The emergence of the principle of symmetry in physics

Historical Studies in the Physical and Biological Sciences

Volumn 35, Issue 1, 2004, Pages 35-65

  Katzir, Shaul ^a  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

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[No Author keywords available]

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EID: 13844280256     PISSN: 08909997     EISSN: None     Source Type: Journal    
DOI: 10.1525/hsps.2004.35.1.35     Document Type: Review

References (141)

1. Luigi A. Radicati, "Remarks on the early developments of the notion of symmetry breaking," in Manuel G. Doncel et al., eds., Symmetries in physics (1600-1980): Proceedings of the first international meeting on the history of scientific ideas (Barcelona, 1987), 195-206, on 197-198; Yoichiro Nambu,"Symmetry breaking, chiral dynamics, and fermion masses," Nuclear physics A, 638 (1998), 35c-44c; P.G. de Gennes, "Pierre Curie et le rôle de la symétrie dans les lois physiques," in Nino Boccara, ed., Symmetries and broken symmetries in condensed matter physics (Paris, 1981), 1-9, on 2.
2. Luigi A. Radicati, "Remarks on the early developments of the notion of symmetry breaking," in Manuel G. Doncel et al., eds., Symmetries in physics (1600-1980): Proceedings of the first international meeting on the history of scientific ideas (Barcelona, 1987), 195-206, on 197-198; Yoichiro Nambu,"Symmetry breaking, chiral dynamics, and fermion masses," Nuclear physics A, 638 (1998), 35c-44c; P.G. de Gennes, "Pierre Curie et le rôle de la symétrie dans les lois physiques," in Nino Boccara, ed., Symmetries and broken symmetries in condensed matter physics (Paris, 1981), 1-9, on 2.
3. Luigi A. Radicati, "Remarks on the early developments of the notion of symmetry breaking," in Manuel G. Doncel et al., eds., Symmetries in physics (1600-1980): Proceedings of the first international meeting on the history of scientific ideas (Barcelona, 1987), 195-206, on 197-198; Yoichiro Nambu,"Symmetry breaking, chiral dynamics, and fermion masses," Nuclear physics A, 638 (1998), 35c-44c; P.G. de Gennes, "Pierre Curie et le rôle de la symétrie dans les lois physiques," in Nino Boccara, ed., Symmetries and broken symmetries in condensed matter physics (Paris, 1981), 1-9, on 2.
4. Pierre Curie, "Sur la symétrie dans les phénoménes physiques, symétrie d'un champ électrique et d'un champ magnétique," OPC, 118-141, on 127-128. Although Curie's two propositions are logically equivalent, he expressed the same principle in two rules probably because they were to be applied in two different directions (learning from the effects about the causes and vice versa). The formulation also allowed him to emphasize that causes and effects are not reciprocal.
5. Whether Curie's principle is rigorously valid is still under dispute since the phenomena of spontaneous symmetry breaking, so central in physics today, contradict it by providing effects with lower symmetry than their causes. However symmetry breaking may only expose hidden (weak or temporal) asymmetry in the causes and may not be spontaneous but are caused by thermal or quantum fluctuations, or microscopic asymmetry. Another issue is the application of Curie's deterministic principle to quantum mechanics, although it often makes use of rules of symmetry. See Jenann Ismael, "Curie's principle," Synthese, 110 (1997), 167-190; Laune M. Brown and Tian Yu Cao, "Spontaneous breakdown of symmetry: Its rediscovery and integration into quantum field theory," HSPS, 21:2 (1991), 211-235, on 215.
6. Whether Curie's principle is rigorously valid is still under dispute since the phenomena of spontaneous symmetry breaking, so central in physics today, contradict it by providing effects with lower symmetry than their causes. However symmetry breaking may only expose hidden (weak or temporal) asymmetry in the causes and may not be spontaneous but are caused by thermal or quantum fluctuations, or microscopic asymmetry. Another issue is the application of Curie's deterministic principle to quantum mechanics, although it often makes use of rules of symmetry. See Jenann Ismael, "Curie's principle," Synthese, 110 (1997), 167-190; Laune M. Brown and Tian Yu Cao, "Spontaneous breakdown of symmetry: Its rediscovery and integration into quantum field theory," HSPS, 21:2 (1991), 211-235, on 215.
7. Curie (ref. 2), 119.
8. Radicati (ref. 1), 197.
9. These traditions employed mostly continuous symmetry, while the symmetries of the phenomena under study were mostly discrete. H.A. Kastrup, "The contributions of Emmy Noether, Felix Klein, and Sophus Lie to the modern concept of symmetries in physical systems," Doncel et al (ref. 1), 113-163; I.M. Yaglom, Felix Klein and Sophus Lie: Evolution of the idea of symmetry in the nineteenth century, transl. Sergei Sossinsky, eds., Hardy Grant and Abe Shenitzer (Boston, 1988).
10. These traditions employed mostly continuous symmetry, while the symmetries of the phenomena under study were mostly discrete. H.A. Kastrup, "The contributions of Emmy Noether, Felix Klein, and Sophus Lie to the modern concept of symmetries in physical systems," Doncel et al (ref. 1), 113-163; I.M. Yaglom, Felix Klein and Sophus Lie: Evolution of the idea of symmetry in the nineteenth century, transl. Sergei Sossinsky, eds., Hardy Grant and Abe Shenitzer (Boston, 1988).
11. Cf. Olivier Darrigol, "Between hydrodynamics and elasticity theory: The first five births of the Navier-Stokes equation," Archive for history of the exact sciences, 56 (2002), 95-150.
12. Ismael (ref. 3).
13. Isaac Todhunter and Karl Pearson, A history of the theory of elasticity and of the strength of materials from Galilei to the present time (2 vols., Cambridge, 1893), 2:2, 305.
14. Curie (ref. 2), 118, 119.
15. Seymour Harold Mauskopf, Crystals and compounds: Molecular-structure and composition in 19th-century French science (Philadelphia, 1976).
16. Kathryn M. Olesko, Physics as a calling: Discipline and practice in the Königsberg seminar for physics (Ithaca, 1991)
17. Curie (ref. 2), 139.
18. Curie also applied in his study techniques and concepts from the mathematical theory of crystals, about whose developments he was also well-informed. In 1884, Curie contributed to the abstract mathematical study and classification of symmetry operations in crystals; Pierre Curie, "Sur les questions d'ordre: répétitions," OPC, 56-77. Among other concepts he employed that of symmetry groups. Erhard Scholz, Symmetrie, Gruppe, Dualität: Zur Beziehung zwischen theoretischer Mathematik und Anwendungen in Kristallographie und Baustatik des 19. Jahrhunderts (Basel, 1989), 13-153.
19. Curie also applied in his study techniques and concepts from the mathematical theory of crystals, about whose developments he was also well-informed. In 1884, Curie contributed to the abstract mathematical study and classification of symmetry operations in crystals; Pierre Curie, "Sur les questions d'ordre: répétitions," OPC, 56-77. Among other concepts he employed that of symmetry groups. Erhard Scholz, Symmetrie, Gruppe, Dualität: Zur Beziehung zwischen theoretischer Mathematik und Anwendungen in Kristallographie und Baustatik des 19. Jahrhunderts (Basel, 1989), 13-153.
20. Scholz (ref. 14), 24-28; on pyroelectricity, René-Just Haüy, Trait de minéralogie (Paris, 1801), 3, 44-58.
21. Scholz (ref. 14), 24-28; on pyroelectricity, René-Just Haüy, Trait de minéralogie (Paris, 1801), 3, 44-58.
22. See also Mauskopf (ref. 11).
23. Kenneth L. Caneva, "Physics and Naturphilosophie: A reconnaissance," History of science, 35 (1997), 35-106; Scholz (ref. 14) 29-32.
24. Kenneth L. Caneva, "Physics and Naturphilosophie: A reconnaissance," History of science, 35 (1997), 35-106; Scholz (ref. 14) 29-32.
25. Scholz (ref. 14), 32-65.
26. According to Delafosse, this is the law that "determines the number and general inclination of the planes that compose the form of a crystalline system." Gabriel Delafosse, "Recherches sur la cristallisation considérée sous les rapports physiques et mathématiques," Mémoires présentés par divers savants à l'Académie royale des sciences, 8 (1843), 641-690, on 644.
27. Auguste Bravais later developed Delafosse's ideas about molecular structure in an influential crystallographic theory. Auguste Bravais, "Etudes cristallographiques," Journal de l'école polytechnique, 20 (1851), 101-278.
28. Gabriel Delafosse, "Recherches relatives à la cristallisation, considérée sous les rapports physiques et mathématiques, 1re partie. Sur la structure des cristaux, et sur les phénomènes physiques qui en dépendent," Académie des Sciences, Paris, Comptes rendus, 11 (1840), 394-400; Delafosse (ref. 19), 644-647, 665-670, 674-676, quote on 642. The first article, a report of the second, was submitted with it.
29. Gabriel Delafosse, "Recherches relatives à la cristallisation, considérée sous les rapports physiques et mathématiques, 1re partie. Sur la structure des cristaux, et sur les phénomènes physiques qui en dépendent," Académie des Sciences, Paris, Comptes rendus, 11 (1840), 394-400; Delafosse (ref. 19), 644-647, 665-670, 674-676, quote on 642. The first article, a report of the second, was submitted with it.
30. François Sulpice Beudant, "Rapport sur le Mémoire cristallographique de M. Delafosse," Comptes rendus, 12 (1841), 205-210. The committee, which included Brongniart and Cordier, reported that the critique and notions of Delafosse were not new. His contribution was the systematic treatment (p. 210).
31. Henri Senarmont, "Sur la conductibilité des substances cristallisées pour la chaleur," ACP, 21 (1847), 457-470, 22 (1847), 179-211,esp.208-211; "Mémoire sur la conductibilité superficielle des corps cristallisés pour l'électricité de tension," ACP, 28 (1850), 257-278.
32. Henri Senarmont, "Sur la conductibilité des substances cristallisées pour la chaleur," ACP, 21 (1847), 457-470, 22 (1847), 179-211,esp.208-211; "Mémoire sur la conductibilité superficielle des corps cristallisés pour l'électricité de tension," ACP, 28 (1850), 257-278.
33. Henri Senarmont, "Sur la conductibilité des substances cristallisées pour la chaleur," ACP, 21 (1847), 457-470, 22 (1847), 179-211,esp.208-211; "Mémoire sur la conductibilité superficielle des corps cristallisés pour l'électricité de tension," ACP, 28 (1850), 257-278.
34. The quotation is given as a question in ACP, 21 (1847), 470, and an affirmative answer in ACP, 22 (1847), 179-211.
35. The quotation is given as a question in ACP, 21 (1847), 470, and an affirmative answer in ACP, 22 (1847), 179-211.
36. Senarmont, "Électricité" (ref. 23), 277-278.
37. Albert-Auguste de Lapparent, "Henri Hureau de Senarmont (1808-1862)," in Ecole polytechnique,Livre du centenaire (Paris, 1897), 1,320 ff. (electronic version www.annales.org/archives/x/senarmont.html). Walter Fischer, "Sénarmont, Henri Hureau de," DSB, 12, 303-306.
38. Albert-Auguste de Lapparent, "Henri Hureau de Senarmont (1808-1862)," in Ecole polytechnique,Livre du centenaire (Paris, 1897), 1,320 ff. (electronic version www.annales.org/archives/x/senarmont.html). Walter Fischer, "Sénarmont, Henri Hureau de," DSB, 12, 303-306.
39. Wiedemann related electric conductivity to crystal structure through axes, not symmetry; like Senarmont he pointed out the agreement among optic, electric and thermal properties of crystals and their origin in "the form and constitution of bodies." Gustav Wiedemann,"Ueber das elektrische Verhalten krystallisirter Körper," APC, 76 (1849), 404-412.
40. A.J. Ångström, "Ueber die Molecular-Constanten der monoklinoëdrischen Krystalle," APC, 86 (1852), 206-237 (originally published in Swedish in 1850);
41. Carl Pape,"Die thermischen und chemischen Axen im 2 + 1 gliedrigen Gyps und im 1 + 1 gliedrigen Kupfervitriol," APC, 135 (1868), 1-29, on 1.
42. Todhunter and Pearson (ref. 9), 2:2, 29-30, 305, and 2:1, 472-475 (on Ångström).
43. Louis Pasteur, "Recherches sur la dissymëtrie moléculaire des produits organiques. naturels," OLP, 1, 314-344, quotes on 322 and 324.
44. Pierre Curie, "Notice sur les travaux scientifiques" (1902), 11 (in the archives of the Académie des Sciences, Paris). I thank Loïc Barbo for a copy of this "Notice."
45. Gerald, L. Geison and James A. Secord, "Pasteur and the process of discovery: The case of optical isomerism," Isis, 79 (1988), 7-36.
46. Louis Pasteur, "Mémoire sur la relation qui peut exister entre la forme cristalline et la composition chimique, et sur la cause de la polarisation rotatoire," OLP, 1, 61-64.
47. Louis Pasteur, "Nouvelles recherches sur les relations qui peuvent exister entre la forme cristalline, la composition chimique et le phénomène de la polarisation rotatoire," OLP, 1, 125-154, on 153-154.
48. Louis Pasteur, "Isomorphisme entre les corps isomères, les uns actifs, les autres inactifs sur la lumière polarisée," OLP, 1, 284-288; Gerald. L. Geison, The private science of Louis Pasteur (Princeton, NJ, 1995), 90-109.
49. Louis Pasteur, "Isomorphisme entre les corps isomères, les uns actifs, les autres inactifs sur la lumière polarisée," OLP, 1, 284-288; Gerald. L. Geison, The private science of Louis Pasteur (Princeton, NJ, 1995), 90-109.
50. Louis Pasteur, "Mémoire sur la fermentation appelée lactique," OLP, 2, 3-13, on 3-4; Geison (ref. 35), 90-109. Geison suggests that Pasteur had been committed to the connection between optical activity and life from the early 1850s.
51. Louis Pasteur, "Mémoire sur la fermentation appelée lactique," OLP, 2, 3-13, on 3-4; Geison (ref. 35), 90-109. Geison suggests that Pasteur had been committed to the connection between optical activity and life from the early 1850s.
52. Pasteur (ref. 30), esp. 329-333, 341-342.
53. Jean-Marie Duhamel,"Sur les équations générales de la propagation de la chaleur dans les corps solides dont la conductibilité n'est pas la même dans tous les sens," Journal de l'École polytechnique, 21 (1832), 356-399, and "Mémoire sur la propagation de la chaleur dans les cristaux," ibid., 32 (1848), 155-188.
54. Jean-Marie Duhamel,"Sur les équations générales de la propagation de la chaleur dans les corps solides dont la conductibilité n'est pas la même dans tous les sens," Journal de l'École polytechnique, 21 (1832), 356-399, and "Mémoire sur la propagation de la chaleur dans les cristaux," ibid., 32 (1848), 155-188.
55. Stokes asserted that his theory was independent of the nature of heat. George G. Stokes, "On the conduction of heat in crystals," Cambridge and Dublin mathematical journal, 6 (1851), 213-238, 221 (quote), 237-238.
56. Gabriel Lamé, Leçons sur la théorie analytique de la chaleur (Paris, 1861), 50.
57. The same was true for William John Macquorn Rankine's employment of symmetry in a, study of elasticity in crystals five years earlier. Rankine's leading concept, "axes of elasticity," signified "all directions with respect to which certain kinds of elastic forces are symmetrical; or speaking algebraically directions for which certain functions of the coefficients of elasticity are null or infinite" (emphasis added). Rankine assumed that different phenomena in the same crystal may be subject to different kinds of symmetry. Although he linked symmetry to mathematical equalities, he did not refer to Neumann's method of the equality of magnitudes in symmetric positions. He seldom applied considerations of symmetry; when he did (as in the case of "Hexagonal symmetry"), he presented his conclusions as self-evident without mathematical elaboration. He usually reasoned about symmetry from the properties of the elastic constants rather than vice versa. William John Macquorn Rankine, "On axes of elasticity and crystalline forms," Royal Society of London, Philosophical transactions, 146 (1856), 261-285, on 261.
58. William Thomson, "On the dynamical theory of heat," Mathematical and physical papers (Cambridge, 1882), 1, 174-332, on 266-268, quotations below on 266,267. The part on pp. 232-291 was first published in 1854.
59. This is only one way by which ordinary matter can become crystallized. "[M]inute fragments of non-crystalline substances may be put together so as to constitute solids, which on a large scale possess the general characteristic of homogeneous crystalline substances; and such bodies may be said to possess the crystalline characteristic by structure," ibid., p. 266.
60. Ibid., 53.
61. Olesko (ref. 12), 61.
62. Franz Neumann, "Theorie der doppelten Strahlenbrechung, abgeleitet aus den Gleichungen der Mechanik," APC, 25 (1832), 418-454, on 423-425.
63. Franz E. Neumann, "Ueber das Elasticitätsmaass krystallinscher Substanzen der homoëdrischen Abtheilung," APC, 31 (1834), 177-192. Neumann classified crystals by "order of symmetry" (i.e., the number of identical parts around an axis). His term viergliedrigen Classe (etc.) and his reference to crystal axes resembles Hessel's term p-gliedrigen Axe. This suggests an influence of Hessel on Neumann despite Scholz's claim that the former had meager influence on later mathematical studies of crystal structure (Scholz (ref. 14), 62), As mentioned, Neumann had introduced axes as characteristics of crystals in 1823.
64. Woldemar Voigt, "L'état actuel de nos connaissances sur l'élasticité des cristaux," in C.D. Guillaume and L. Poincaré, eds., Rapports présentés au congrès international de physique (Paris, 1900), 7, 277-318, on 308-309.
65. Mauskopf (ref. 11), 63.
66. Olesko (ref. 12), 63, 33-33 and 61-64, 81-82;
67. Christa Jungnickel and Russell McCormmach, Intellectual mastery of nature: Theoretical physics from Ohm to Einstein (2 vols., Chicago, 1986) 1, 84.
68. Moritz L. Frankenheim, Die Lehre von der Cohäsion, umfassend die Elasticität der Gase, die Elasticität und Coharenz der flüssigen und festen Körper und die Krystallkunde (Breslau,1835), 285-296, on 292 ("Unter den physischen Eigenschaften der Krystalle nimmt die Structur der ersten Rang ein.").
69. Ibid.; Scholz (ref. 14), 67. Scholz writes "that [for Frankenheim] the symmetry determines the outer form as well as the optic and the electric properties of the crystal;" but according to Frankenheim (ref. 51, 287), the form is known from the symmetry. In discussing physical properties, however, he did not mention symmetry, only structure (pp. 293-294).
70. Ibid.; Scholz (ref. 14), 67. Scholz writes "that [for Frankenheim] the symmetry determines the outer form as well as the optic and the electric properties of the crystal;" but according to Frankenheim (ref. 51, 287), the form is known from the symmetry. In discussing physical properties, however, he did not mention symmetry, only structure (pp. 293-294).
71. Ibid.; Scholz (ref. 14), 67. Scholz writes "that [for Frankenheim] the symmetry determines the outer form as well as the optic and the electric properties of the crystal;" but according to Frankenheim (ref. 51, 287), the form is known from the symmetry. In discussing physical properties, however, he did not mention symmetry, only structure (pp. 293-294).
72. Although Stocks did carry out experimental research, at least until 1853 it was secondary to his mathematical work. E.M. Parkinson, "Stokes, George Gabriel," DSB, 13, 74-79.
73. Olesko (ref. 12).
74. Franz Neumann, "Elasticität krystallinischer Stoffe," Vorlesungen über die Theorie der Elasticität der festen Körper und des Lichtäthers gehalten an der Universität Königsberg, ed. Oskar Emil Meyer (Leipzig, 1885), 164-202. This chapter, which includes the consideration of symmetry, was taken from Voigt's notes for a course of 1873/4.
75. Experimental evidence favoring the "multi-constant" assumption accumulated in the 1840s and 1850s, notably in experiments by Gustav Kirchhoff (1859). Neumann's employment of 36 independent constants was uncommon; most "multi-constant" theorists assumed 21 constants against the "rari-constant" hypothesis of 15, Augustus E.H. Love, A treatise on the mathematical theory of elasticity (Cambridge, 1892), 14-18. Instead of strains Neumann used explicit notation of differential displacement.
76. Gustav Kirchhoff, Vorlesungen Uber Mathematische Physik- Mechanik (Leipzig, 1876), 389-392. Kirchhoff took Neumann's courses between 1843 and 1847, which probably did not include explicit discussion of elastic properties based on planes of symmetry (see ref. 55). Kirchhoff probably delivered his own lectures in the summer of 1875, when he started teaching theoretical physics in Berlin. Jungnickel and McCormmach (ref. 50), 2, 31.
77. Like Kirchhoff Voigt employed the elastic potential function; Woldemar Voigt, "Allgemeine Formeln für die Bestimmung der Elasticitätsconstanten von Krystallen durch die Beobachtung der Biegung und Drillung," APC, 16 (1882), 273-321, 398-416, on 273-278.
78. Hermann Aron, "Ueber die Herleitung der Krystallsysteme aus der Theorie der Elasticität," APC, 20 (1883), 272-279; "Aron, Herman," in Walther Killy, ed., Deutsche Biographische Enzyklopädie (Darmstadt, 1995), 1, 194-195.
79. Hermann Aron, "Ueber die Herleitung der Krystallsysteme aus der Theorie der Elasticität," APC, 20 (1883), 272-279; "Aron, Herman," in Walther Killy, ed., Deutsche Biographische Enzyklopädie (Darmstadt, 1995), 1, 194-195.
80. Voigt (ref. 48), 309.
81. Bernhard Minnigerode, "Untersuchungen über die Symmetrieverhältnisse und die Elasticität der Krystalle," in Akademie der Wissenschaften, Göttingen, Nachrichten, 1884, 195-226, on 218. Minnigerode emphasized that he based himself on axes rather than planes of symmetry. Axes had been used by Voigt in 1882 but did not become central until later.
82. Bernhard Minnigerode, "Ueber Wärmeleitung in Krystallen," Neues Jahrbuch für Mineralogie, Geologie und Plaeontologie, 1 (1886), 1-13; Olesko (ref. 12), 271.
83. Bernhard Minnigerode, "Ueber Wärmeleitung in Krystallen," Neues Jahrbuch für Mineralogie, Geologie und Plaeontologie, 1 (1886), 1-13; Olesko (ref. 12), 271.
84. Woldemar Voigt, "Allgemeine Theorie der piezo- und pyroelectrischen Erscheinungen an Krystallen," in Akademie der Wissenschaften, Göttingen, Abhandlungen, 36 (1890), 1-99. Shaul Katzir, A history of piezoelectricity: The first two decades (Ph.D. dissertation, Tel Aviv University, 2001), 80-81.
85. Woldemar Voigt, "Allgemeine Theorie der piezo- und pyroelectrischen Erscheinungen an Krystallen," in Akademie der Wissenschaften, Göttingen, Abhandlungen, 36 (1890), 1-99. Shaul Katzir, A history of piezoelectricity: The first two decades (Ph.D. dissertation, Tel Aviv University, 2001), 80-81.
86. Pierre Curie and Jacques Curie, "Développement par compression de l'électricité polaire dans les cristaux hémièdres à faces inclinées," Société minéralogique de France, Bulletin, 3 (1880), 90-93.
87. Friedel, who made Ms major contributions in organic chemistry, studied with Pasteur in Strasbourg and later with Adolphe Wurtz in Paris, where he also studied mineralogy and was associated with Senarmont at the Ecole des mines. Georges Lemoine, "Notice sur Charles Friedel," Académie des sciences, Paris, Comptes rendus, 131 (1900), 205-210; "Friedel Charles," Encyclopaedia britannica, 1911 edn. (http://49.1911encyclopedia.org/ F/FR/ FRIEDEL_CHARLES.htm).
88. Friedel, who made Ms major contributions in organic chemistry, studied with Pasteur in Strasbourg and later with Adolphe Wurtz in Paris, where he also studied mineralogy and was associated with Senarmont at the Ecole des mines. Georges Lemoine, "Notice sur Charles Friedel," Académie des sciences, Paris, Comptes rendus, 131 (1900), 205-210; "Friedel Charles," Encyclopaedia britannica, 1911 edn. (http://49.1911encyclopedia.org/ F/FR/ FRIEDEL_CHARLES.htm).
89. Paul Langevin and Marie Curie claimed that symmetry considerations led Jacques and Pierre Curie to their discovery. For discussion of the discovery and its origins see Shaul Katzir, "The discovery of the piezoelectric effect," Archive for history of the exact sciences, 57 (2003), 61-91, esp. 77-81.
90. Jacques and Pierre Curie, "Phénomènes électriques des cristaux hémièdres à faces inclinées," Journal de physique théorique et appliquée, 1 (1882), 245-251, on 247.
91. Katzir (ref. 63), 73-79.
92. Ernest Mallard, Traité de Cristallographie géométrique et physique (2 vols., Paris, 1884), 2, 560-562, 571-573.
93. No one, not even Mallard, pointed out that symmetry rules out the induction of electric ity by uniform heating in crystals like quartz, a question hotly disputed in 1883. Instead of a general proof Jacques Curie and Friedel raised theoretical and experimental arguments to prove that particular classes cannot be pyroelectric. Voigt was the first to point out the consequence in a general way; Katzir (ref. 63), 54-60.
94. Following the publication of Voigt's theory, Pierre Curie suspended his plan to publish an analogous one; Marie Curie, "Préface," OPC, v-xxi, on xiv.
95. Voigt (ref. 63), 8. Three years earlier Voigt explained this rule: "Observations have shown that in all known physical properties (e.g., with respect to light and heat) crystals possess at least the symmetry of their form, and in most cases still higher symmetries. Therefore it seems appropriate to deduce from the crystalline form the most general law of symmetry of the crystalline substance, and to assume that the crystal displays the law including the symmetries in all physical properties." Woldemar Voigt,"Theoretische Studien über die Elasticitätverhältnisse der Krystalle," Akademie der Wissenschaften, Göttingen, Abhandlungen (1887), 52 pp., on 30.
96. Voigt (ref. 63), 8. Three years earlier Voigt explained this rule: "Observations have shown that in all known physical properties (e.g., with respect to light and heat) crystals possess at least the symmetry of their form, and in most cases still higher symmetries. Therefore it seems appropriate to deduce from the crystalline form the most general law of symmetry of the crystalline substance, and to assume that the crystal displays the law including the symmetries in all physical properties." Woldemar Voigt,"Theoretische Studien über die Elasticitätverhältnisse der Krystalle," Akademie der Wissenschaften, Göttingen, Abhandlungen (1887), 52 pp., on 30.
97. Curie (ref. 14), 56.
98. Pierre Curie, "Sur la symétrie," OPC, 78-113, on 112-113.
99. Curie (ref. 2).
100. Ibid., 119-135.
101. Loïc Barbo, Pierre Curie 1859-1906: Le rêve scientifique (Paris, 1999), 63-90, esp. 74
102. where Barbo used Curie's course notes from 1896.
103. The new symmetry group can be identical with one of the original groups.
104. Curie (ref. 2), 135, 141.
105. Curie admitted that his discussion is not conclusive and referred readers to Voigt's theory, ibid., 138-139.
106. Connections between magnetism, torsion, and pressure, which probably included phenomena later associated with Wiedemann's name, were observed during the first half of the 19th century. Guillame Wertheim's study of 1852 was probably the first to detect specifically the induction of current (as a way to observe changes in magnetic field) by torsion in an iron wire under magnetic influence. Guillaume Wertheim, "Sur des courants d'induction produits par la torsion,"Académie des sciences, Paris, Comptes rendus, 35 (1852), 702-704. From 1858 to 1862 Wiedemann studied the phenomena extensively, returning to them in 1886, following a renewed interest in them. Gustav Wiedemann, "Magnetische Untersuchungen," APC, 117 (1862), 193-217, and "Ueber die Beziehungen zwischen Magnetismus, Wärme und Torsion," APC, 103 (1858), 563-577.
107. Connections between magnetism, torsion, and pressure, which probably included phenomena later associated with Wiedemann's name, were observed during the first half of the 19th century. Guillame Wertheim's study of 1852 was probably the first to detect specifically the induction of current (as a way to observe changes in magnetic field) by torsion in an iron wire under magnetic influence. Guillaume Wertheim, "Sur des courants d'induction produits par la torsion,"Académie des sciences, Paris, Comptes rendus, 35 (1852), 702-704. From 1858 to 1862 Wiedemann studied the phenomena extensively, returning to them in 1886, following a renewed interest in them. Gustav Wiedemann, "Magnetische Untersuchungen," APC, 117 (1862), 193-217, and "Ueber die Beziehungen zwischen Magnetismus, Wärme und Torsion," APC, 103 (1858), 563-577.
108. Connections between magnetism, torsion, and pressure, which probably included phenomena later associated with Wiedemann's name, were observed during the first half of the 19th century. Guillame Wertheim's study of 1852 was probably the first to detect specifically the induction of current (as a way to observe changes in magnetic field) by torsion in an iron wire under magnetic influence. Guillaume Wertheim, "Sur des courants d'induction produits par la torsion,"Académie des sciences, Paris, Comptes rendus, 35 (1852), 702-704. From 1858 to 1862 Wiedemann studied the phenomena extensively, returning to them in 1886, following a renewed interest in them. Gustav Wiedemann, "Magnetische Untersuchungen," APC, 117 (1862), 193-217, and "Ueber die Beziehungen zwischen Magnetismus, Wärme und Torsion," APC, 103 (1858), 563-577.
109. Felix Auerbach, "Beziehungen des Magnetismus zu anderen Erscheinungen," in Adolph Winkelmann, ed., Handbuch der Physik (Breslau, 1895), 3:2, 233-296, on 240-244.
110. Wiedemann, "Magnetismus" (ref. 81) on 571-572; Auerbach (ref. 81). Wiedemann also pointed out the similarities between torsion and magnetism; Gustav Wiedemann, Die Lehre von der Elektricität (4 vols., Braunschweig, 1895), 3, 767-812. In 1862 and in later editions of his Lehre he also described clearly the relations observed in the laboratory between the current in the electromagnet and the wire and torsion; Wiedemann, "Magnetische" (ref. 81), 203-211. So close a description, free as possible from theoretical interpretation, proved helpful for scientists with different theoretical views, like Curie.
111. Wiedemann, "Magnetismus" (ref. 81) on 571-572; Auerbach (ref. 81). Wiedemann also pointed out the similarities between torsion and magnetism; Gustav Wiedemann, Die Lehre von der Elektricität (4 vols., Braunschweig, 1895), 3, 767-812. In 1862 and in later editions of his Lehre he also described clearly the relations observed in the laboratory between the current in the electromagnet and the wire and torsion; Wiedemann, "Magnetische" (ref. 81), 203-211. So close a description, free as possible from theoretical interpretation, proved helpful for scientists with different theoretical views, like Curie.
112. Auerbach (ref. 81) mentions only molecular explanations. For Wiedemann's claim, Gustav Wiedemann,"Magnetische Untersuchungen," APC, 27 (1886), 376-403, on 400.
113. Thomson (ref. 42), on 281 (note added by the author in 1882).
114. Curie (ref. 2), 137-138.
115. Maxwellian's confrontation with the effect helped change their concept of electric charge and current toward the corpuscular view of electricity. The discovery also modified corpuscular theories by showing that current does not consist of two equal streams of opposite charges going in reverse directions. Jed Buchwald, From Maxwell to microphysics: Aspects of electromagnetic theory in the last quarter of the nineteenth century (Chicago, 1985), 86-129, esp. 88-101.
116. Since asymmetry can only point to possibilities, this was not a problem for Curie. In contrast, fundamental identity between current and displacement current in Maxwell's theory made failure to detect the Hall effect in the latter case into a problem. Buchwald (ibid.), 93.
117. Pierre Curie, "Sur la possibilité d'existence de la conductibilité magnétique et du magnétisme libre," OPC, 142-144.
118. Emmy Noether showed the formal connection between symmetry and conservation twenty years later. Her theorem concerns spatial and temporal symmetries, very different from the symmetry of crystals and physical magnitudes discussed here.
119. Some physicists regarded conservation of electric charge as a principle, though others derived it from what they conceived to be more fundamental laws of electrodynamics. Gabriel J. Lippmann "Principe de la conservation de l'électricité ou second principe de la théorie des phénomènes électriques," ACP, 24 (1881), 145-177.
120. Even Curie did not call it a principle. The earliest such usage of symmetry in physical context I found is by Langevin who, in a lecture of 1904, made it and the two laws of thermodynamics to the trunk of the tree of physics; Bernadette Bensaude- Vincent, Langevin, 1872-1946: Science et vigilance (Paris, 1987), 51. On the other hand, Poincaré's discussions of the principles of physics are a good example of the neglect of considerations of symmetry; Henri Poincaré, La valeur de la science (Paris, 1970), 129-140 (text of 1904).
121. Even Curie did not call it a principle. The earliest such usage of symmetry in physical context I found is by Langevin who, in a lecture of 1904, made it and the two laws of thermodynamics to the trunk of the tree of physics; Bernadette Bensaude- Vincent, Langevin, 1872-1946: Science et vigilance (Paris, 1987), 51. On the other hand, Poincaré's discussions of the principles of physics are a good example of the neglect of considerations of symmetry; Henri Poincaré, La valeur de la science (Paris, 1970), 129-140 (text of 1904).
122. It might appear that physicists regarded the rules of symmetry merely as methodological tools not deserving much discussion. Curie himself compared them to dimensional analysis, which did not have the status of a principle; Curie (ref. 2), 119. Two arguments stand against this view: other principles of physics, like the law of least action, were no less methodological;.Curie's rules eventually were regarded as a principle.
123. Brown and Cao (ref. 3, 232) observe that the "macroscopic, in the sense of 'phenomenological' approach to spontaneous symmetry breaking has become standard in the Standard Model."
124. Shaul Katzir,"From explanation to description: Molecular and phenomenological theories of piezoelectricity," HSPS, 34:1 (2003), 69-94.
125. Still, the assumption that the phenomena are subject to symmetry carried the somewhat metaphysical premise that the structure of crystals (whether based on molecules, system of forces, or something else) determines its physical qualities.
126. Barbo (ref. 77), 116-118, 289-291. Pierre Curie presented his brother's results in Paris, since Jacques lived in Montpellier.
127. Olivier Darrigol, Electrodynamics from Ampère to Einstein (Oxford, 2000). In a paper on piezoelectricity in 1894 Voigt pointed out that Maxwell's theory (in Hertz's version) does not account for phenomena like polarization in dielectrics and ferromagnetism. Katzir (ref. 63), 187-191.
128. In the introduction to a course on electricity in 1904 Curie said that "we will be occu pied principally with theoretical questions...I will give a series of lectures on questions of symmetry of the phenomena studied in physics, on diverse modes of distribution of vectors in space with application to general theories of electric phenomena." Quoted in Barbo (ref. 77), 290-291.
129. Mach viewed the conservation of energy in this way. Hermann von Helmholte connected the principle in later writing to causality; Yehuda Elkana, The discovery of the conservation of energy (Cambridge, 1974), 169. In 1906 Paul Langevin referred to the principle of symmetry as "a new and fertile form of the principle of causality;" Paul Langevin, "Pierre Curie," Revue du mois, 2 (1906), 5-36, on 31. Ismael (ref. 3) shows that Curie's principle is necessary on the basis of deterministic (i.e., causal) laws of nature.
130. Mach viewed the conservation of energy in this way. Hermann von Helmholte connected the principle in later writing to causality; Yehuda Elkana, The discovery of the conservation of energy (Cambridge, 1974), 169. In 1906 Paul Langevin referred to the principle of symmetry as "a new and fertile form of the principle of causality;" Paul Langevin, "Pierre Curie," Revue du mois, 2 (1906), 5-36, on 31. Ismael (ref. 3) shows that Curie's principle is necessary on the basis of deterministic (i.e., causal) laws of nature.
131. The discovery of conservation of energy has not received a synthetic history that integrates the findings of the many detailed studies made since the publication of Thomas Kuhn's classical article in 1959, "Energy conservation as an example of simultaneous discovery," in Kuhn, The essential tension: Selected studies in scientific tradition and change (Chicago, 1977), 66-104.
132. The denial of perpetual motion is an example of a partial rule under the energy principle. The rule that symmetry must be conserved can be viewed as its counterpart.
133. E.g., The emergence of the work concept in French engineering science between 1800 and 1830 (Ivor Grattan-Guinness, "Work for the workers: Advances in engineering mechanics and instruction in France, 1800-1830," Annals of science, 41 (1984), 1-33), and modifications in the concept of symmetry.
134. The agreement between symmetry and inner form, and the mechanical conservation of vis-viva, are examples of rules that were later conceived as special cases of the more general principles. Elkana (ref. 99) has pointed out that the term generalization is misleading, since it assumes the general rule before the more restricted one. The problem does not appear with the term extension, which does not presume pre-existence of the general rule.
135. In this manner French engineers applied the conservation of vis-viva, action of gravity (later called potential energy), and work in mechanics in the 1820s; Grattan-Guinness (ref. 102), 20-21. In 1837 Green employed a potential function (equal to later potential energy) as a basis for a theory of elasticity. Augustus E.A. Love (ref. 56), 11-12. The principle of excluded perpetual motion, which is only one aspect of the conservation of energy, was applied to deduce relations between many phenomena, for example by Peter Mark Roget in 1828 ("against the contact theory of galvanism") by Michael Faraday in 1838 ("to conversions in general"); Kuhn (ref. 100), 69, 80.
136. In this manner French engineers applied the conservation of vis-viva, action of gravity (later called potential energy), and work in mechanics in the 1820s; Grattan-Guinness (ref. 102), 20-21. In 1837 Green employed a potential function (equal to later potential energy) as a basis for a theory of elasticity. Augustus E.A. Love (ref. 56), 11-12. The principle of excluded perpetual motion, which is only one aspect of the conservation of energy, was applied to deduce relations between many phenomena, for example by Peter Mark Roget in 1828 ("against the contact theory of galvanism") by Michael Faraday in 1838 ("to conversions in general"); Kuhn (ref. 100), 69, 80.
137. In this manner French engineers applied the conservation of vis-viva, action of gravity (later called potential energy), and work in mechanics in the 1820s; Grattan-Guinness (ref. 102), 20-21. In 1837 Green employed a potential function (equal to later potential energy) as a basis for a theory of elasticity. Augustus E.A. Love (ref. 56), 11-12. The principle of excluded perpetual motion, which is only one aspect of the conservation of energy, was applied to deduce relations between many phenomena, for example by Peter Mark Roget in 1828 ("against the contact theory of galvanism") by Michael Faraday in 1838 ("to conversions in general"); Kuhn (ref. 100), 69, 80.
138. In 1846, a year before the publication of his famous memoir, Helmholtz failed to notice that mechanical work might increase the heat in a body. Kuhn (ref. 100), 95 (note 68).
139. Helmholtz, who offered the first complete formulation of the rule, saw in the application of the principle a major object of his memoir on the conservation of "Kraft," Elkana (ref. 99), 158.
140. Since no extensive survey of the application of proto ideas about the conservation of energy outside mechanics had been carried out, the difference in the relation between formulation and application of the two principles might be a historiographical artifact.
141. Kuhn (ref. 100), Elkana (ref. 99). Recently Darrigol has emphasized the contribution of the development of conservative mechanics to the belief in the conservation of nature; Olivier Darrigol, "God, waterwheels, and molecules: Saint-Venant's anticipation of energy conservation," HSPS, 31:2 (2001), 285-353.