebastian, and Butterfield, Jeremy. 2017. “A Schema for Duality, Illustrated by Bosonization.” In Foundations of Mathematics and Physics One Century after Hilbert, ed. Kouneiher, J., 305–76. Cham: Springer.Google Scholar
Dieks, Dennis, Dongen, Jeroen van, and Haro, Sebastian de. 2015. “Emergence in Holographic Scenarios for Gravity.” Studies in History and Philosophy of Science B 52:203–16.Google Scholar
Figueroa-O’Farrill, J. M. 1998. “Electromagnetic Duality for Children.” Unpublished manuscript, University of Edinburgh.Google Scholar
Frenkel, Edward. 2007. “Lectures on the Langlands Program and Conformal Field Theory.” In Frontiers in Number Theory, Physics, and Geometry II, ed. Cartier, P. et al., 387–533. Berlin: Springer.Google Scholar
Giveon, Amit, Porrati, Massimo, and Rabinovici, Eliezer. 1994. “Target Space Duality in String Theory.” Physics Reports 244 (2–3): 77–202.CrossRefGoogle Scholar
Glymour, Clark. 1970. “Theoretical Equivalence and Theoretical Realism.” In PSA 1970: Proceedings of the 1970 Biennial Meeting of the Philosophy of Science Association, 275–88. East Lansing, MI: Philosophy of Science Association.Google Scholar
Glymour, Clark. 1980. Theory and Evidence. Princeton, NJ: Princeton University Press.Google Scholar
Halvorson, Hans. 2012. “What Scientific Theories Could Not Be.” Philosophy of Science 79 (2): 183–206.CrossRefGoogle Scholar
Huggett, Nick. 2017. “Target Space ≠ Space.” Studies in History and Philosophy of Science B 59:81–88.CrossRefGoogle Scholar
Huggett, Nick, and Wüthrich, Christian. 2013. “Emergent Spacetime and Empirical (In)Coherence.” Studies in History and Philosophy of Science B 44 (3): 276–85.Google Scholar
Karch, Andreas, and Tong, David. 2016. “Particle-Vortex Duality from 3d Bosonization.” Physical Review X 6 (3): 031043.Google Scholar
Le Bihan, Baptiste, and Read, James. 2018. “Duality and Ontology.” Philosophy Compass 13 (12): e12555.Google Scholar
Leinster, Tom. 2014. Basic Category Theory. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Maldacena, Juan. 1999. “The Large-N Limit of Superconformal Field Theories and Supergravity.” International Journal of Theoretical Physics 38 (4): 1113–33.CrossRefGoogle Scholar
Matsubara, Keizo. 2013. “Realism, Underdetermination and String Theory Dualities.” Synthese 190 (3): 471–89.CrossRefGoogle Scholar
Montonen, Claus, and Olive, David. 1977. “Magnetic Monopoles as Gauge Particles?” Physics Letters B 72 (1): 117–20.Google Scholar
Nguyen, James. 2017. “Scientific Representation and Theoretical Equivalence.” Philosophy of Science 84 (5): 982–95.CrossRefGoogle Scholar
Polchinski, Joseph. 2017. “Dualities of Fields and Strings.” Studies in History and Philosophy of Science B 59:6–20.CrossRefGoogle Scholar
Read, James. 2016. “The Interpretation of String-Theoretic Dualities.” Foundations of Physics 46 (2): 209–35.CrossRefGoogle Scholar
Rickles, Dean. 2011. “A Philosopher Looks at String Dualities.” Studies in History and Philosophy of Modern Physics 42 (1): 54–67.CrossRefGoogle Scholar
Rickles, Dean. 2017. “Dual Theories: ‘Same but Different’ or ‘Different but Same’?” Studies in History and Philosophy of Science B 59:62–67.CrossRefGoogle Scholar
Rosenstock, Sarita. 2019. “Structure and Equivalence in Physical Theories.” PhD diss., University of California, Irvine.Google Scholar
Rosenstock, Sarita, Barrett, Thomas William, and Weatherall, James Owen. 2015. “On Einstein Algebras and Relativistic Spacetimes.” Studies in History and Philosophy of Science B 52:309–16.Google Scholar
Seiberg, Nathan, Senthil, T., Wang, Chong, and Witten, Edward. 2016. “A Duality Web in 2+ 1 Dimensions and Condensed Matter Physics.” Annals of Physics 374:395–433.CrossRefGoogle Scholar
Seiberg, Nathan, and Witten, Edward. 1994. “Electric-Magnetic Duality, Monopole Condensation, and Confinement in N = 2 Supersymmetric Yang-Mills Theory.” Nuclear Physics B 426(1): 19–52.CrossRefGoogle Scholar
Sklar, Lawrence. 1982. “Saving the Noumena.” Philosophical Topics 13 (1): 89–110.CrossRefGoogle Scholar
Weatherall, James Owen. 2016. “Are Newtonian Gravitation and Geometrized Newtonian Gravitation Theoretically Equivalent?” Erkenntnis 81 (5): 1073–91.CrossRefGoogle Scholar
Weatherall, James Owen. 2019. “Theoretical Equivalence in Physics.” Pts. 1 and 2. Philosophy Compass 14 (5): e12591, e12592.Google Scholar
Weatherall, James Owen. Forthcoming. “Why Not Categorical Equivalence?” In Hajnal Andréka and István Németi on Unity of Science: From Computing to Relativity Theory through Algebraic Logic, ed. Madarasz, Judit and Szekely, Gergely. Heidelberg: Springer.Google Scholar