The Greatest Story Ever Told—So Far

by Lawrence M. Krauss

  But when the Cooper pairs form, the two electrons each act in concert, and since both of them have spin ½, the combined object has integral (2 × ½) spin. Voilà, a new kind of boson is created. The lowest-energy state of the system, to which it relaxes at low temperature, is a condensate of Cooper pairs—all condensed into a single state. When that happens, the properties of the material change completely.

  Before the condensate forms, when a voltage is applied to a wire, individual electrons begin to move to form an electric current. As they bump into atoms along the way, they dissipate energy, producing an electrical resistance that we are all familiar with, and heating up the wire. Once the condensate forms, however, the individual electrons and even each Cooper pair no longer have any individual identity. Like the Borg in Star Trek, they have assimilated into a collective. When a current is applied, the whole condensate moves as one entity.

  Now, if the condensate were to bounce off an individual atom, the trajectory of the whole condensate would change. But this would take a lot of energy, much more than would have been required to redirect the flow of an individual electron. Classically we can think of the result as follows: at low temperatures, not enough heat energy is available in the random jittering of atoms to cause a change of motion of the bulk 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 condensate 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 initiated, will flow forever, even if the battery initially attached to the wire is removed.

  This was the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity, 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 symmetry 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 suddenly, once the condensate of Cooper pairs forms, a large minimum energy 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, has to do with the story we have been focusing on, namely understanding 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 1950s and ’60s the road to enlightenment was not so direct.

  In 1956, Yoichiro Nambu, who had recently moved to the University of Chicago, heard a seminar by Robert Schrieffer on what would become the BCS theory of superconductivity, and it left a deep impression 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 characteristic 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 characteristic 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 symmetry 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 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 consequence of the spontaneous symmetry breaking in the theory of superconductivity that later provided the key to unlock the true mystery of the strong and weak nuclear forces. Nambu’s focus on symmetry breaking was inspired, but the analogies that he and others drew to superconductivity 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 imagine would be the case for those physicists, this myopia was not immediately obvious to the physics community.

  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 benefit of hindsight, but remember that objects viewed in the rearview mirror 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 useful, but largely for reasons very different from what Nambu and others imagined at the time. In hindsight the answer may seem almost obvious, 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-energy threshold was reached, new strongly interacting cousins of neutrons and protons were produced. The process seemed as if it would be endless. This embarrassment of riches meant that both theorists and experiment
alists were driven to focus on the mystery of the strong nuclear force, which seemed to be where the biggest challenge to existing theory lay.

  A potentially infinite number of elementary particles with everhigher masses seemed to characterize the microscopic world. But this was incompatible with all the ideas of quantum field theory—the successful 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 popular, 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 complicated, 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 1960s, 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 electrodynamics 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 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 1, or a so-called vector spin. The new predicted particles were thus dubbed massive vector mesons. They would couple to various 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 interaction was exploited to try to make sense of the otherwise complex interactions 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 Eightfold Way. It not only allowed a classification of eight different vector mesons, 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 predicted particle was subsequently discovered, it led to a Nobel Prize for Gell-Mann.

  But Gell-Mann is remembered most often for a more fundamental 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 his proposal of electric and magnetic fields), were imagined to comprise all strongly interacting particles such as protons and neutrons, the symmetry 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 particles 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 between 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 electrodynamics 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 directly in the field of condensed matter physics associated with superconductivity 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 superconductors, especially the new high-temperature superconductors that allow superconductivity to become manifest at liquid-nitrogen temperatures, is to levitate a magnet above the superconductor as shown below:

  Creative Commons/Photograph by Mai-Linh Doan

  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 particular, 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 current 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 electromagnetic 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 external 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 because, when you slowly bring a magnet in closer from a large distance, the superconductor generates a current to counter the changing magnetic field that increases as the magnet approaches. But since the material 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 l
arger current flows to counter the new increase. And so on. Thus, because electric currents can flow without dissipation in a superconductor, 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 superconductor. The result was suggestive. Each different type of superconductor 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 microscopic theory of superconductivity at the time.

  Nevertheless, the presence of a penetration depth is striking because it implies that the electromagnetic field behaves differently inside a superconductor—it is no longer long-range. But if electromagnetic fields become short-range inside the surface, then the carrier of electromagnetic forces must behave differently. The net effect? The photon behaves as if it has mass inside the superconductor.