In the early 1970s, John Iliopoulos made a series of important contributions to the development of the Standard Model of particle physics. Under the Standard Model, the question of mass and its origins is addressed with considerable—though not complete—success. Iliopoulos is well placed to write about this particular subject.
The Origin of Mass first appeared in a French edition in 2015.1 Iliopoulos originally wrote the book in response to the discovery of the Higgs boson, which was first announced at CERN in June 2012. Scores of books have been written about the discovery, examining every aspect of the event and the process by which the breakthrough was made. I have not read any of them. But, dare I say it? This one is probably the best.
“We want to show that [the Higgs boson] is not just a new particle,” Iliopoulos writes in the introduction, “but, probably, the trace of one of the strangest events that occurred in the early Universe: the phenomenon which allowed most elementary particles to acquire a mass.”2 Indeed, The Origin of Mass is not solely focused on the discovery at CERN. Iliopoulos is far more concerned with its physical significance and implications for the field.
In the introduction, Iliopoulos confronts a common problem in communicating science: the units to be used. Although it may appear trivial, this can become a serious obstacle for a lay audience. Understanding that energy and mass may have related or even the same units is relatively easy. Most readers are familiar with E = mc2, in which c is a mere conversion factor, like the one from pounds to pence. In 1971, the latter changed from an unwieldy value of 240 to a much simpler value of 100—in decimal units. The value of c has changed far more than that, from about 300,000 km/s to c = 1 in natural units! Understanding that energies and inverse distances can also be specified in the same units is much more difficult. Some knowledge of quantum mechanics is needed—not only special relativity.
In its second chapter, the book offers “a brief history of cosmology: its origins and its evolution, together with our present ideas (some would say prejudices) regarding the history of the Universe.”3 Here, Iliopoulos deploys the style that comes to characterize The Origin of Mass: a mix of science, history, and a series of brief but entertaining biographies of scientific figures. Much of the pleasure derived from reading the book arises from the author’s gift for interweaving these elements.
Despite this balance between accessibility and technical detail, some of the chapters will inevitably prove challenging for lay readers. Consider section 5.5, “Spontaneous Symmetry Breaking in the Presence of Gauge Interactions.” Iliopoulos writes: “This is the most important section of this book. It is here that the significance of the CERN discovery will be presented.”4 It should come as no surprise that this section is, indeed, difficult. Still, any reader able to follow the concepts introduced in preceding chapters should be able to navigate it. The book also contains two appendices focused on elementary particles and Lie–Cartan groups. These sections are superb, but they are also notably much more technical than the rest of the book.
Although there is much to commend about The Origin of Mass, a few points emerge that are worthy of criticism. In section 5.5, the problem being discussed is described as a “complex and purely quantum phenomenon, for which we have no classical analogue.”5 The author of the book’s foreword, François Englert, would not agree. Indeed, I have heard Englert give a talk introducing just such a classical analogue. It was a talk that I found considerably harder to follow than the actual quantum story, at least in the way it is told by Iliopoulos.
In the preceding section of the book, even though it is defined, there is no mention of the problems associated with the vacuum. This apparently simple substance is merely described as “not ‘empty.’”6 Such a statement has cosmological consequences that the author chooses to mention only in passing when referring to dark energy.7 Avoiding a longer discussion of the vacuum is, in fact, prudent. It is not easy to explain something that we do not understand.
The topic of chirality is also discussed. But what Iliopoulos describes in the book, following the parlance of high-energy physics, is actually helicity rather than chirality. Helicity, as he notes, can be flipped via a Lorentz transformation. Chirality, the zero-mass limit of helicity, is Lorentz invariant: it is impossible to overtake a particle moving at the speed of light in order to observe a change in the relative directions of its spin and speed. The author is, of course, well versed in all these details, and this is the sole example of haphazardly employed nomenclature.
Elsewhere, Iliopoulos explains the generally accepted view concerning the masses of protons and neutrons in comparison to the masses of their constituent quarks.8 This leads to the conclusion that our own mass, dominated by that of our atomic nuclei, is mainly due to the mass contributed by gluons, which provide the binding energy of our protons and neutrons. If the Higgs mechanism were switched off, quarks would become massless, and this book would lose much of its interest. We would, however, still retain the bulk of our mass. Although widely embraced, this point of view is not necessarily correct.
In the section entitled “The Standard Theory and Experiment,” figure 6.5 shows how the effective strength, αs, of the strong interactions varies with the energy scale Q.9 The scale of this figure does extend below Q = 1 GeV. Our current understanding of quantum chromodynamics is, in fact, insufficient to extend the scale to Q = 0. A similar situation arises in relation to the masses of the u and d light quarks constituting the proton. The mass of the proton is measured at Q = 0, while the quark masses quoted by Iliopoulos are measured at a much higher scale. If one could extend the scale-dependent quark masses to Q = 0, they would grow toward much higher values. At Q = 0, the uud mass quoted by Iliopoulos would likely be much closer to the mass of the proton.
The book contains a few very minor errors. In a footnote, the theory of quantum chromodynamics is attributed to David Gross, David Politzer, and Frank Wilczek.10 I know quite a few people who, having developed the subject, would have a fit at this point. In another footnote discussing the life and work of Élie Cartan, École normale supérieure is misspelled as “École Normale Supeure” several times.11 This is a surprising mistake, especially given the book’s publisher.
While preparing a new book, I recently found myself attempting to explain the origin of mass, among other things. As it turns out, I was fortunate to have not yet read The Origin of Mass. It would have been difficult to avoid imitating the ways in which Iliopoulos explains these ideas. It is a masterful account.
