Lawrence Krauss - The Greatest Story Ever Told--So Far

by Why Are We Here (pdf)

  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

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  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.

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  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

  ͞�
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  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