by David Kaiser
On paper, the Higgs boson acquired a central role in what emerged as the Standard Model of particle physics. Though the hypothetical Higgs particle was the plainest of all the particles described by the model—zero electric charge, zero intrinsic angular momentum, no abstruse quantum properties such as “strangeness” or “color charge”—its function, to bestow mass on would-be massless particles, became critical. The Higgs would give the others their heft. Nobel laureate Frank Wilczek playfully dubbed the Higgs boson the “quantum of ubiquitous resistance”; CERN theorist John Ellis made an analogy to people trudging across a snow-covered meadow.5
The idea was compelling, but it remained only an idea for decades. As the years wore on, particle physicists learned that it was one thing to posit a universal medium through which all matter lumbers along and quite another to produce empirical evidence that such a medium exists—in essence, to break off tiny pieces of that medium (individual Higgs particles) and measure their properties.
The strategy to find evidence of Higgs particles seemed straightforward enough: smash particles like protons together at such high speeds that Higgs bosons (along with a great deal of other stuff) would coagulate from the residual energy. After search upon search came up empty, physicists were able to place limits on the Higgs boson’s mass: if such objects really existed in nature, individual Higgs particles should weigh nearly as much as an atom of gold. Unlike gold atoms, however, physicists expected Higgs particles to be remarkably evanescent, with a lifetime of roughly a trillion-trillionth of a second. Such objects, physicists knew, wouldn’t sit around long enough to be photographed, nor would they leave much of a track: the furthest they could travel before decaying into other particles would be about one ten-trillionth of a centimeter.6
The only hope of finding evidence of Higgs particles was to sift through their decay products, or the decay products of their decay products, trying to distinguish signals of a long-since-vanished Higgs boson amid all the other subatomic wreckage that streams away from the collision region in a particle accelerator. This is a bit like trying to infer the existence of a particular long-deceased grandmother—and measure her height and weight—by sifting all the data of a national census. One must look for statistical deviations from the expected patterns of ordinary particles that get trapped in the detectors. Are there more particles of a particular type, with particular energies, than would be expected in the absence of a Higgs boson that had decayed into them?
No “golden event,” captured in a single photograph, can terminate such a search; no shriek of “Eureka!” marks its conclusion. Rather, by necessity, discovery claims depend upon complicated statistical arguments.7 Physicists must collect terabytes of data from all the trillions of scatterings and interactions and stack them into histograms: graphs showing the numbers of events of a given type at a given energy. Then they must carefully subtract away the “background,” or expected patterns of particle decays from known processes other than the creation and decay of a Higgs boson, and check whether any excess signal remains. (One of my favorite books in graduate school was The Higgs Hunter’s Guide, filled with the arcana of calculating the expected signals and backgrounds for Higgs decay at various energies.8 The title made me feel like Indiana Jones.) Higgs hunting is a game of looking for bumps in the night: tiny but otherwise unexplainable deviations in those histograms.
Figure 12.2. Statistical evidence of an excess number of decay events associated with a mass of around 125 GeV/c2, which would be consistent with a Higgs boson decaying into a pair of Z bosons, which in turn decay into four leptons (such as electrons, muons, or neutrinos). The number of events at that particular mass was significantly higher than would be expected in the absence of a genuine Higgs boson with a mass of about 125 GeV/c2, given the low level of other “background” events that should have been measured at that energy. (Source: ATLAS Collaboration, courtesy of CERN.)
In December 2011, representatives from two large teams at CERN convened a press conference to share evidence that they were on the trail of the elusive Higgs particle. But they had to stop shy of claiming a discovery. By that time, each group had collected and analyzed impressive amounts of data, culled from trillions of collisions among subatomic particles—but not enough to rule out statistical flukes.9
The teams at CERN needed to collect information from even more scatterings in order to clarify that the tiny bumps in their data were due to a new particle rather than to an unlikely string of events arising from ordinary, non-Higgs phenomena. Toss a coin ten times and it may well come up heads six times. In fact, you can expect to get six heads out of ten tosses about 20 percent of the time—a not-uncommon statistical fluke. Such a limited data set (only ten coin tosses) is not large enough to determine with confidence whether you are using a fair coin or a biased coin that favors heads over tails. But if you tossed the coin ten thousand times and got six thousand heads, that would point more convincingly toward some real effect—an inherent bias toward heads—rather than an ordinary coin on a lucky streak.
Years ago, particle physicists adopted the convention that discovery claims for new particles would require statistical significance of at least five standard deviations (usually denoted “five sigma”). That means that the odds that the observed events could have been due to mundane particles on a lucky streak—rather than arising from a genuinely new particle—are about three million to one. Neither of the teams at CERN that were searching for the Higgs boson had collected sufficient data to reach the five-sigma mark in December 2011. That changed a few months later. At a dramatic press conference on 4 July 2012, both teams announced that they had crossed the five-sigma mark with data collected through June. They had amassed clear evidence of the Higgs boson.10 The following year, Peter Higgs and François Englert shared the Nobel Prize.
Figure 12.3. ATLAS Collaboration spokesperson Fabiola Gianotti (left) and particle theorist Peter Higgs (right) congratulate each other at the press conference at CERN on 4 July 2012, soon after Gianotti presented her group’s evidence that they had detected the long-elusive Higgs boson. (Source: Photograph by Denis Balibouse / AFP, courtesy of Getty Images.)
How can we take the measure of such an achievement? One can certainly focus on the money: billions of dollars spent on the ill-fated Superconducting Supercollider; billions more expended at CERN to build and maintain the LHC. Budget lines certainly provide an important measure—not least during times of financial hardship—but they are not the only ones to consider.
A different kind of accounting may help to explain physicists’ exuberance at the CERN press conference on 4 July 2012. By that time, one of the standard databases of scientific publications included more than 16,000 articles on the Higgs particle, stretching back to the early articles from the 1960s.11 More than 90 percent of those articles had been published since 1990, and nearly 1,000 had appeared in 2011 alone. Those 16,000 articles were written by about 11,000 authors: physicists around the world who had been focusing on the Higgs particle, its theoretical roles and possible experimental detection, for decades. Five hundred of those authors had each published at least 55 articles on the topic, dedicating a large portion of their careers to the Higgs particle. (Four of my papers showed up on that list, less than 0.03 percent of the global effort. John Ellis from CERN led the pack with 150 articles. When he compares the Higgs field to a snow-covered meadow, you can be sure he knows what he’s talking about.)
Hence the jubilation that greeted the news from the LHC that July—a celebration not just for the five thousand or so physicists affiliated with the two teams at CERN but for the thousands more around the world who had contributed to the quest over half a century. Physicist Matthew Strassler declared 4 July 2012 to be “IndependHiggs Day.”12 I couldn’t imagine a better reason for fireworks.
13
When Fields Collide
Sometimes I need to kick myself—hard—for overlooking things that were right under my nose. I had one of those experiences about a deca
de ago when I noticed a paper posted to the world’s central electronic physics preprint server, arXiv.org. The authors of the new paper proposed a beautiful model, soon dubbed “Higgs inflation,” that could account for specific phenomena during the very early universe. Their idea was elegant and simple: what if the Higgs particle of the Standard Model also had a particular, nonstandard coupling to gravity, of the sort that had been hypothesized (in a rather different context) several decades earlier. Then the selfsame Higgs boson, which particle physicists already needed as part of the Standard Model, might answer even larger questions about the structure and evolution of our universe as a whole.1
I kicked myself for not proposing the idea myself. After all, I had already published several papers exploring aspects of Higgs-like fields in the early universe, which incorporated the nonstandard gravitational interactions; in fact, the authors of the new paper cited some of my previous research.2 Yet I had never taken the next step—a step that should have seemed obvious to me—and now they had. Stepping back from my initial frustration, the experience offered an opportunity to think about why certain questions come to seem obvious to various researchers, even if other scholars—trained in different ways, viewing the field from a different perch—had overlooked such questions altogether. In my own case, the new model fit squarely within my own specialty, a subfield of physics known as “particle cosmology.”
Particle cosmology is flourishing these days. The field investigates the smallest units of matter and their role in determining the shape and fate of the entire universe. In recent years the field has received generous funding from governments and private foundations; these have supported state-of-the-art satellite missions and enormous ground-based telescopes, as well as underwriting the research of thousands of theoretical physicists around the world. An average of more than two new preprints on the topic are posted to arXiv.org every hour of every single day—nights, weekends, and holidays included.3
The field’s dramatic success is all the more striking given that it barely existed forty years ago. The rapid rise of particle cosmology illustrates the potent alchemy of ideas and institutions that I find so fascinating—an entanglement often clearest in hindsight. In this case, the new subfield took form as some physicists aimed to push beyond the still-new Standard Model of particle physics; the newer ideas, emerging during the mid-1970s, took on special salience as unprecedented changes shook the discipline, especially in the United States. A generation before Congress killed the Superconducting Supercollider, particle physicists in the United States had faced a similar crisis. Their responses—institutional and curricular—enacted rapidly in the mid-1970s, helped to push certain questions to the research frontier, even as other research programs faltered.
These complex forces are thrown into starkest relief by following the fortunes of two sets of ideas: one introduced by gravitational specialists, the other puzzled over by particle physicists. Neither of these sets of ideas drove the union of particle physics and cosmology. Rather, tracing their fates over time clarifies larger processes. To unpack some of the ways that changes in politics and institutions can affect intellectual life, we may turn to the problem of mass.
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During the 1950s and 1960s, physicists in at least two subfields struggled to understand why objects have mass. Mass seems like such an obvious, innate property of matter that one might not even think it requires an explanation. Yet finding descriptions of the origin of mass that remained compatible with other ideas from modern physics proved no easy feat.4 The problem took different forms. Experts on gravitation and cosmology framed the problem in terms of Mach’s principle. Mach’s principle—named for the physicist and philosopher Ernst Mach (1838–1916), famed critic of Newton and inspiration to the young Einstein—remains stubbornly difficult to formulate, but a good approximation might be phrased this way: are local inertial effects the result of distant gravitational interactions? In other words, does an object’s mass—a measure of its resistance to changes in its motion—ultimately derive from that object’s gravitational interactions with all the other matter in the universe? If so, do Einstein’s gravitational field equations, the governing equations of general relativity, properly reflect this dependence?5
Within the much larger community of particle physicists, the problem of mass arose in a different form. Theorists struggled to incorporate masses for elementary particles without violating the symmetries that seemed to govern nuclear forces. Beginning in the 1950s, particle theorists faced a dilemma: either they could model the symmetries of these nuclear forces, which seemed to require the absurd step of setting all particles’ masses to zero, or they could incorporate particle masses in their equations but destroy the symmetries.6
Around the same time, physicists in both specialties developed schemes to explain the origin of mass. Both proposals postulated that a new field existed in the universe, whose interactions with all other types of matter would account for why we see those objects as possessing mass. On the gravitation side, Princeton graduate student Carl Brans and his thesis adviser, Robert Dicke, pointed out in a 1961 article that in Einstein’s general theory of relativity—by then physicists’ reigning description of gravity—the strength of gravity was fixed once and for all by Newton’s constant, G. According to Einstein, G had the same value on Earth as it did in the most distant galaxies; its value was the same today as it had been billions of years ago. Brans and Dicke suggested, instead, that Mach’s principle could be satisfied if the strength of gravity varied over time and space. To make this variation concrete, they hypothesized that some new, physical field φ permeated all of space, taking on different values here versus there, now versus then. The new field fixed the force of gravity: G ~ 1/φ, so that G would now vary inversely as φ did. (In regions of space in which φ had a large value, G would be small, and vice versa.) They swapped 1/φ for G throughout Einstein’s gravitational equations. In the resulting model, ordinary matter would respond both to the curvature of space and time, as in ordinary general relativity, and to variations in the local strength of gravity, coming from φ. All matter interacted with φ, and hence the new field’s behavior helped to determine how ordinary matter moved through space and time. Any measurement of an object’s mass would therefore depend on the local value of φ. Brans and Dicke’s idea seemed so compelling that members of the gravity research group at Caltech used to joke that they believed in Einstein’s general theory of relativity on Mondays, Wednesdays, and Fridays, and in Brans-Dicke gravity on Tuesdays, Thursdays, and Saturdays. (On Sundays they relaxed at the beach.)7
Figure 13.1. Top, Carl Brans during his graduate studies at Princeton, 1959. (Source: Courtesy of Carl Brans.) Bottom, Brans’s dissertation adviser at Princeton, Robert Dicke. (Source: Photograph by Mitchell Valentine, courtesy of AIP Emilio Segrè Visual Archives, Physics Today Collection.)
Figure 13.2. A double-well potential, V(φ). The energy of the system has a minimum when the field reaches either of the values +v or −v. Although the field’s potential energy is symmetric, the field’s solution will pick out only one of these two minima, breaking the symmetry of the governing equations. (Source: Illustration by the author.)
Several specialists in particle physics attacked the problem of mass around the same time, also introducing a new, hypothetical field that might pervade the universe. Jeffrey Goldstone, for example, observed in 1961 that the solutions to various equations need not respect the same symmetries that the equations themselves do. As a simple illustration he introduced a new field, which he also labeled φ. The potential energy for his new field had two minima, one at a value of −v for the field φ and the other at the value +v.
The energy of the system is lowest at these minima, and hence the field will eventually settle into one of these values. The potential energy is exactly the same—symmetric—for each of these values of the field, even though the field must eventually land in only one of them. This ingenious idea quickly became known as “spont
aneous symmetry breaking”: whereas the curve of potential energy is fully left-right symmetric, any given solution for φ would be concentrated only on the left or on the right.8
A few years later, in 1964, Peter Higgs revisited Goldstone’s work. He found that when he inserted Goldstone’s idea into models of the highly symmetric nuclear forces, spontaneous symmetry breaking would yield massive particles. In such models, the new field φ would interact with other particles, including the force-carrying particles that generated nuclear forces. The equations governing these interactions, Higgs demonstrated, obeyed all the requisite symmetries. Before φ settled into one of the minima of its potential, these other particles would skip lightly along, merrily unencumbered. Once the φ field arrived at either +v or −v, however, it would exert a drag on anything interacting with it—like all those marbles mired in molasses. Once that happened, the subatomic particles would behave as if they had some nonzero mass; any measurements of their mass, in turn, would depend on the local value of φ.9
Figure 13.3. Top, Jeffrey Goldstone identified the idea of spontaneous symmetry breaking in 1961. (Source: AIP Emilio Segrè Visual Archives, Physics Today Collection.) Bottom, Peter Higgs incorporated Goldstone’s symmetry-breaking idea into a model of nuclear forces in 1964. (Source: Photograph by Robert Palmer, courtesy of AIP Emilio Segrè Visual Archives.)