Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-05-08T15:17:14.476Z Has data issue: false hasContentIssue false
  • English
  • Français

Spontaneous Symmetry Breaking and Chance in a Classical World

Published online by Cambridge University Press:  01 January 2022

Chuang Liu
Get access Rights & Permissions [Opens in a new window]

Abstract

This essay explores the nature of spontaneous symmetry breaking (SSB) in connection with a cluster of interrelated concepts such as Curie's symmetry principle, ergodicity, and chance and stability in classical systems. First, a clarification of the two existing senses of SSB is provided and an argument developed for a proposal for SSB, in which not only the possibilities but also the actual breakings are referred to. Second, a detailed analysis is given of classical SSB that answers the questions: (i) how we are justified in regarding it as a matter of chance, and (ii) why the breakings in it are equally probable. The answer provides some support to the applicability of ergodicity in special systems (such as ours).

Type
Research Article
Information
Philosophy of Science , Volume 70 , Issue 3 , July 2003 , pp. 590 - 608
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

‡

I would like to thank Craig Callender for reading an earlier draft of the paper and commenting on a shorter version of the paper at the APA Eastern Division Meeting in Philadelphia on December 30, 2002. I also thank two anonymous referees for their constructive suggestions.

References

Aitchison, Ian J.R. (1984), An Informal Introduction to Gauge Field Theories. Cambridge: Cambridge University Press.Google Scholar
Albert, David (2000), Time and Chance. Cambridge, MA: Harvard University Press.Google Scholar
Clark, Peter (1987), “Determinism and Probability in Physics”, Proceedings of the Aristotelian Society, Suppl. LXII: 185–210.Google Scholar
Coleman, Sidney (1975), “An Introduction to Spontaneous Symmetry Breakdown and Gauge Fields”, in Zichichi, Antonio (ed.), Laws of Hadronic Matter. New York: Academic Press, 138–215.Google Scholar
Earman, John (1986), A Primer on Determinism. Dordrecht: D. Reidel.CrossRefGoogle Scholar
Earman, John, and Rédei, Miklós (1996), “Why Ergodic Theory Does Not Explain the Success of Equilibrium Statistical Mechanics”, Why Ergodic Theory Does Not Explain the Success of Equilibrium Statistical Mechanics 47:63–78.Google Scholar
Emch, Gérard G. (1977), “An Algebraic Approach for Spontaneous Symmetry Breaking in Quantum Statistical Mechanics”, in Kramer, Peter and Cin, Mario Dal (eds.), Groups, Systems and Many-Body Physics. Braunschweig: Friedr. Vieweg & Sohn, 246–284.Google Scholar
Emch, Gérard G., and Liu, Chuang. (2001), The Logic of Thermostatistical Physics. Berlin, Springer-Verlag.CrossRefGoogle Scholar
Goldenfeld, Nigel (1992), Lectures on Phase Transitions and the Renormalization Group. Reading, MA: Addison-Wesley.Google Scholar
Greenberger, D.M. (1978), “Esoteric Elementary Particle Phenomena in Undergraduate Physics—Spontaneous Symmetry Breaking and Scale Invariance”, Esoteric Elementary Particle Phenomena in Undergraduate Physics—Spontaneous Symmetry Breaking and Scale Invariance 46:394–398.Google Scholar
Guttmann, Yair M. (1999), The Concept of Probability in Statistical Physics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Ismael, Jenann (1997), “Curie’s Principle”, Curie’s Principle 110:167–190.Google Scholar
Liu, Chuang (2003), “Classical Spontaneous Symmetry Breaking”, Philosophy of Science (Proceedings), forthcoming.CrossRefGoogle Scholar
Loewer, Barry (2001), “Determinism and Chance”, Determinism and Chance 32:609–620.Google Scholar
Poincaré, Henri (1952), Science and Method. New York: Dover.Google Scholar
Sinai, Ya. G. (1970), “Dynamical Systems with Elastic Reflections”, Dynamical Systems with Elastic Reflections 25:137–189.Google Scholar
Sivardiere, J. (1983), “A Simple Mechanical Model Exhibiting a Spontaneous Symmetry Breaking”, A Simple Mechanical Model Exhibiting a Spontaneous Symmetry Breaking 51:1016–1018.Google Scholar
Sklar, Lawrence (1993), Physics and Chance. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Smith, Peter (1998), Explaining Chaos. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Strocchi, Franco (1985), Elements of Quantum Mechanics on Infinite Systems. Singapore: World Scientific.CrossRefGoogle Scholar
Toda Morikazu, R. Kubo, and Saitô, N. (1995), Statistical Physics I. 2d ed. Berlin: Springer-Verlag.Google Scholar
van Fraassen, Bas (1989), Laws and Symmetry. Oxford: Clarendon Press.CrossRefGoogle Scholar
van Fraassen, Bas; (1991), Quantum Mechanics: An Empirical View. Oxford: Clarendon Press.CrossRefGoogle Scholar
Vranas, Peter (1998), “Epsilon-Ergodicity and the Success of Equilibrium Statistical Mechanics”, Epsilon-Ergodicity and the Success of Equilibrium Statistical Mechanics 65:688–708.Google Scholar
Weinberg, Steven (1996), The Quantum Theory of Fields, vol. II: Modern Applications. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Wigner, Eugene P. (1979), Symmetries and Reflections: Scientific Essays of Eugene P. Wigner. Woodbridge, CT: Ox Bow Press.Google Scholar