The Higgs mechanism and superconductivity: A case study of formal analogies

Abstract

Following the experimental discovery of the Higgs boson, physicists explained the discovery to the public by appealing to analogies with condensed matter physics. The historical root of these analogies is the analogies to models of superconductivity that inspired the introduction of spontaneous symmetry breaking (SSB) into particle physics in the early 1960s. We offer a historical and philosophical analysis of the analogies between the Higgs model of the electroweak (EW) interaction and the Ginsburg-Landau (GL) and Bardeen-Cooper-Schrieffer (BCS) models of superconductivity, respectively. The conclusion of our analysis is that both sets of analogies are purely formal in virtue of the fact that they are accompanied by substantial physical disanalogies. In particular, the formal analogies do not map the temporal, causal, or modal structures of SSB in superconductivity to temporal, causal, or modal structures in the Higgs model. These substantial physical disanalogies mean that analogies to models of superconductivity cannot supply the basis for the physical interpretation of EW SSB; however, an appreciation of the contrast between the physical interpretations of SSB in superconductivity and the Higgs model does help to some foundational issues. Unlike SSB in superconductivity, SSB in the Higgs sector of the Standard Model (without the addition of new physics) is neither a temporal nor a causal process. We discuss the implications for the 'eating' metaphor for mass gain in the Higgs model. Furthermore, the distinction between the phenomenological GL model and the dynamical BCS model does not carry over to EW models, which clarifies the desiderata for so-called 'dynamical' models of EW SSB (e.g., minimal technicolor). Finally, the development of the Higgs model is an illuminating case study for philosophers of science because it illustrates how purely formal analogies can play a fruitful heuristic role in physics.

Naturalness, Wilsonian renormalization, and “fundamental parameters” in quantum field theory

“…From the perspective described in the previous section, in which Wilsonian EFTs do not have fundamental parameters, this particular justification for the naturalness principle appears to rest on an excessively "literal" or "phys-ical" interpretation of the analogy between condensed matter physics (CMP) and high energy physics (HEP). To clarify our meaning, it will be useful to employ a distinction between "formal" and "physical" interpretations of the high-energy/condensed-matter analogy, which has recently been developed in the work of D. Fraser and of D. Fraser & A. Koberinski (Fraser, 2018), (Fraser and Koberinski, 2016).…”

Explanations and candidate explanations in physics

“…Unlike in the Higgs-inspirational case of superconductivity, there is no underlying dynamics and no phase transition. In fact, as has been recently argued by Fraser and Koberinski (2016), the Higgs mechanism is no temporal process at all; the Higgs field is just there and so are the particle masses.…”

Symmetry Breaking

“…The transition between these two phases then could have occurred physically during the cooling of the early universe. The formal analogy between spontaneous symmetry breaking in these different contexts has received further discussion recently in (Fraser 2012, Fraser andKoberinski 2016).…”