Hostname: page-component-7479d7b7d-68ccn Total loading time: 0 Render date: 2024-07-10T06:31:45.789Z Has data issue: false hasContentIssue false
  • English
  • Français

Unpacking “For Reasons of Symmetry”: Two Categories of Symmetry Arguments

Published online by Cambridge University Press:  01 January 2022

Giora Hon  and
Bernard R. Goldstein
Get access Rights & Permissions [Opens in a new window]

Abstract

Hermann Weyl succeeded in presenting a consistent overarching analysis that accounts for symmetry in (1) material artifacts, (2) natural phenomena, and (3) physical theories. Weyl showed that group theory is the underlying mathematical structure for symmetry in all three domains. But in this study Weyl did not include appeals to symmetry arguments which, for example, Einstein expressed as “for reasons of symmetry” (wegen der Symmetrie; aus Symmetriegründen). An argument typically takes the form of a set of premises and rules of inference that lead to a conclusion. Symmetry may enter an argument both in the premises and the rules of inference, and the resulting conclusion may also exhibit symmetrical properties. Taking our cue from Pierre Curie, we distinguish two categories of symmetry arguments, axiomatic and heuristic; they will be defined and then illustrated by historical cases.

Type
Research Article
Information
Philosophy of Science , Volume 73 , Issue 4 , October 2006 , pp. 419 - 439
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

‡

We are grateful to Michael Dickson, John Norton, and an anonymous referee for helpful suggestions.

References

Beck, Anna (1989), The Collected Papers of Albert Einstein. Vol. 2, The Swiss Years: Writings, 1900–1909. English translation. Peter Havas, consultant. Princeton, NJ: Princeton University Press.Google Scholar
Brading, Katherine, and Castellani, Elena (2003a), “Introduction,” in Brading and Castellani 2003b, 1–18.CrossRefGoogle Scholar
Brading, Katherine, and Castellani, Elena. 2007. “Symmetries and Invariances in Classical Physics,” in Jeremy Butterfield and John Earman (eds.), Handbook of the Philosophy of Science. Vol. 2, Philosophy of Physics. Amsterdam: Elsevier, 1331–1367.Google Scholar
Brading, Katherine, and Castellani, Elena, eds. (2003b), Symmetries in Physics: Philosophical Reflections. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Castellani, Elena (2003), “On the Meaning of Symmetry Breaking,” in Brading and Castellani 2003b, 321–334.CrossRefGoogle Scholar
Curie, Pierre ([1894/1908] 1984), “Sur la symétrie dans les phénomènes physiques, symétrie d’un champ électrique et d’un champ magnétique,” Journal de Physique 3: 393ff. Reprinted, with new pagination, in Oeuvres de Pierre Curie, publiées par les soins de la Société française de physique. Paris: Gauthier-Villars, 1908, 118–141 which, in turn, was reprinted, Paris and Montreux: Ed. des archives sociales, 1984.Google Scholar
Einstein, Albert (1905a), “Eine neue Bestimmung der Moleküldimensionen,” in Stachel et al. 1989, 184–202. For the English translation, see Beck 1989, 104–122.Google Scholar
Einstein, Albert (1905b), “Zur Elektrodynamik bewegter Körper,” Annalen der Physik 17:891–921.CrossRefGoogle Scholar
Föppl, August (1894), Einführung in die Maxwell’sche Theorie der Elektricität. Leipzig: Teubner.Google Scholar
Gell-Mann, Murray (1962a), “Symmetries of Baryons and Mesons,” Physical Review 125:1067–1084.CrossRefGoogle Scholar
Gell-Mann, Murray (1962b), “A Brief Comment, Predicting a New Particle, Ω−,” in a discussion following a paper by George A. Snow, “Strong Interactions of Strange Particles,” published in Proceedings of the International Conference on High-Energy Physics, Sponsored by the International Union of Pure and Applied Physics (IUPAP). Edited by J. Prentki. Geneva: CERN, 805. Reprinted in Murray Gell-Mann and Yuval Ne’eman (1964), The Eightfold Way. New York: Benjamin, 87.Google Scholar
Gross, David J. (1996), “The Role of Symmetry in Fundamental Physics,” Proceedings of the National Academy of Sciences 93:14256–14259.CrossRefGoogle ScholarPubMed
Hilbert, David (1904), “Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen (erste Mitteilung),” Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse aus dem Jahre 1904, 49–91.Google Scholar
Hon, Giora, and Goldstein, Bernard R. (2005a), “How Einstein Made Asymmetry Disappear: Symmetry and Relativity in 1905,” Archive for History of Exact Sciences 59:437–544.CrossRefGoogle Scholar
Hon, Giora, and Goldstein, Bernard R. (2005b), “Legendre’s Revolution (1794): The Definition of Symmetry in Solid Geometry,” Archive for History of Exact Sciences 59:107–155.CrossRefGoogle Scholar
Hon, Giora, and Goldstein, Bernard R. (2005c), “From Proportion to Balance: The Background to Symmetry in Science,” Studies in History and Philosophy of Science 36:1–21.CrossRefGoogle Scholar
Hon, Giora, and Goldstein, Bernard R. (2006), “Symmetry and Asymmetry in Electrodynamics from Rowland to Einstein,” Studies in History and Philosophy of Modern Physics 37:635–660.CrossRefGoogle Scholar
Huggard, E. M., trans. ([1951/1985] 1990), G. W. Leibniz: Theodicy: Essays on the Goodness of God, the Freedom of Man, and the Origin of Evil. Edited with an introduction by Austin Farrer. Chicago and La Salle, IL: Open Court.Google Scholar
Kirchhoff, Gustav ([1869] 1882), “Ueber die Bewegung eines Rotationskörpers in einer Flüssigkeit,” Borchardt’s Journal [Journal für die reine und angewandte Mathematik], 71. Reprinted in Gustav Kirchhoff (1882), Gesammelte Abhandlungen. Leipzig: Barth, 376–403.Google Scholar
Kirchhoff, Gustav (1883), Vorlesungen über mathematische Physik. Vol. 1, Mechanik. 3rd ed. Leipzig: Teubner.Google Scholar
Klein, Felix (1926), Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert. Part 1. Berlin: Springer.Google Scholar
Klein, Felix ([1926] 1979), Development of Mathematics in the 19th Century. In Lie Groups: History, Frontiers and Applications, Vol. 9. Translated by M. Ackerman. Brookline, Mass.: Math Sci Press.Google Scholar
Larmor, Joseph ([1884] 1929), “On Hydrokinetic Symmetry,” Quarterly Journal for Pure and Applied Mathematics 20:261–266. Reprinted in Joseph Larmor, Mathematical and Physical Papers. Cambridge: Cambridge University Press, 1:77–81.Google Scholar
Leibniz, Gottfried W. ([1710] 1720), Essais de Theodicée sur la bonté de Dieu, la liberté de l’homme et l’origine du mal. Amsterdam: Mortier. See Huggard [1951/1985] 1990.Google Scholar
Leibniz, Gottfried W. ([1714/1840] 1954), G. W. Leibniz: Principes de la nature et de la grâce fondés en raison et principes de la philosophie ou monadologie. Edited by André Robinet. Paris: Presses Universitaires de France. See Rescher 1991.Google Scholar
Lie, Sophus ([1895] 1989), “Influence de Galois sur le développement des mathématiques,” in Le centenaire de l’École Normale 1795–1895. Paris: Hachette. Reprinted in Évariste Galois: Oeuvres mathématiques. Supplement. Sceaux: Jacques Gabay.Google Scholar
Mach, Ernst ([1883/1912] 1988), Die Mechanik in ihrer Entwicklung historisch-kritisch dargestellt. Edited by Renate Wahsner and Horst-Heino von Borzeszkowski. 7th ed. Berlin: Akademie-Verlag.Google Scholar
Mach, Ernst ([1883/1893/1960] 1974), The Science of Mechanics: A Critical and Historical Account of Its Development. Translated by McCormack, Thomas J.. 6th ed. La Salle, IL: Open Court.Google Scholar
Minkowski, Hermann (1908), “Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegte Körpern,” Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse aus dem Jahre 1908, 53–111.Google Scholar
Ne’eman, Yuval (1964), “Introduction,” in Gell-Mann, Murray and Ne’eman, Yuval, The Eightfold Way. New York: Benjamin, 1–5.Google Scholar
Norton, John D. (2004), “Einstein’s Investigations of Galilean Covariant Electrodynamics prior to 1905,” Archive for History of Exact Sciences 59:45–105.CrossRefGoogle Scholar
Pais, Abraham (1982), “Subtle Is the Lord … ”: The Science and the Life of Albert Einstein. Oxford: Clarendon.Google Scholar
Poincaré, Henri ([1899] 1954), “La théorie de Lorentz et le phénomène de Zeeman,” L’Éclairage électrique, 19:5–15. Reprinted in Henri Poincaré (1954), Oeuvres de Henri Poincaré. Vol. 9. Paris: Gauthier-Villars, 442–460.Google Scholar
Rescher, Nicholas, trans. (1991), G. W. Leibniz’s Monadology: An Edition for Students (with commentary). London: Routledge.CrossRefGoogle Scholar
Rosen, Joe, and Copié, P. (1982), “On Symmetry in Physical Phenomena, Symmetry of an Electric Field and of a Magnetic Field,” a translation of Curie ([1894/1908], 1984), in Joe Rosen (1982), Symmetry in Physics: Selected Reprints. Stony Brook, NY: American Association of Physics Teachers, 17–25.Google Scholar
Stachel, John et al., eds. (1989), The Collected Papers of Albert Einstein. Vol. 2, The Swiss Years: Writings, 1900–1909. Princeton, NJ: Princeton University Press.Google Scholar
Thomson, William, and Tait, Peter G. (1867), Treatise on Natural Philosophy. Vol. 1. Oxford: Clarendon.Google Scholar
Thomson, William, and Tait, Peter G. (1883), Treatise on Natural Philosophy. Vol. 1, Part 2, new ed. Cambridge: Cambridge University Press.Google Scholar
Vahlen, Karl Theodor (1899), “Rationale Funktionen der Wurzeln: Symmetrische und Affektfunktionen,” in Wilhelm Franz Meyer, ed. (1898–1904), Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen. Vol. 1, Part 1, Arithmetik und Algebra. Leipzig: Teubner, 449–479.Google Scholar
van Fraassen, Bas C. (1989), Laws and Symmetry. Oxford: Clarendon.CrossRefGoogle Scholar
Voigt, Woldemar (1895), Kompendium der theoretischen Physik. Vol. 1, Mechanik starrer und nichtstarrer Körper: Wärmelehre. Leipzig: Veit.CrossRefGoogle Scholar
Voigt, Woldemar (1898), Die fundamentalen physikalischen Eigenschaften der Krystalle in elementarer Darstellung. Leipzig: Veit.Google Scholar
Waller, Ivar (1972), “Presentation Speech in Honour of Murray Gell-Mann: Nobel Prize in Physics, 1969,” in Nobel Lectures, Physics 1963–1970. Amsterdam: Elsevier, 295–298.Google Scholar
Weyl, Hermann (1928), Gruppentheorie und Quantenmechanik. Leipzig: S. Hirzel.Google Scholar
Weyl, Hermann ([1946] 1966), The Classical Groups: Their Invariants and Representations. Princeton, NJ: Princeton University Press.Google Scholar
Weyl, Hermann (1952), Symmetry. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Weyl, Hermann, and Helmer, Olaf ([1927] 1949), Philosophy of Mathematics and Natural Science. Revised and augmented English edition (by the author), based on a translation by Olaf Helmer. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Wick, Gerald L. (1972), Elementary Particles, Frontiers of High Energy Physics. London: Chapman.CrossRefGoogle Scholar