Events, Laws of Nature, and Invariance Principles

  • E. P. Wigner
Part of the The Scientific Papers book series (WIGNER, volume A / 3)


It is a great and unexpected honor to have the opportunity to speak here today. Six years ago, Yang and Lee spoke here, reviewing symmetry principles in general and their discovery of the violation of the parity principle in particular’. There is little point in repeating what they said, on the history of the invariance principles, or on my own contribution to these which they, naturally, exaggerated. What.I would like to discuss instead is the general role of symmetry and invariance principles in physics, both modem and classical. More precisely, I would like to discuss the relation between three categories which play a fundamental role in all natural sciences: events, which are the raw materials for the second category, the laws of nature, and symmetry principles for which I would like to support the thesis that the laws of nature form the raw material.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chen Ning Yang, The law of parity conservation and other symmetry laws of physics; Tsung Dao Lee, Weak interactions and nonconservation of parity, Nobel Lectures, Physics 1942–1962,Elsevier, Amsterdam, 1964, pp. 393–403 and pp. 406–418.Google Scholar
  2. 2.
    See, for instance, A. C. Crombie, Augustine to Galileo,Falcon Press, London, 1952, pp. 316 ff. The growth of the understanding of the realm of the explainable, from the end of the 13th century on, can be traced through almost every chapter of this book.Google Scholar
  3. 3.
    C.F. v. Weizsäcker, Z. Astrophys.,22 (1944) 319; S. Chandrasekhar, Rev. Mod. Phys., 18 (1946) 94.Google Scholar
  4. 4.
    An interesting and well understood case is that of « focussing collisions » in which neutrons, having velocities which are rather high but with random orientation, are converted into lower velocity neutrons but with preferential directions of motion. See R. H. Silsbee, J. Appl.Phys.,28 (1957) 1246; Chr.Lehmann and G.Leibfried, Z. Physik,172 (1963) 465.Google Scholar
  5. 5.
    See, for instance, the section What is the State Vector in the writer’s article, Am. J. Phys.,31 (1963) 6.Google Scholar
  6. 6.
    The possibility of an invariance principle in which velocities are replaced by positions, and conversely, was studied by M. Born, Nature,141 (1938) 327; Proc.Roy. Soc. (London), Ser.A, 165 (1938) 291, 166 ( 1938) 552 . Google Scholar
  7. 7.
    The crossing relations were established by M. L. Goldberger, Phys. Rev.,99 (1955) 979; M. Gell-Mann and M. L. Goldberger, Phys. Rev.,96 (1954) 1433. For further literature, see, for instance M. L. Goldberger and K. M. Watson, Collision Theory,Wiley, New York, 1964, chapter io. The relations of the various types of symmetry principles were considered in two recent articles: Nuovo Cimento, Suppl.,in the press, and Phys. Today,17 (1964) 34. See also E. Wigner, Progr. Theoret. Phys. (Kyoto), 11 (1954) 437.Google Scholar
  8. 8.
    V. A. Fock, The Theory of Space, Time and Gravitation,Pergamon, Oxford, 1959. The character of the postulate of invariance with respect to general coordinate transformations as a geometrical invariance was questioned already by E. Kretschman, Ann.Physik,53 (1917) 575.Google Scholar
  9. 9.
    M. A. Melvin, Rev. Mod. Phys., 32 (1960) 477.Google Scholar
  10. 10.
    A. Einstein, Zur Elektrodynamik bewegter Körper, Ann. Physik, 17 (1905) 891.Google Scholar
  11. 11.
    A. Einstein and S. B. Preuss, Akad. Wiss.,(1915) 778, 779, 844; Ann. Physik,49 (1916) 769. Similar results were obtained almost simultaneously by D. Hilbert, Nachr.kgl.Ges. Wiss. (Göttingen),(1915) 395.Google Scholar
  12. 12.
    J. Schwinger, Phys. Rev.,76 (1949) 790. See also S. S. Schweber, An Introduction to Relativistic Quantum Field Theory,Row, Peterson and Co., New York, 1961, Section 15, where further references can also be found.Google Scholar
  13. 13.
    See A. S. Wightman, Quelques Problèmes Mathématiques de la Théorie Quantique Relativiste, and numerous other articles in Les Problèmes Mathématiques de la Théorie Quantique des Champs,Centre National de la Recherche Scientifique, Paris, 1959.Google Scholar
  14. 14.
    G. Hamel, Z.Math.Physik,50 (1904) 1; G.Herzglotz, Ann.Physik,36 (1911) 493; F. Engel, Nachr. kgl. Ges. Wiss. (Göttingen),(1918) 171; E. Noether, Nachr. kgl. Ges. Wiss. (Göttingen),(1918)235; E. Bessel-Hagen, Math. Ann.,84 (1921) 258; the quantum theoretical derivation given by E. Wigner, Nachr. kgl. Ges. Wiss. (Göttingen), (1927) 375, contains also the parity conservation law which was shown, in refs, to be only approximately valid. See also the article ofref.16.Google Scholar
  15. 15.
    I heard this remark, for the first time, from C. N. Yang, at the centennial celebration of Bryn Mawr College.Google Scholar
  16. 16.
    See the writer’s article Unitary Representations of the Inhomogeneous Lorentz Group including Reflections, in Elementary Particle Physics,Gordon and Breach, New York, 1964, for a systematic discussion of the reflection operations.Google Scholar
  17. 17.
    See the writer’s book, Gruppentheorie and ihre Anwendung auf die Quantenmechanik der Atomspektren,Vieweg, Braunschweig, 1931, or the English translation by J. Griffin, Academic Press, New York, 1959.Google Scholar
  18. 18.
    H. A. Kastrup, Physics Letters,3 (1962) 78. The additional invariance operations probably form the conformal group. This was discovered by E. Cunningham (Proc. London Math. Soc.,8 (1909) 77) and by H. Bateman (Proc.London Math. Soc.,8 (1910) 223) to leave Maxwell’s equations for the vacuum invariant, i.e.,the equations which describe light, always propagating at light velocity. For more recent considerations, see T. Fulton, F. Rohrlich and L. Witten, Rev. Mod. Phys.,34 (1962) 442 and Y. Murai, Progr. Theoret.Phys. (Kyoto), II (1954) 441 The latter articles contain also more extensive references to the subject.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • E. P. Wigner

There are no affiliations available

Personalised recommendations