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
electromagnetic 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 electromagnetic field, giving photons a mass, and a new degree
of freedom, making the electromagnetic force short-range in the
superconductor.
Anderson suggested that this phenomenon—whereby the
otherwise 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 explicit
application of all these ideas to particle physics was yet to occur.
As
a
result,
the
possible
profound
implications
of
superconductivity for understanding fundamental particle physics
were not immediately recognized by the physics community and
remained hidden in the shadows.
Still, the notion that we might live in some kind of cosmic
superconductor stretches credulity. After all, humans are capable of
generating wild stories to explain what is otherwise not understood,
inventing fantastical and hidden causes, such as gods and demons.
Was the claimed existence of some hidden condensate of fields
throughout space to explain the nature of what were otherwise
inexplicable strong nuclear forces any more plausible?
͞͝͠
C h a p t e r 1 6
T H E B E A R A B L E H E AV I N E S S
O F
B E I N G :
S Y M M E T RY
B R O K E N, P H YS I C S F I X E D
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
common 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,
because the romance of possibly discovering some new and beautiful
hidden 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, 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
condensed matter physics—to the subatomic realm were dismissed
by many particle physicists, who deeply distrusted whether this
emerging 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 borrow 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,
argued 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 borrowed 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
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 disappeared 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
mathematical 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. E
very four years or so,
during three weeks, advanced 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.
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, lectured 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 2000, 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, examining
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 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 properly 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 symmetry transformation will take
you from one gauge to another.
Even though the theory might look quite different in these
different 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
Gilbert had pointed out as plaguing Klein and Lee’s proposal. But
this apparent 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 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 superconductors 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 spontaneous 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 argument 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
simply 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 François Englert and Robert Brout that had been received
by the journal a month or so earlier. Much to Higgs’s surprise, they
had independently arrived at essentially the same conclusions.
Indeed, the similarity between the papers is made clear by their titles.
Higgs’s paper was called “Broken Symmetries and the Masses of
Gauge Bosons.” The Englert and Brout paper was entitled “Broken
Symmetry and the Mass of Gauge Vector Mesons.” It is hard to
imagine a closer match without coordinating names.
As if to add to the remarkable serendipity, twenty years later
Higgs met Nambu at a conference and learned that Nambu had
refereed both papers. How much more fitting could it be that the
man who first brought the ideas of symmetry breaking and
superconductivity to particle physics should referee the papers of the
people who would demonstrate just how prescient this idea was.
And like Nambu, all of these authors were fixated on the strong
interaction, and on the possibility of figuring out how protons,
neutrons, and mesons could have large masses.
Illustrating that the time was ripe for this discovery, within a
month or so another team, Gerald Guralnik, C. R. Hagen, and Tom
Kibble, also published a paper including many of the same ideas.
You may wonder why we call it the Higgs boson and not the
Higgs-Brout-Englert-Guralnik-Hagen-Kibble boson. Besides the
obvious answer that this label doesn’t trip lightly off the tongue, of
all the papers the only one to explicitly predict an accompanying
massive scalar boson in massive gauge theories with spontaneous
͞͞͝
symmetry breaking was Higgs’s paper. And, interestingly, Higgs only
included the extra remark because the original version of his paper
without that remark had been rejected.
One last bit of poetry. A couple of years after the original paper
was published, Higgs completed a longer paper and was invited (in
1966) to speak at several locations in the USA, where he was
Lawrence Krauss - The Greatest Story Ever Told--So Far Page 23
