A field guide to the Higgs

James Ladyman on the discovery at CERN and the rationality of science. This article appears in Issue 59 of The Philosophers’ Magazine. Please support TPM by subscribing.

Atoms turned out not to be atomic because, as we know to our peril, there can be nuclear fission. The triumph of the search for the fundamental building blocks of matter and the discovery of the chemical elements of the Periodic Table was a Pyrrhic victory because, as Henri Poincare said, the atom turned out to be a world in itself. The discovery of the Higgs boson at CERN announced on July 4th means a new particle is added to the bewildering menagerie that already includes quarks, electrons and the W and Z bosons previously discovered at CERN. The latter two particles are bosons, meaning that they obey Bose-Einstein statistics which allow many of them to be in exactly the same state, unlike quarks and electrons which obey the Pauli Exclusion Principle and are known as fermions (obeying Fermi-Dirac statistics). All these particles are fundamental in the sense that they are not composed of other particles.

However, whereas the other fundamental bosons, the W and Z particles and the photon, are all force-carrying particles, the Higgs is not. Rather, it is there to explain why other particles have mass. Electromagnetism holds atoms together by causing the attraction of the positively charged nucleus and the negatively charged electrons. Richard Feynman complained about the lack of an explanation for the mass of the electron, which is very much lighter than the particles that make up the nucleus (nearly 2,000 times lighter than each, and there may be many). If electrons were even a tiny bit more or less massive there would be no stable atoms at all. However, the mystery goes deeper, because in fact the quantum field theory of the electromagnetic and weak interactions that unified them (in a single theory called “electroweak”) calls for electrons to have no mass at all. Meanwhile, it has been found that quarks and W and Z bosons are very massive, while photons are massless. Some mechanism was needed to explain why particles have the masses that they do. This was the problem that Peter Higgs and others proposed to solve by positing a new field and with it new particles.

It is really the Higgs field whose discovery is being celebrated, because particles are not really particles in the everyday sense but rather excitation states of fields. The Higgs boson has no charge, no colour charge (the charge of the strong force that quarks exhibit) and no spin. It does have a mass because the Higgs field interacts with itself, and it is by the mass of the Higgs and the particles into which it decays that it is known. “The” Higgs boson that has been discovered is in fact the lowest excitation state of the Higgs field, which is posited to have a non-zero ground state everywhere to explain the ubiquity of the masses of other particles. While there is only one type of Higgs particle in the Standard Model, there are non-standard models with more, so what has been found is a particle with the mass and properties consistent with a Higgs particle but not necessarily the only one.

Furthermore, while the mystery of how particles can have mass is solved by the Higgs mechanism, and this is confirmed by the discovery at CERN, the current theory of the former gives no explanation for why particles have the particular masses that they do. The electron is simply supposed to interact with the Higgs field via a “coupling constant” whose value is designed to reproduce the known mass of the electron, and likewise for quarks and other particles. So while the discovery of the Higgs is an important result, it is far from the end of the story.

For philosophers the Higgs affair illustrates many issues in the philosophy of science. The theory-ladenness of observation is exemplified by the discovery of a particle that cannot be seen directly – its existence is inferred from the detection of other particles which themselves are known only indirectly. Furthermore, the Higgs particle was not predicted to have its exact mass, rather previous attempts to find it at lower masses all failed, so the theory of the Higgs particle underdetermines this property which is determined from the data. We know from previous experience that our theories and understanding of the Higgs field may be revised, however we can be confident that the Higgs mechanism for symmetry breaking and the structure of the standard model will be retained in future physics at least as an approximation.

Finally this episode in the history of physics demonstrates a fundamental epistemological issue; neither scientific theory nor mathematical statistics can tell us when to stick our necks out and announce a discovery. The convention in this case is when an apparent event has a probability of less than one in about three million of being due to an error. There is no particular reason why this number is chosen instead of one significantly bigger or smaller. As with climate change, experiment and logic and mathematics can only tell us how likely or unlikely our results are given our theory, not how sure we need to be to believe.

James Ladyman is professor of philosophy at the University of Bristol.

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