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condensate of particles. It would again be like trying to move a truck by 
throwing popcorn at it. Quantum mechanically the result is similar. In 
this case we would say that to change the configuration of the conden-
sate would require the whole condensate of particles to shift by a large 
fixed amount to a new quantum state that differs in energy from the 
state it is in. But no such energy is available from the thermal bath at low 
temperature. Alternatively, we might wonder if the collision could break 
apart two electrons from a Cooper pair in the condensate—sort of like 
knocking off the rearview mirror when a truck collides with a post. But 
at low temperatures everything is moving too slowly for that to happen. 
So the current flows unimpeded. The Borg would say, resistance is futile. 
But in this case resistance is simply nonexistent. A current, once initi-
ated, will flow forever, even if the battery initially attached to the wire 
is removed. 
This was the Bardeen-Cooper-Schrieffer (BCS) theory of supercon-
ductivity, a remarkable piece of work, which ultimately explained all of 
the experimental properties of superconductors such as mercury. These 
new properties signal that the ground state of the system has changed 
from what it had been before it became a superconductor, and like ice 
crystals on a window, these new properties reflect spontaneous sym-
metry breaking. In superconductors the breaking of symmetry is not 
as visually obvious as it is in the ice crystals on a windowpane, but it is 
there, under the surface. 
Mathematically, the signature of this symmetry breaking is that sud-
denly, once the condensate of Cooper pairs forms, a large minimum en-
ergy is now required to change the configuration of the whole material. 
The condensate acts like a macroscopic object with some large mass. 
The generation of such a "mass gap" (as it is called—expressed as the 
minimum energy it takes to break the system out of its superconducting 
state) is a hallmark of the symmetry-breaking transition that produces 
a superconductor. 
You might be wondering what all of this, as interesting as it might be, 
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has to do with the story we have been focusing on, namely understand-
ing the fundamental forces of nature. With the benefit of hindsight, the 
connection will be clear. However, in the tangled and confused world 
of particle physics in the 19505 and '6os the road to enlightenment was 
not so direct. 
In 1956, Yoichiro Nambu, who had recently moved to the Univer-
sity of Chicago, heard a seminar by Robert Schrieffer on what would 
become the BCS theory of superconductivity, and it left a deep impres-
sion on him. He, like most others interested in particle physics at the 
time, had been wrestling with how the familiar particles that make up 
atomic nuclei—protons and neutrons—fit within the particle zoo and 
the jungle of interactions associated with their production and decay. 
Nambu, like others, was struck by the almost identical masses of the 
proton and the neutron. It seemed to him, as it had to Yang and Mills, 
that some underlying principle in nature must produce such a result. 
Nambu, however, speculated that the example of superconductivity 
might provide a vital clue—in particular the appearance of a new char-
acteristic energy scale associated with the excitation energy required to 
break apart the Cooper-pair condensate. 
For three years Nambu explored how to adapt this idea to symmetry 
breaking in particle physics. He proposed a model by which a similar 
condensate of some fields that might exist in nature and the minimum 
energy to create excitations out of this condensate state could be charac-
teristic of the large mass/energy associated with protons and neutrons. 
Independently, he and the physicist Jeffrey Goldstone discovered that 
a hallmark of such symmetry breaking would be the existence of other 
massless particles, now called Nambu-Goldstone (NG) bosons, whose 
interactions with other matter would also reflect the nature of the sym-
metry breaking. An analogy of sorts can be made here to a more familiar 
system such as an ice crystal. Such a system spontaneously breaks the 
symmetry under spatial translation because moving in one direction 
things look very different from when moving in another direction. But 
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in such a crystal, tiny vibrations of individual atoms in the crystal about 
their resting positions are possible. These vibrational modes—called 
phonons, as I have mentioned—can store arbitrarily small amounts of 
energy. In the quantum world of particle physics, these modes would 
be reflected as Nambu-Goldstone massless particles, because where the 
equivalence between energy and mass is manifest, excitations that carry 
little or no energy correspond to massless particles. 
And, lo and behold, the pions discovered by Powell closely fit the bill. 
They are not exactly massless, but they are much lighter than all other 
strongly interacting particles. Their interactions with other particles 
have the characteristics one would expect of NG bosons, which might 
exist if some symmetry-breaking phenomenon existed in nature with 
a scale of excitation energy that might correspond to the mass/energy 
scale of protons and neutrons. 
But, in spite of the importance of Nambu's work, he and almost all of 
his colleagues in the field overlooked a related but much deeper conse-
quence of the spontaneous symmetry breaking in the theory of super-
conductivity that later provided the key to unlock the true mystery of 
the strong and weak nuclear forces. Nambu's focus on symmetry break-
ing was inspired, but the analogies that he and others drew to supercon-
ductivity were incomplete. 
It seems that we are much closer to the physicists on that ice crystal 
on the windowpane than we ever imagined. But just as one might imag-
ine would be the case for those physicists, this myopia was not immedi-
ately obvious to the physics community. 
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Chapter 15 
LIVING INSIDE A 
SUPERCONDUCTOR 
Everyone lies to their neighbor; they flatter with their 
lips but harbor deception in their hearts. 
-PSALMS 12:2 
The mistakes of the past may seem obvious with the ben-
efit of hindsight, but remember that objects viewed in the rearview mir-
ror are often closer than they appear. It is easy to castigate our 
predecessors for what they missed, but what is confusing to us today 
may be obvious to our descendants. When working on the edge, we 
travel a path often shrouded in fog. 
The analogy to superconductivity first exploited by Nambu is use-
ful, but largely for reasons very different from what Nambu and others 
imagined at the time. In hindsight the answer may seem almost obvi-
ous, just as the little clues that reveal the murderer in Agatha Christie 
stories are clear after the solution. But, as in her mysteries, we also find 
lots of red herrings, and these blind alleys make the eventual resolution 
even more surprising. 
We can empathize with the confusion in particle physics at the time. 
New accelerators were coming online, and every time a new collision-
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energy threshold was reached, new strongly interacting cousins of neu-
trons and protons were produced. The process seemed as if it would be 
endless. This embarrassment of riches meant that both theorists and 
experimentalists were driven to focus on the mystery of the strong nu-
clear force, which seemed to be where the biggest challenge to existing 
theory lay. 
A potentially infinite number of elementary particles with ever-
higher masses seemed to characterize the microscopic world. But this 
was incompatible with all the ideas of quantum field theory—the suc-
cessful framework that had so beautifully provided an understanding of 
the relativistic quantum behavior of electrons and photons. 
Berkeley physicist Geoffrey Chew led the development of a popu-
lar, influential program to address this problem. Chew gave up the 
idea that any truly fundamental particles exist and also gave up on any 
microscopic quantum theory that involved pointlike particles and the 
quantum fields associated with them. Instead, he assumed that all of 
the observed strongly interacting particles were not pointlike, but com-
plicated, bound states of other particles. In this sense, there could be 
no reduction to primary fundamental objects. In this Zen-like picture, 
appropriate to Berkeley in the 196os, all particles were thought to be 
made up of other particles—the so-called bootstrap model, in which no 
elementary particles were primary or special. So this approach was also 
called nuclear democracy. 
While this approach captivated many physicists who had given up 
on quantum field theory as a tool to describe any interactions other 
than the simple ones between electrons and photons, a few scientists 
were sufficiently impressed by the success of quantum electrodynam-
ics to try to mimic it in a theory of the strong nuclear force—or strong 
interaction, as it has become known—along the lines earlier advocated 
by Yang and Mills. 
One of these physicists, J. J. Sakurai, published a paper in 1960 rather 
ambitiously titled "Theory of Strong Interactions." Sakurai took the 
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193 
Yang-Mills suggestion seriously and tried to explore precisely which 
photonlike particles might convey a strong force between protons and 
neutrons and the other newly observed particles. Because the strong 
interaction was short-range—spanning just the size of the nucleus at 
best—it seemed the particles required to convey the force would be 
massive, which was incompatible with any exact gauge symmetry. But 
otherwise, they would have many properties similar to the photon's, 
having spin i, or a so-called vector spin. The new predicted particles 
were thus dubbed massive vector mesons. They would couple to vari-
ous currents of strongly interacting particles similar to the way photons 
couple to currents of electrically charged particles. 
Particles with the general properties of the vector mesons predicted 
by Sakurai were discovered experimentally over the next two years, and 
the idea that they might somehow yield the secret of the strong interac-
tion was exploited to try to make sense of the otherwise complex inter-
actions between nucleons and other particles. 
In response to this notion that some kind of Yang-Mills symmetry 
might be behind the strong interaction, Murray Gell-Mann developed 
an elegant symmetry scheme he labeled in a Zen-like fashion the Eight-
fold Way. It not only allowed a classification of eight different vector me-
sons, but also predicted the existence of thus-far-unobserved strongly 
interacting particles. The idea that these newly proposed symmetries 
of nature might help bring order to what otherwise seemed a hopeless 
menagerie of elementary particles was so exciting that, when his pre-
dicted particle was subsequently discovered, it led to a Nobel Prize for 
Gell-Mann. 
But Gell-Mann is remembered most often for a more fundamen-
tal idea. He, and independently George Zweig, introduced what Gell-
Mann called quarks—a word borrowed from James Joyce's Finnegans 
Wake—which would physically help explain the symmetry properties 
of his Eightfold Way. If quarks, which Gell-Mann viewed simply as a 
nice mathematical accounting tool (just as Faraday had earlier viewed 
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his proposal of electric and magnetic fields), were imagined to comprise 
all strongly interacting particles such as protons and neutrons, the sym-
metry and properties of the known particles could be predicted. Once 
again, the smell of a grand synthesis that would unify diverse particles 
and forces into a coherent whole appeared to be in the air. 
I cannot stress how significant the quark hypothesis was. While 
Gell-Mann did not advocate that his quarks were real physical parti-
cles inside protons and neutrons, his categorization scheme meant that 
symmetry considerations might ultimately determine the nature not 
only of the strong interaction, but of all fundamental particles in nature. 
However, while one sort of symmetry might govern the structure of 
matter, the possibility that this symmetry might be extended to some 
kind of Yang-Mills gauge symmetry that would govern the forces be-
tween particles seemed no closer. The nagging problem of the observed 
masses of the vector mesons meant that they could not truly reflect any 
underlying gauge symmetry of the strong interaction in a way that could 
unambiguously determine its form and potentially ensure that it made 
quantum-mechanical sense. Any Yang-Mills extension of quantum elec-
trodynamics required the new photonlike particles to be massless. Period. 
Faced with this apparent impasse, an unexpected wake-up call from 
superconductivity provided another, more subtle, and ultimately more 
profound, possibility. 
The first person to stir the embers was a theorist who worked di-
rectly in the field of condensed matter physics associated with super-
conductivity in materials. Philip Anderson, at Princeton, later a Nobel 
laureate for other work, suggested that one of the most fundamental, 
ubiquitous phenomena in superconductors might be worth exploring in 
the context of particle physics. 
One of the most dramatic demonstrations one can perform with su-
perconductors, especially the new high-temperature superconductors that 
allow superconductivity to become manifest at liquid-nitrogen tempera-
tures, is to levitate a magnet above the superconductor as shown below: 
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195 
Pnotopapn biPm 
This is possible for a reason discovered in an experiment in 1933 by 
Walther Meissner and colleagues, explained by theorists Fritz and Heinz 
London two years later, which goes by the name the Meissner effect. 
As Faraday and Maxwell discovered sixty years earlier, electric 
charges respond in different ways to magnetic and electric fields. In par-
ticular, Faraday discovered that a changing magnetic field can cause a 
current to flow in a distant wire. Equally important, but which I didn't 
emphasize earlier, is that the resulting current will flow in a way that 
produces a new magnetic field in a direction that counters the changing 
external magnetic field. Thus, if the external field is decreasing, the cur-
rent generated will produce a magnetic field that counters that decrease. 
If it is increasing, the current generated will be in an opposite direction, 
producing a magnetic field that works to counter that increase. 
You may have noticed that when you are talking on your cell phone 
and get in certain elevators, particularly ones in which the outer part of 
the elevator cage is encased in metal, when the door closes your call gets 
dropped. This is an example of something called a Faraday cage. Since 
the phone signal is being received as an electromagnetic wave, the metal 
shields you from the outside signal because currents flow in the metal 
in a way that counters the changing electric and magnetic fields in the 
signal, diminishing its strength inside the elevator. 
If you had a perfect conductor, with no resistance, the charges in the 
metal could essentially cancel any effects of the outside changing elec-
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tromagnetic field. No signal of these changing fields—i.e., no telephone 
signal—would remain to be detected inside the elevator. Moreover, a 
perfect conductor will also shield out the effects of any constant exter-
nal electric field, since the charges can realign in the superconductor in 
response to any field and completely cancel it out. 
But the Meissner effect goes beyond this. In a superconductor, all 
magnetic fields—even constant magnetic fields such as those due to the 
magnet above—cannot penetrate into the superconductor. This is be-
cause, when you slowly bring a magnet in closer from a large distance, 
the superconductor generates a current to counter the changing mag-
netic field that increases as the magnet approaches. But since the mate-
rial is superconducting, the current continues to flow and does not stop 
if you stop moving the magnet. Then as you bring the magnet in closer, 
a larger current flows to counter the new increase. And so on. Thus, 
because electric currents can flow without dissipation in a supercon-
ductor, not only are electric fields shielded, but so are magnetic fields. 
This is why magnets levitate above superconductors. The currents in the 
superconductor expel the magnetic field due to the external magnet, 
and this repels the magnet just as if another magnet were at the surface 
of the superconductor with north pole facing north pole or south pole 
facing south pole. 
The London brothers, who first attempted to explain the Meissner 
effect, derived an equation describing this phenomenon inside a su-
perconductor. The result was suggestive. Each different type of super-
conductor would create a unique characteristic length scale below the 
surface of the superconductor—determined by the microscopic nature 
of the supercurrents that are created to compensate any external field—
and any external magnetic field would be canceled on this length scale. 
This is called the London penetration depth. The depth is different for 
different superconductors and depends on their detailed microphysics 
in a way the brothers couldn't determine since they didn't have a micro-
scopic theory of superconductivity at the time. 
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Nevertheless, the presence of a penetration depth is striking because 
it implies that the electromagnetic field behaves differently inside a su-
perconductor—it is no longer long-range. But if electromagnetic fields 
become short-range inside the surface, then the carrier of electromag-
netic forces must behave differently. The net effect? The photon behaves 
as if it has mass inside the superconductor. 
In superconductors, virtual photons—and the electric and magnetic 
fields they mediate—can only propagate below the surface through a 
distance comparable to the London penetration depth, just as would be 
the case if electromagnetism inside the superconductor resulted from 
the exchange of massive—not massless—photons. 
Now imagine what it would be like to live inside a superconductor. 
To you, electromagnetism would be a short-range force, photons would 
be massive, and all the familiar physics that we associate with electro-
magnetism as a long-range force would disappear. 
I want to emphasize how remarkable this is. No experiment you 
could perform within the superconductor, as long as it remained su-
perconducting, would reveal that photons are massless in the outside 
world. If you were Plato's philosopher inside such a superconductor, you 
would have to intuit an incredible amount about the outside world be-
fore you could infer that a mysterious and invisible phenomenon was 
the cause of an illusion. It might take several thousand years of thinking 
and experiment before you or your descendants could guess the nature 
of the reality underlying the shadow world in which you live, or be-
fore you could build a device with enough energy to break apart Cooper 
pairs and melt the superconducting state, restoring electromagnetism 
to its normal form, and revealing the photon to be massless. 
In retrospect, we physicists might have expected, just on the grounds 
of symmetry, and without considering the Meissner effect directly, that 
photons should behave as massive particles inside a superconductor. The 
Cooper-pair condensate, being made of electron pairs, has a net electric 
charge. This breaks the gauge symmetry of electromagnetism because 
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in this background any positive charges one adds to the material will 
behave differently from negative charges added to the material. So now 
there is a real distinction between positive and negative. But recall that 
the masslessness of photons is a sign that the electromagnetic field is 
long-range, and the long-range nature of the electromagnetic field re-
flects that it allows local variations in the definition of electric charge 
in one place to not affect the physics globally throughout the material. 
But if gauge invariance is gone, then local variations in the definition of 
electric charge will have a real physical effect, so there can be no such 
long-range field that cancels out such variations. One way to get rid of a 
long-range field is to make the photon massive. 
Now the $64,000 question: Could something like this happen in the 
world in which we find ourselves living? Could the masses of heavy pho-
tonlike particles arise because we are actually living in something akin 
to a cosmic superconductor? This was the fascinating question that An-
derson raised, at least by analogy with regular superconductors. 
Before we can answer this question, we need to understand a techni-
cal bit of wizardry that allows the generation of mass for a photon in a 
superconductor. 
Recall that in an electromagnetic wave the electric (E) and magnetic 
(B) fields oscillate back and forth in directions that are perpendicular to 
the direction of the wave, as shown: 
Since there are two perpendicular directions, one could draw an 
electromagnetic wave in two ways. The wave could look like that shown 
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199 
above, or one could interchange the E and B fields. This reflects that 
electromagnetic waves have two degrees of freedom, which are called 
two different polarizations. 
This arises from the gauge invariance of electromagnetism, or equiv-
alently from the masslessness of photons. If, however, photons had a 
mass, then not only would gauge invariance be broken, but a third pos-
sibility can arise. The electric and magnetic fields could oscillate along 
the direction of motion, instead of just oscillating perpendicular to this 
direction. (Since the photons will no longer be traveling at the speed of 
light, oscillations along the direction of motion of the particles become 
possible.) 
But this means that the corresponding massive photons would have 
three degrees of freedom, not just two. How can photons pick up this 
extra degree of freedom in superconductors? 
Anderson explored this issue in superconductors, and its resolution 
is intimately related to a fact that I described earlier. In the absence of 
electromagnetic interactions in a superconductor, it's possible to pro-
duce slight spatial variations in the Cooper-pair condensate that would 
have arbitrarily small energy cost because Cooper pairs would not in-
teract with each other. However, when electromagnetism is taken into 
account, those low-energy modes (which would destroy superconduc-
tivity) disappear precisely because of the interactions of the charges in 
the condensate with the electromagnetic field. That interaction causes 
photons in the superconductor to behave as if they are massive. The new 
polarization mode of the massive photons in the superconductor comes 
about as the condensate oscillates in response to the passing electro-
magnetic wave. 
In particle physics language, the massless Nambu-Goldstone modes 
that correspond to the particle version of the otherwise vanishingly 
small energy oscillations in the condensate get "eaten" by the electro-
magnetic field, giving photons a mass, and a new degree of freedom, 
making the electromagnetic force short-range in the superconductor. 
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Anderson suggested that this phenomenon—whereby the other-
wise massless photon disappears in superconductors and the otherwise 
massless Nambu-Goldstone mode also disappears, and the two combine 
to produce a massive photon—might be relevant for the long-standing 
problem of creating massive Yang-Mills photonlike particles that might 
be associated with strong nuclear forces. 
Anderson stopped short at this point and left hanging the suggestion 
that this mechanism, motivated by analogy to superconductors, might 
be applicable in particle theory. Just as when Nambu had stopped short 
by considering spontaneous symmetry breaking in particle physics using 
the analogy of superconductivity but did not exploit the phenomenon 
associated with superconductivity that Anderson later focused on—the 
Meissner effect that gives mass to photons in superconductors—the ex-
plicit application of all these ideas to particle physics was yet to occur. 
As a result, the possible profound implications of superconductiv-
ity for understanding fundamental particle physics were not immedi-
ately recognized by the physics community and remained hidden in the 
shadows. 
Still, the notion that we might live in some kind of cosmic supercon-
ductor stretches credulity. After all, humans are capable of generating 
wild stories to explain what is otherwise not understood, inventing fan-
tastical and hidden causes, such as gods and demons. Was the claimed 
existence of some hidden condensate of fields throughout space to ex-
plain the nature of what were otherwise inexplicable strong nuclear 
forces any more plausible? 
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Chapter 16 
THE BEARABLE HEAVINESS 
OF BEING: SYMMETRY 
BROKEN, PHYSICS FIXED 
Gather up the fragments that remain, that 
nothing be lost. 
-JOHN 6:12 
There is remarkable poetry in nature, as there often is in 
human dramas. And in my favorite epic poems from ancient Greece, 
written even as Plato was writing about his cave, there emerges a com-
mon theme: the discovery of a beautiful treasure previously hidden from 
view, unearthed by a small and fortunate band of unlikely travelers, who, 
after its discovery, are changed forever. 
Oh, to be so lucky. That possibility drove me to study physics, be-
cause the romance of possibly discovering some new and beautiful hid-
den corner of nature for the first time had an irresistible allure. This 
story is all about those moments when the poetry of nature merges with 
the poetry of human existence. 
Much poetry exists in almost every aspect of the episodes I am about 
to describe, but to see it clearly requires the proper perspective. Today, 
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in the second decade of the twenty-first century, we might easily agree 
about which of the great theories of the twentieth century are most 
beautiful. But to appreciate the real drama of the progress of science, 
one has to understand that, at the time they are proposed, beautiful 
theories often aren't as seductive as they are years later—like a fine wine, 
or a distant love. 
So it was that the ideas of Yang and Mills, and Schwinger and the 
rest, based on the mathematical poetry of gauge symmetry, failed at the 
time to inspire or compete with the idea that quantum field theory, with 
quantum electrodynamics as its most beautiful poster child, wasn't a 
productive approach to describe the other forces in nature—the weak 
and strong nuclear forces. For forces such as these, operating on short 
ranges appropriate to the scale of atomic nuclei, many felt that new rules 
must apply, and that the old techniques were misplaced. 
So too the subsequent attempts by Nambu and Anderson to apply 
ideas from the physics of materials—called many-body physics, or con-
densed matter physics—to the subatomic realm were dismissed by 
many particle physicists, who deeply distrusted whether this emerg-
ing field could provide any new insights for "fundamental" physics. The 
skepticism in the community was expressed by the delightful theorist 
Victor Weisskopf, who was reported to have said at a seminar at Cornell, 
"Particle physicists are so desperate these days that they have to bor-
row from the new things coming up in many-body physics.... Perhaps 
something will come of it." 
There was some basis for the skepticism. Nambu had, after all, ar-
gued that spontaneous symmetry breaking might explain the large and 
similar masses of protons and neutrons, and he hoped it might do so 
while explaining why the pion was so much lighter. But the ideas he bor-
rowed had at their foundation the understanding that the hallmark of 
spontaneous symmetry breaking was the existence of exactly massless, 
not very light, particles. 
Anderson's work was also interesting, to be sure. But because it 
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203 
was written down in the context of a nonrelativistic condensed matter 
setting—combined with its violating Goldstone's theorem from particle 
physics, which implied that symmetry breaking and massless particles 
were inseparable—meant that his claim that massless states disap-
peared in his example—in electromagnetism in superconductors—was 
largely also ignored by particle physicists. 
Julian Schwinger, however, had not given up the idea that a Yang-
Mills gauge theory might explain nuclear forces, and he had continued 
to argue that the Yang-Mills versions of photons could be massive, albeit 
without demonstrating how this could come to pass. 
Schwinger's work caught the attention of a mild-mannered young 
British theorist, Peter Higgs, who was then a lecturer in mathemati-
cal physics at the University of Edinburgh. A gentle soul, no one would 
imagine him to be a revolutionary. But reluctant revolutionary he was, 
although, due to some shortsighted journal editors, he almost didn't get 
the chance. 
In 1960 Higgs had just taken up his post and had been asked to 
serve on the committee that coordinated the first Scottish Universities 
Summer School in Physics. This became a venerable school, devoted to 
different areas of physics. Every four years or so, during three weeks, ad-
vanced graduate students and young postdocs would attend lectures on 
particle physics by senior scientists amid meals lubricated by fine wine 
and, afterward, hearty whiskey. Among the students that year were the 
future Nobelists Sheldon Glashow and Martinus Veltman, and Nicola 
Cabibbo, who in my opinion should also have won the prize. Apparently 
Higgs, who had been made the wine steward, noticed that these three 
students never made the morning lectures. They apparently spent the 
evenings debating physics while drinking wine that they sneaked out of 
the dining room during meals. Higgs didn't have the opportunity to join 
the discussions then and therefore didn't learn from Glashow about his 
novel proposal for unifying the electromagnetic and weak forces, which 
he had already submitted for publication. 
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The Scottish summer schools have a poetry of their own. They rotate 
around the country and periodically return to the beautiful coastal city 
of St. Andrews, right next to the famous Old Course, the birthplace of 
golf. In 1980 at St. Andrews, Glashow, fresh from having won a Nobel 
Prize, and Gerardus 't Hooft, a famous former student of Veltman's, lec-
tured at the school, and I was privileged to attend as a graduate student. 
I arrived late and got the smallest room, up in an attic overlooking 
the Old Course, and enjoyed not only the physics, but also the alcohol, 
as well as being fleeced for free drinks by one of the lecturers, Oxford 
physicist Graham Ross, at a miniature-golf putting range next door 
nicknamed the Himalayas, for good reason. Besides being a physicist of 
almost otherworldly ability, 't Hooft is also a remarkable artist. He won 
the 1980 summer school's annual T-shirt design contest, and I still have 
my autographed 't Hooft T-shirt. Can't bear to part with it, even as eBay 
beckons. (Twenty years after that program, in z000, I returned to the 
summer school, but this time as a lecturer. Unlike Glashow, 't Hooft, 
Veltman, and Higgs, I didn't return with a Nobel Prize, but I finally got 
to wear a kilt. Another bucket-list item ticked.) 
Following Higgs's stint at the summer school in 1960, he began to 
study the literature on symmetry and symmetry breaking, examin-
ing the work of Nambu, Goldstone, Salam, Weinberg, and Anderson. 
Higgs became depressed by the seemingly hopeless task of reconciling 
Goldstone's theorem with the possibility of massive Yang-Mills vector 
particles that might mediate the strong force. Then in 1964, the magical 
year when Gell-Mann introduced quarks, Higgs read two papers that 
gave him hope. 
First was a paper by Abraham Klein and Ben Lee—who, before he 
died in a car crash while driving to a physics meeting, was one of the 
brightest upcoming particle physicists in the world. They suggested a 
way to avoid Goldstone's theorem and get rid of otherwise unobserved 
massless particles in quantum field theories. 
Next, Walter Gilbert, a young physicist at Harvard who would soon 
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206 
decide to leave the confusion dominating particle physics for the greener 
pastures of molecular biology—where he too would win a Nobel Prize, 
in this case for helping to develop DNA-sequencing techniques—wrote 
a paper showing that the proposed solution of Klein and Lee's appeared 
to introduce a conflict with relativity and therefore was suspect. 
As we've seen, gauge theories have the interesting property that you 
can arbitrarily change the definition of positive versus negative charges 
at each point in space without changing any of the observable physical 
properties of the system, as long as you allow the electromagnetic field 
to have the interactions it has and to also change in a way that prop-
erly accounts for this new local variation. As a result, you can perform 
mathematical calculations in any gauge—that is, using any specific local 
definitions of charges and fields consistent with the symmetry. A sym-
metry transformation will take you from one gauge to another. 
Even though the theory might look quite different in these differ-
ent gauges, the symmetry of the theory ensures that calculations of any 
physically measurable quantity are independent of the gauge choice—
namely that the apparent differences are illusions that do not reflect the 
underlying physics that determines the measured values of all physically 
observable quantities. Thus one could choose whichever gauge made 
the calculation easier to do and expect to arrive at the same predictions 
for physically observable quantities by calculating in any other gauge. 
As Higgs read Schwinger's papers, Higgs realized that some gauge 
choices could appear to have the same conflict with relativity that Gil-
bert had pointed out as plaguing Klein and Lee's proposal. But this ap-
parent conflict was simply an artifact of that choice of gauge. In other 
gauges it disappeared. Therefore it didn't reflect any real conflict with 
relativity when it came to making physical predictions that could be 
tested. Maybe in a gauge theory Klein and Lee's proposal for getting rid 
of massless particles associated with spontaneous symmetry breaking 
might be workable after all. 
Higgs concluded that spontaneous symmetry breaking in a quantum 
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THE GREATEST STORY EVER TOLD-SO FAR 
field theory setting involving a gauge symmetry might obviate Goldstone's 
theorem and produce a mass for vector bosons that might mediate the 
strong nuclear force without any leftover massless particles. This would 
correlate with Anderson's finding of electromagnetism in superconduc-
tors in the nonrelativistic case. In other words, the strong force could be a 
short-range force because of spontaneous symmetry breaking. 
Higgs worked for a weekend or two to write down a model adding 
electromagnetism to the model Goldstone had used to explore sponta-
neous symmetry breaking. Higgs found just what he had expected: the 
otherwise massless mode that would have been predicted by Goldstone's 
theorem became instead the additional polarization degree of freedom 
of a now massive photon. In other words, Anderson's nonrelativistic ar-
gument in superconductors did carry over to relativistic quantum fields. 
The universe could behave like a superconductor after all. 
When Higgs wrote up his result and submitted it to the European 
journal Physics Letters, the paper was promptly rejected. The referee sim-
ply didn't think it was relevant to particle physics. So, Higgs added some 
passages commenting on possible observable consequences of his idea 
and submitted it to the US journal Physical Review Letters. In particular, 
he added, "It is worth noting that an essential feature of this type of theory 
is the prediction of incomplete multiplets of scalar and vector bosons." 
In English this means that Higgs demonstrated that while one could 
remove the massless scalar particle (aka Goldstone boson) in favor of a 
massive vector particle (massive photon) in his model, there would also 
exist a leftover massive scalar (i.e., spinless) boson particle associated 
with the field whose condensate broke the symmetry in the first place. 
The Higgs boson was born. 
Physical Review Letters promptly accepted the paper, but the referee 
asked Higgs to comment on the relation of his paper to a paper by Fran-
cois Englert and Robert Brout that had been received by the journal a 
month or so earlier. Much to Higgs's surprise, they had independently ar-
rived at essentially the same conclusions. Indeed, the similarity between 
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