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 electromagnetism 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 superconducting, 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 before 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 before 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 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 reflects 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 photonlike particles arise because we are actually living in something akin to a cosmic superconductor? This was the fascinating question that Anderson raised, at least by analogy with regular superconductors.
Before we can answer this question, we need to understand a technical 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 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 equivalently from the masslessness of photons. If, however, photons had a mass, then not only would gauge invariance be broken, but a third possibility 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 produce slight spatial variations in the Cooper-pair condensate that would have arbitrarily small energy cost because Cooper pairs would not interact with each other. However, when electromagnetism is taken into account, those low-energy modes (which would destroy superconductivity) 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 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?
Chapter 16
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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 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 insp
ire 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. Every 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 t
hat 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.
The Greatest Story Ever Told—So Far Page 19