Symmetry and conservation laws

MAR 01, 1964

Professor Wigner’s article is based on a paper presented on October 22, 1963, during a session on “The Nature of Matter” which was held as part of the program arranged in celebration of the one hundredth anniversary of the founding of the National Academy of Sciences. This and other papers presented on that occasion will be published in the Proceedings of the Academy’s centennial meeting.

DOI: 10.1063/1.3051467

Eugene P. Wigner

Symmetry and invariance considerations, and even conservation laws, played undoubtedly an important role in the thinking of the early physicists, such as Galileo and Newton, and probably even before then. However, these considerations were not thought to be particularly important and were articulated only rarely. Newton’s equations were not formulated in any special coordinate system and thus left all directions and all points in space equivalent. They were invariant under rotations and displacements, as we now say. The same applies to his gravitational law. There was little point in emphasizing this fact, and in conjuring up the possibility of laws of nature which show a lower symmetry. As to the conservation laws, the energy law was useful and was instinctively recognized in mechanics even before Galileo. The momentum and angular‐momentum conservation theorems in their full generality were not very useful even though, in the special case of central motion, they are one of Kepler’s laws. Most books on mechanics, written around the turn of the century and even later, do not mention the general theorem of the conservation of angular momentum. It must have been known quite generally because those dealing with the three‐body problem, where it is useful, write it down as a matter of course. However, people did not pay very much attention to it.

References

1. G. Hamel, in his Theoretische Mechanik (B. G. Teubner, Leipzig, 1912) mentions (page 130) Jordanus de Nemore (ca. 1300) as having recognized essential features of what we now call mechanical energy and Leonardo da Vinci as having postulated the impossibility of the Perpetuum Mobile.
2. F. Cajori’s History of Physics (Macmillan, New York, 1929) gives exactly half a line to it (page 108).
3. See, for instance, his semipopular booklet Relativitats‐theorie, Friedr, Vieweg uncl Sohn, Braunschweig, various editions, 1916–1956.
4. F. Engel, Ges. d. Wiss. Göttingen, 1916, p. 270,
also G. Hamel, Z. Math. Phys. 50, 1 (1904).
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also Y. Murai, Progr. Theoret. Phys. (Kyoto) 11, 441 (1954),
and more recently D. M. Greenberger, Ann. Phys. (N.Y.) 25, 290 (1963).https://doi.org/PTPKAV
6. R. Utiyama, Phys. Rev. 101, 1597 (1956),
also C. N. Yang and R. L. Mills, Phys. Rev. 96, 191 (1954).https://doi.org/PHRVAO , Phys. Rev.
7. H. Poincaré, Compt. Rend. 140, 1504 (1905),
Rend. Circ. Math. Palermo 21, 129 (1906).https://doi.org/COREAF
8. Thus Aristotle’s Physics postulated that motion necessarily required the continued operation of a cause. Hence, all bodies would come to an absolute rest if they were removed from the cause which imparts them a velocity, (Cf. e.g., A. C. Crombie’s Augustine to Galileo, Falcon Press, London, 1952, page 82 or 244). This cannot be true for coordinate systems moving with respect to each other. The coordinate systems with respect to which it is true then have a preferred state of motion.
9. E. Mach, The Science of Mechanics, various editions, Open Court Publishing Company, Chicago, Chapter III, Section 3.
10. V. Fock, The Theory of Space, Time and Gravitation, Pergamon, New York, 1959.
11. For the strong interaction, cf. Y. Ne’eman, Nucl. Phys. 26, 222 (1961)
and M. Gell‐Mann, Phys. Rev. 125, 1067 (1962). https://doi.org/NUPHA7
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also S. S. Gershstein and A. B. Zeldovitch, Zh. Eksperim. i Teor. Fiz. 29, 698 (1955)
[Soviet Physics—JETP, 2, 576 (1956)].https://doi.org/ZETFA7
12. For the baryon conservation law and the strong interaction, this was suggested by the present writer, Proc. Am. Phil. Soc. 93, 521 (1949)
and Proc. Nat. Acad. Sci. 38, 449 (1952).
The baryon conservation law was first postulated by E. C. G. Stueckelberg, Helv. Phys. Acta 11, 299 (1938).https://doi.org/HPACAK
13. For the experimental verification of these and the other conservation laws, see G. Feinberg and M. Goldhaber, Proc. Nat. Acad. Sci. 45, 1301 (1959). https://doi.org/PNASA6
The conservation law for leptons was proposed by G. Marx in Acta Phys. Hung. 3, 55 (1953),
also A. B. Zeldovitch, Dokl. Akad. Nauk SSSR 91, 1317 (1953)
and E. J. Konopinski and H. M. Mahmoud, Phys. Rev. 92, 1045 (1953).https://doi.org/DANKAS
14. For the baryon conservation and strong interaction, this was emphatically pointed out in a very interesting article by J. J. Sakurai, Ann. Phys. (N.Y.) 11, 1 (1960). https://doi.org/APNYA6
Concerning the conservation of lepton number, see G. Marx, Z. Naturfors. 9a, 1051 (1954).
15. M. L. Goldberger, Phys. Rev. 99, 979 (1955),
also M. L. Goldberger and K. M. Watson, Collision Theory, Wiley, New York, 1964, Chapter 10.