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Between symmetry and asymmetry: spontaneous symmetry breaking as narrative knowing

  • Symmetries and Asymmetries in Physics
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Abstract

The paper presents a historical-epistemological analysis of the notion of “spontaneous symmetry breaking”, which I believe today provides a template for conceiving the relationship between symmetry and asymmetry in physics as well as in other areas of the natural sciences. The central thesis of the paper is that spontaneous symmetry breaking represents an instance of “narrative knowing” in the sense developed by recent research in history and philosophy of science (Morgan and Wise (eds) SI narrative in science, Studies in history and philosophy of science, 2017a). Spontaneous symmetry breaking is best understood as a hybrid narrative comprising formulas, verbal statements, images, and at times also other media. This flexible notion can be deployed in different variations, allowing to explain a broad range of non-symmetric phenomena or models as resulting from (not necessarily observable) processes of loss of symmetry. I will support this thesis by first analysing in detail the way in which spontaneous symmetry breaking, and in particular electroweak symmetry breakdown, are presented in today’s physics textbooks and reference works, and then by reconstructing the emergence of the hybrid construct from the late 1950s until the 1970s, when spontaneous symmetry breaking definitively established itself as a key physical notion.

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Notes

  1. Although in principle distinctions between asymmetry, broken symmetry and lack of symmetry might be made, as we shall see, in the case of high energy physics the three notions have today become mutually entangled.

  2. I have discussed this issue in some detail in Borrelli (2012, pp. 201‒202, pp. 211‒212).

  3. Stöltzner incorrectly presents the notion that stories may include mathematical elements as a difference to my own work, overlooking the fact that I had expressed precisely this idea in the same paper which he quotes, where I characterize the naturalness problem as "a hybrid narrative combining words, formulas, numbers and analogies" (Borrelli 2015a, p. 69).

  4. The following overview is compiled on the basis of the following texts: Castellani (2003), Brown and Cao (1991, pp. 215–217), Cheng and Li (1984, pp. 141–151, pp. 240–247), Earman (2003), Itzykson and Zuber (1980, pp. 519–526, pp. 540–549, pp. 612–616), Kibble (2015), Mandl and Shaw (1984, pp. 279–289), Morrison (2003), Weinberg (1996, pp. 163–165) and Zee (2010, pp. 223–230).

  5. I list here once again all the reference works, papers and textbooks in physics and philosophy where I have endeavoured to find an overarching definition of spontaneous symmetry breaking: Castellani (2003), Brown and Cao (1991), Cheng and Li (1984), Earman (2003), Itzykson and Zuber (1980), Kibble (2006, 2015), Liu and Emch (2005), Lyre (2008), Mandl and Shaw (1984), Morrison (2003), Peskin and Schroeder (1995), Strocchi (2008), 't Hooft (1997), Weinberg (1996) and Zee (2010). It may be also noted that, should such a definition exists, it would most probably be quoted by recent physics texts, given the great and growing importance of priority claims among physicists.

  6. I wish to remind readers that, as discussed in Sect. 5 above, there is at present no overarching mathematical framework for spontaneous symmetry breaking which includes the Higgs mechanism, so that the narrative employed by Peskin and Schroeder cannot be seen as a didactic simplification of some refined mathematical argument.

  7. For an overview of the development of particle physics in the 1950s and ‘60s see (Brown et al. 1989). For a more specific, detailed discussion of spontaneous symmetry breaking and of the quest fot the 'origin of mass' see (Borrelli 2015c).

  8. “Es ist keineswegs vom vornerein sicher, daß es auch einen Zustand “Vakuum” geben muß, der alle Symmetrieeigenschaften der Ausgangsgleichung besitzt. […] Wenn es sich als unmöglich erweist, einen voll symmetrischen Zustand “Vakuum” zu konstruieren, so kann dies anschaulich wohl nur so gedeutet werden, daß es sich bei dem unsymmetrischen Grundzustand nicht eigentlich um ein Vakuum, sondern um einen Zustand "Welt" handelt, der die Grundlage für die Existenz der Elementarteilchen bildet” (Dürr et al. 1959, p. 446).

  9. A central tenet of Heisenberg’s view was that physically significant predictions could not be obtained from that theory using perturbative expansions, but only by means of nonperturbative techniques. Such nonperturbative tools, however, still largely had to be developed, and this constituted the main problem of Heisenberg's approach.

  10. The term “renormalization” indicates a procedure necessary to extract finite prediction from perturbative computations in quantum field theory. In those computation divergent integrals appear which have to be formally subtracted following a mathematically non-rigorous, yet carefully defined procedure of “renormalization” which was developed around 1950 contemporary but independently by Richard Feynman, Julian Schwinger and Shinichiro Tomonaga (Schweber 1994).

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Acknowledgements

The research presented here was funded by the project “Exploring the “dark ages” of particle physics: isospin, strangeness and the construction of physical–mathematical concepts in the pre-Standard-Model era (ca. 1950–1965)” (German Research Council (Deutsche Forschungsgemeinschaft (DFG)) grant BO 4062/2-1), and by the Institute for Advances Study on Media Cultures of Computer Simulation (MECS), Leuphana Universität Lüneburg (DFG research Grant KFOR 1927).

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    Arianna Borrelli

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Borrelli, A. Between symmetry and asymmetry: spontaneous symmetry breaking as narrative knowing. Synthese 198, 3919–3948 (2021). https://doi.org/10.1007/s11229-019-02320-8

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