The Greatest Story Ever Told—So Far

by Lawrence M. Krauss

  For these reasons, among others, the Yang-Mills paper made far less of a stir at the time than the later Yang and Lee opus. To most physicists it was an interesting curiosity at best, and the discovery of parity violation seemed much more exciting.

  But not to Julian Schwinger, who was no ordinary physicist. A child prodigy who had graduated from university by the age of eighteen, he received his PhD by the age of twenty-one. Perhaps no two physicists could have been as different as he and Richard Feynman, who shared the Nobel Prize in 1965 for their separate but equivalent work developing the theory of quantum electrodynamics. Schwinger was refined, formal, and brilliant. Feynman was brilliant, casual, and certainly not refined. Feynman relied often on intuition and guesswork, building on prodigious mathematical skill and experience. Schwinger’s mathematical skill was every bit Feynman’s equal, but Schwinger worked in an orderly fashion, manipulating complicated mathematical expressions with an ease not possible for ordinary mortals. He joked about Feynman diagrams, which Feynman had developed to make what had previously been perilously laborious calculations in quantum field theory manageable, saying, “Like the silicon chips of more recent years, the Feynman diagram was bringing computation to the masses.” Both of them shared one characteristic, however. They marched to the beat of a different drummer . . . in opposite directions.

  Schwinger took the Yang-Mills idea seriously. The mathematical beauty must have appealed to him. In 1957, the same year that parity violation was discovered, Schwinger made a bold and seemingly highly unlikely suggestion that the weak interaction responsible for the decay of neutrons into protons, electrons, and neutrinos might benefit from the possibility of Yang-Mills fields, but in a new and remarkable way. He proposed that the observed gauge symmetry of electromagnetism might simply be one part of a larger gauge symmetry in which new gauge particles might mediate the weak interaction that caused neutrons to decay.

  An obvious objection to this kind of unification is that the weak interaction is far weaker than electromagnetism. Schwinger had an answer for this. If somehow the new gauge particles were very heavy, almost one hundred times heavier than protons and neutrons, then the interaction they might mediate would be of much shorter range than even the size of a nucleus, or even a single proton or neutron. In this case, one could work out that the probability that this interaction would cause a neutron to decay would be small. Thus, if the range of the weak interaction was small, these new fields, the strength of whose intrinsic coupling to electrons and protons on small scales could be comparable to the strength of electromagnetism, could nevertheless, on the scale of nuclei and larger, appear to be much, much weaker.

  Put more bluntly, Schwinger proposed the outrageous idea that electromagnetism and the weak interaction were part of a single Yang-Mills theory, in spite of the remarkable and obvious differences between them. He thought that perhaps the photon could be the neutral member of a Yang-Mills-type set of three gauge particles required by treating isotopic spin as a gauge symmetry, with the charged versions conveying the weak interaction and being responsible for mediating the decay of neutrons. Why the charged particles would have a huge mass while the photon was massless, he had no idea. But, as I have often said, lack of understanding is neither evidence for God, nor evidence that one is necessarily wrong. It just is evidence of lack of understanding.

  Schwinger was not only a brilliant physicist but a brilliant teacher and mentor. While Feynman had few successful students, probably because none of them could keep up with him, Schwinger seemed to have a knack for guiding brilliant PhD students. In his life he supervised more than seventy PhDs, and four of his students later won the Nobel Prize.

  Schwinger was sufficiently interested in relating the weak interaction to electromagnetism that he encouraged one of his dozen graduate students at Harvard at the time to explore the issue. Sheldon Glashow graduated in 1958 with a thesis on the subject and continued to explore the issue for the next few years as a National Science Foundation postdoctoral researcher in Copenhagen. In his Nobel lecture twenty years later, Glashow indicated that he and Schwinger had planned to write a manuscript on the subject after Glashow graduated, but one of them lost the first draft of the manuscript, and they never got back to it.

  Glashow was no clone of Schwinger’s. Refined and brilliant, yes, but also brash, playful, and boisterous, Glashow did research that was not characterized by mathematical acrobatics, but rather by a keen focus on physical puzzles and exploring new possible symmetries of nature that might resolve them.

  When I was a young graduate student in physics at MIT, I was initially drawn to deep mathematical questions in physics and had written my admissions essay for my PhD application on just this subject. Within a few years I found myself depressed by the nature of the mathematical investigations I was pursuing. I met Glashow at a summer school for PhD students in Scotland and became friends with both him and his family—a friendship that continued to blossom when we later became colleagues at Harvard. The year after we met, he spent a sabbatical year at MIT. During this important time for me, when I was considering alternatives, he said to me, “There’s physics, and there’s formalism, and you have to know the difference.” Implicit in this advice was the suggestion that I should pursue physics. When I saw the fun he was having, it became easier to consider joining in.

  I soon realized that for me to make progress in physics I needed to work on questions driven primarily by physical issues, not ones driven primarily by mathematical issues. The only way I could do that would be to keep in touch with ongoing experiments—and new experimental results. By watching Shelly and how he did physics, I realized that he had an uncanny ability to know which experiments were interesting, and which results might be significant or might point toward something new. Part of this was undoubtedly innate, but part was based on a lifetime of keeping in touch with what was happening on the ground. Physics is an empirical science, and we lose touch with that at our peril.

  In Copenhagen, Glashow realized that if he wanted to properly implement Schwinger’s proposal to connect the weak interaction with the electromagnetic interaction, then simply making the photon be the neutral member of a triplet of gauge particles, with the charged members becoming massive by some as yet unknown miracle, wouldn’t fly. This couldn’t explain the proper nature of the weak interaction, in particular the strange fact that the weak interaction seemed to apply only to left-handed electrons (and neutrinos), whereas electromagnetic interactions don’t depend on whether the electrons are left- or right-handed.

  The only solution to this problem would be if another neutral gauge particle existed—in addition to the photon—which itself coupled to only left-handed particles. But clearly the new neutral particle would also have to be heavy since the interactions it mediated would have to be weak as well.

  Glashow’s ideas were reported to the physics community by Murray Gell-Mann at the 1960 Rochester meeting, as Gell-Mann had by then recruited Glashow to Caltech to work in Gell-Mann’s group. Glashow’s paper on the subject, submitted in 1960, appeared in 1961 in print. Yet, no sudden stampede occurred in response.

  After all, two fundamental problems remained with Glashow’s proposal. The first was the long-familiar problem of how one could have the different masses of the particles needed to convey the different forces, when gauge symmetries required all the gauge particles to be massless. Glashow simply stated in the introduction of his paper, following in a long line of such hubris, “It is a stumbling block we must overlook.”

  The second problem was more subtle, but from an experimental perspective equally severe. Neutron decay, pion decay, and muon decay, if they were indeed mediated by some new particles conveying the weak force, all appeared to require only the exchange of new charged particles. No weak interaction had been observed that would require the exchange of a new neutral particle. If such a new neutral particle did exist, calculations at the time suggested it would allow the other known heavier mesons that decayed i
nto two or three pions (and were responsible for the original confusion that led to the discovery of parity violation) to decay much more rapidly than they were observed to decay.

  For these reasons, Glashow’s proposal drifted into the background as physicists became entranced with the new particle zoo that was emerging out of accelerators, and the concomitant opportunity for new discoveries. Yet several of the key theoretical ingredients needed to complete a revolution in fundamental physics were in place, but it was far from obvious at the time. That within slightly more than a decade after Glashow’s paper was published all of the known forces in nature save gravity would be unveiled and understood would have seemed like pure fantasy at the time.

  And symmetry would be the key.

  Chapter 14

  * * *

  COLD, STARK REALITY: BREAKING BAD OR BEAUTIFUL?

  From whose womb has come the ice? And the frost of heaven, who has given it birth?

  —JOB 38:29

  It is easy to pity the poor protagonists in Plato’s cave, who may understand everything there is to know about the shadows on the wall, except that they are shadows. But appearances can be deceiving. What if the world around us is just a similar shadow of reality?

  Imagine, for example, that you wake up one cold winter morning and look out your window, and the view is completely obscured by beautiful ice crystals, forming strange patterns on the glass. It might look like this:

  Photograph by Helen Filatova

  The beauty of the image is striking at least in part because of the remarkable order on small scales lurking within the obvious randomness on large scales. Ice crystals have grown gorgeous treelike patterns, starting in random directions and bumping into each other at odd angles. The dichotomy between small-scale order and large-scale randomness suggests that the universe would look very different to tiny physicists or mathematicians confined to live on the spine of one of the ice crystals in the image.

  One direction in space, corresponding to the direction along the spine of the ice crystal, would be special. The natural world would appear to be oriented around that axis. Moreover, given the crystal lattice structure, electric forces along the spine would appear to be quite different from the forces perpendicular to it: the forces would behave as if they were different forces.

  If the physicist or mathematician living on the crystal was clever, or, like the mathematician in Plato’s cave, lucky enough to leave the crystal, it would soon become clear that the special direction that governed the physics of the world they were used to was an illusion. They would find, or surmise, that other crystals could point in many other directions. Ultimately if they could observe the window from the outside on large enough scales, the underlying symmetry of nature under rotations in all directions, reflected in the growth of the crystals in all directions, would become manifest.

  The notion that the world of our experience is a similar accident of our particular circumstances rather than a direct reflection of underlying realities has become central to modern physics. We even give it a fancy name: spontaneous symmetry breaking.

  I mentioned one sort of spontaneous symmetry breaking earlier when discussing parity, or left-right symmetry. Our left hands look different from our right hands even though electromagnetism—the force that governs the building of large biological structures such as our bodies—doesn’t distinguish between left and right.

  Two other examples I know of, both presented by distinguished physicists, also help illuminate spontaneous symmetry breaking in different ways that might be useful. Abdus Salam, who won a Nobel Prize in 1979 for work that depended crucially on this phenomenon, described a situation that is familiar to all of us: sitting down with a group of people at a round dining table set for, say, eight people. When you sit down, it may not be obvious which wineglass is yours and which is your neighbor’s—the one on the right or the one on the left. But regardless of the laws of etiquette, which dictate it should be on your right, once the first person picks up her glass, everyone else at the table has only one option if everyone is to get a drink. Even though the underlying symmetry of the table is manifest, the symmetry gets broken when a direction is chosen for the wineglasses.

  Yoichiro Nambu, another Nobelist who was the first physicist to describe spontaneous symmetry breaking in particle physics, gave another example that I will adapt here. Take a rod, or even a drinking straw, hold it up with one end on a table, and press down on the top end of the rod. Ultimately the rod will bend. It could bend in any direction, and if you try the experiment several times, you may find it bending in different directions each time. Before you press down, the rod has complete cylindrical symmetry. Afterward, one direction among many possibilities has been chosen, not determined by the underlying physics of the rod but by the accident of the particular way you press on the rod each time. The symmetry has been broken spontaneously.

  If we now return to the world of the frozen window, the characteristics of materials can change as we cool systems down. Water freezes, gases liquefy, and so on. In physics, such a change is called a phase transition, and as the window example demonstrates, whenever a system undergoes a phase transition, it is not unusual to find that symmetries associated with one phase will disappear in the other phase. Before the ice froze into the crystals on the window, the water droplets wouldn’t have been so ordered, for example.

  One of the most astonishing phase transitions ever witnessed in science was first observed by the Dutch physicist Kamerlingh Onnes on April 8, 1911. Onnes had—remarkably—been able to cool materials to temperatures never before achieved, and he was the first person to liquefy helium, at just four degrees above absolute zero. For this experimental prowess he was later awarded a Nobel Prize. On April 8, when cooling a mercury wire down to 4.2 degrees above absolute zero in a liquid helium bath and measuring its electrical resistance, to his astonishment he discovered that the resistance suddenly dropped to zero. Currents could flow in the wire indefinitely once they began, even after any battery that started the flow was removed. Demonstrating that his talent for public relations was as astute as his experimental talents, he coined the term superconductivity to describe this remarkable and completely unexpected result.

  Superconductivity was so unexpected and strange that it would take almost fifty years after the discovery of quantum mechanics, on which it depends, before a fascinating physics explanation was developed by the team of John Bardeen, Leon Cooper, and Robert Schrieffer, in 1957. (That was same year that parity violation was observed, and that Schwinger proposed a model to try to unify the weak and electromagnetic interaction.) Their work was a tour de force, built on a succession of insights made over several decades of work. Ultimately the explanation relies on an unexpected phenomenon that can only occur in certain materials.

  In empty space, electrons repel other electrons because like charges repel each other. However, in certain materials, as they are cooled, electrons can actually bind to other electrons. This happens in the material because a free electron tends to attract around it positively charged ions. If the temperature is extremely low, then another electron can be attracted to the positively charged field around the first electron. Pairs of electrons can bind together, with the glue, if you wish, being the positively charged field caused by the attraction of the first electron on the lattice of positive charges associated with the atoms in the material.

  Since the nuclei of atoms are heavy and pinned in place by relatively strong atomic forces, the first electron slightly distorts the lattice of nearby atoms, moving some of the atoms slightly closer to the electron than they would otherwise be. Distortions of the lattice in general cause vibrations, or sound waves, in the material. In the quantum world these vibrations are quantized and are called phonons. Leon Cooper discovered that these phonons can bind pairs of electrons, as I have described above, so these are called Cooper pairs.

  The true magic of quantum mechanics occurs next. When mercury (or any of several other materials) i
s cooled below a certain point, a phase transition occurs and all the Cooper pairs suddenly coalesce into a single quantum state. This phenomenon, called Bose-Einstein condensation, occurs because unlike fermions, particles with integral quantum mechanical spin, such as photons, or even particles with zero spin, instead prefer to all be in the same state. This was proposed first by the Indian physicist Satyendra Nath Bose and later elaborated upon by Einstein. Once again light played a crucial role, as Bose’s analysis involved the statistics of photons, and Bose-Einstein condensation is intimately related to the physics governing lasers, in which many individual photons all behave coherently in the same state. For this reason particles with integral spin such as photons are called bosons, to distinguish them from fermions.

  In a gas or a solid at room temperature, normally so many collisions occur between particles that their individual states are changing rapidly and any collective behavior is impossible. However, a gas of bosons can coalesce at a low enough temperature into a Bose-Einstein condensate, in which the individual particles’ identities disappear. The whole system behaves like a single, sometimes macroscopic, object, but in this case acting via the rules of quantum mechanics, rather than classical mechanics.

  As a result, a Bose-Einstein condensate can have exotic properties, the way laser light can behave very differently from normal light coming from flashlights. Since a Bose-Einstein condensate is a huge amalgamation of what would otherwise be individual noninteracting particles, now tied together into a single quantum state, creating such a condensate required exotic and special atomic physics experiments. The first direct observation of such a condensation from a gas of particles did not take place until 1995, by the US physicists Carl Wieman and Eric Cornell, another feat that was deemed worthy of a Nobel Prize.

  What makes the possibility of such a condensation inside bulk materials such as mercury so strange is that the fundamental particles initially involved are electrons—which not only normally repel other electrons, but in addition have spin ½ and, as fermions, have precisely the opposite behavior of bosons, as I described above.