“Maybe the Higgs boson is fictitious!”

That’s an intriguing and, as he remarks, plausible speculation by the noted condensed-matter physicist Philip Warren Anderson. It appears in a short article penned by him in Nature Physics on January 26, in which he discusses how the Higgs mechanism as in particle physics was inspired by a similar phenomenon observed in superconductors.

According to the Bardeen-Cooper-Schrieffer theory, certain materials lose their resistance to the flow of electric current completely and become superconductors below a critical temperature. Specifically, below this temperature, electrons don’t have the energy to sustain their mutual Coulomb repulsion. Instead, they experience a very weak yet persistent attractive force between them, which encourages them to team up in pairs called Cooper pairs (named for Leon Cooper).

If even one Cooper pair is disrupted, all Cooper pairs in the superconductor will break, and it will cease to be a superconductor as well. As a result, the energy to break one pair is equivalent to the energy necessary to break all pairs – a coercive state of affairs that keeps the pairs paired up despite energetic vibrations from the atoms in the material’s lattice. In this energetic environment, the Cooper pairs all behave as if they were part of a collective (described as a Bose-Einstein condensate).

This transformation can be understood as the spontaneous breaking of a symmetry: the gauge symmetry of electromagnetism, which dictates that no experiment can distinguish between the laws governing electricity and magnetism. With a superconductor, however, the laws governing electricity in the material become different below the critical temperature. And when a gauge symmetry breaks, a massive1 boson is formed. In the case of BCS superconductivity, however, it is not an actual particle as much as the collective mode of the condensate.

In particle physics, a similar example exists in the form of electroweak symmetry breaking. While we are aware of four fundamental forces in play around us (strong, weak, electromagnetic and gravitational), at higher energies the forces are thought to become unified into one ‘common’ force. And on the road to unification, the first to happen is of the electromagnetic and weak forces – into the electroweak force. Axiomatically, the electroweak symmetry was broken to yield the electromagnetic and weak forces, and the massive Higgs boson.

Anderson, who first discussed the ‘Higgs mode’ in superconductors in a paper in 1958, writes in his January 26 article (titled Higgs, Anderson and all that),

… Yoichiro Nambu, who was a particle theorist and had only been drawn into our field by the gauge problem, noticed in 1960 that a BCS-like theory could be used to create mass terms for massless elementary particles out of their interactions. After all, one way to describe the energy gap in BCS is that it represents a mass term for every point on the Fermi surface, mixing the particle with its opposite spin and momentum antiparticle. In 1960 Nambu and Jona-Lasinio developed a theory in which most of the mass of the nucleon comes from interactions — this theory is still considered partially correct.

But the real application of the idea of a superconductivity-like broken symmetry as a source of the particle spectrum came with the electroweak theory — which unified the electromagnetic and weak interactions — of Sheldon Glashow, Abdus Salam and Steven Weinberg.

What is fascinating is that these two phenomena transpire at outstandingly different energy scales. The unification of the electromagnetic and weak forces into the electroweak force happens beyond 100 GeV. The energy scale at which the electrons in magnesium diboride become superconducting is around 0.002 eV. As Terry Pratchett would have it, the “aching gulf” of energy in between spans 12 orders of magnitude.

At the same time, the parallels between superconductivity and electroweak symmetry breaking are more easily drawn than between other, more disparate fields of study because their occurrence is understood in terms of the behavior of fundamental particles, especially bosons and fermions. It is this equivalence that makes Anderson’s speculative remark more attractive:

If superconductivity does not require an explicit Higgs in the Hamiltonian to observe a Higgs mode, might the same be true for the 126 GeV mode? As far as I can interpret what is being said about the numbers, I think that is entirely plausible. Maybe the Higgs boson is fictitious!

To help us along, all we have at the moment is the latest in an increasingly asymptotic series of confirmations: as reported by CERN, “the results draw a picture of a particle that – for the moment – cannot be distinguished from the Standard Model predictions for the Higgs boson.”

1Massive as in having mass, not as in a giant boson.

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