I remember the serendipitous early summer day I was driving from Hanover, New Hampshire, to New York City and decided to stop by Brown with the hopes of seeing Professor Cooper. It had been almost a decade since I had seen him in person. I caught wind that he was retiring (but still fully engaged in research, as he still is). During summers, many faculty are traveling to conferences, but when I got to the physics building at Brown, Cooper was there in his spacious office, filled with books and covered with blackboards, doing a calculation. We sat down for a chat. He immediately asked me what I was working on.
I thought that I was going to impress him with my new take on the matter-antimatter asymmetry in the universe. Cooper stopped me and said, “You should find a real problem and solve it. Many people put their hands up in surrender when a problem gets too hard and claim it’s impossible.” I took this to be both a challenge and validating. What might at face value look like Cooper’s rejection of my idea I took instead as him holding me to a higher standard and the expectation to solve a big problem. Even today, I try to live up to my former adviser’s version of tough love with my students—to recognize and help awaken their hidden talents. Up till that point, I was playing it safe and avoiding physics problems that I thought only the most able of physicists should have the permission to work on. I asked Cooper, “How did you solve superconductivity?” What he said gave me some strategies for approaching my own problems.
Cooper went on to tell me that he was trained in another field, theoretical particle physics, and had mastery of the techniques new to that field, such as Feynman diagrams. When he was invited to work with John Bardeen in condensed-matter physics, as the field working on superconductivity was known, he had an unsullied and less-biased take on the nature of the problems those physicists were facing. For one, as we’ve seen in this book, particle physics concerned itself with discovering the nature of subatomic forces by exploiting the quantum scattering processes between elementary and nuclear particles. Solid state environments concern the behavior of billions of interacting electrons in an environment filled with other atoms usually organized in the form of a periodic crystal lattice. Superconductivity was both a conceptual and mathematically technical dragon to slay. One major obstacle was that the problem seemed to require solving the Schrödinger equation for a wave function of billions of electrons interacting with a lattice of metallic atoms—the many-body wave function. No one working on the problem, no matter how technically skilled, has been able to surmount the mathematically crippling wall of solving the many-body wave function. According to Cooper, Bardeen “omitted to mention that practically every famous physicist of the 20th century had worked on the problem and failed.”2
Cooper quickly encountered the daunting and insurmountable equations. On a seventeen-hour trip to New York City, he tirelessly tried his extensive bag of mathematical tricks but got nowhere. He ran out of technical steam and started feeling that the equations were preventing him from seeing the root of the problem. So he decided to step back from the equations and think intuitively about the problem. And then he made a simple and ingenious guess. Part of his mental wizardry was to simplify the problem and avoid unnecessary details, decisions geared toward making the problem more tractable.
As a hint into Cooper’s insight, recall that electrons carry a tiny magnetic pole. This pole can also obstruct their motion, say when they are flowing in a current, due to the magnetic forces of surrounding electrons, which cause deflection and electrical resistance. It seemed that, if superconductivity were going to be possible, then the golden rule that electrons necessarily repelled each other had to be broken. Cooper realized that if the electrons could pair up, with their spins oppositely aligned, then the members of each pair would lose their identity as electrons, and their overall spin would vanish, mitigating the local resistance. An emergent phenomenon, the Cooper pair, was born. But the grouping doesn’t stop there. When all the electrons pair up, they clump together to collectively behave as one object and move in a ghostly fashion through obstructions in the metal. Cooper likened it to a line of ice-skaters, arm in arm: “If one skater hits a bump, she is supported by all the other skaters moving along with [the line].” In other emergent phenomena in condensed matter, this long-range order is a collective behavior of the individual electrons or atoms.
The formation of Cooper pairs led to a handful of other emergent properties in the superconductor. First, in order for the supercurrent to maintain itself, the superconducting environment would have to expel any magnetic field. This observation is known as the Meissner effect and is predicted by the BCS theory—it is the reason magnets levitate above superconductors. The underlying physics in superconductivity was later found in other systems, such as neutron stars. The extremely dense environment of neutron stars enables neutrons to Cooper pair and exhibit the collective behavior of a superconducting fluid, called a superfluid. Another Nobel Prize was awarded to Yoichiro Nambu, who applied the BCS theory to understand the emergence of particles called the pion, which was found to be a Cooper pair of quarks. BCS theory also inspired some of the architects of the standard model of particle physics to think about how mass could emerge from a similar type of symmetry breaking, and we will discuss this in an upcoming chapter.
In a seminal essay entitled “More Is Different,” Nobel laureate Philip Anderson puts emergence at center stage over reductionism in physics: “The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe.… At each stage of [emergence] entirely new laws, concepts, and generalizations are necessary.” Anderson goes on to identify the organizing principle that is behind most emergence in condensed-matter systems, that is, symmetry breaking. When we see symmetries, we often see an underlying pattern of phenomena. For example, in relativity, the space-time symmetry inherent in the laws of motion functions to give relative lengths and time for different moving observers. Emmy Noether proved that symmetries are linked with conservation laws. And symmetry breaking signals new properties that are hidden from the symmetric realm.
To see this, consider a piece of metal, like iron. Like a checkerboard is a repeating arrangement of black and red squares, all metals are repeating periodic arrangements of atoms with electrons waiting to easily flow from one site to the other. At each atomic site the electrons carry a tiny magnetic pole due to their quantum spin. Recall that the quantum spin can either be up or down, reflecting its quantum nature. At high temperatures the billions of the electron spins point in a random direction. If we add all the spins, because of the random orientations, the total spin of the system cancels out to zero. Since the total spin and magnetization is zero there is no preferred direction of all the spins and the system has a symmetry that is invariant under rotations. This means that the iron has a symmetry that is analogous to the symmetry of a sphere. However, as we lower the temperature to a critical value, the spins all on average spontaneously pick a direction, attaining a net magnetic field. This is like balancing a pencil on its tip. As a result, the spherical symmetry is broken by the emergence of magnetism. Not only is magnetism emergent, but the preferred direction that breaks the symmetry creates rigid directions that can support the transmission of magnetic waves. In all the examples in condensed-matter physics, the constituents, such as electrons or other fermions, exhibit cooperative behavior similar to the swarm of ants or bees that collectively perform a task that an individual member cannot accomplish alone.
FIGURE 10: An example of spontaneous symmetry breaking. In image A the forces acting on the pencil have a rotational symmetry. However, this system is unstable because the gravitational force in the z-direction will break the symmetry. In image B the pencil picks a direction, which results in breaking the original rotational symmetry. Any direction could have been selected, and this randomness is a sign of the symmetry being spontaneously broken.
In hindsight it was also discovered that superconductivity emerged from the breaking of an
other type of symmetry, not related to space-time but closer to those found in the fundamental interactions, such as the strong and weak nuclear forces. The principle of emergence and symmetry breaking turns out to be at the heart of important matters in the fundamental forces. As we will explore in the next chapter, the nuclear interactions, such as the weak and strong forces, are governed by symmetries associated with the charges of elementary fields and particles. And the breaking of these symmetries also has essential properties, such as the origin of mass and the emergence of matter over antimatter in our universe. Even stranger is the idea that space and time are also emergent properties. By analogy, these are atoms of space and time whose collective behavior can give rise to the malleable space-time fabric that Einstein discovered.
There has always been a deep interplay between physics and other scientific disciplines like biology, chemistry, and the social sciences, where even more mysterious forms of emergence occur. Does the organizing principle of symmetry breaking seen in physical systems apply to understanding emergence in other domains? Are there other organizing principles that go beyond symmetry breaking? And maybe even beyond physics?
6
IF BASQUIAT WERE A PHYSICIST
The wisdom of John Bardeen, a two-time Nobel laureate, to seek and integrate the outsiders’ perspective of Leon Cooper not only enabled cracking the code of superconductivity but opened the floodgate for breakthroughs in other branches of the physical sciences and technology. If we want to catalyze more solutions to the current mysteries we face, we could try to replicate these examples of scientific inclusivity that Bardeen and others exemplified. These days there is a big push for and rhetoric surrounding diversity and inclusivity in science. But science has fallen short in benefiting from effectively embracing outsiders, or even wanting to do so. Science is carried out by individuals and groups of individuals, and the principle of emergence also acts on scientific societies sustaining forces that act to prevent the full benefits from the contributions and presence of outsiders. In this chapter, we explore through the lens of the science of groups of people—the science of sociology—to see how the scientific community and individuals can inspire and enhance more innovations and innovators. To gain insight into these issues, I present two stories.
SCENE 1
Eleven years ago, Jim Gates, a theoretical physicist with a Frederick Douglass–style ’fro, was the chair of Howard University’s physics department. I considered going to Howard as an undergraduate; it is a prominent, historically Black university with famous alums like Thurgood Marshall, but I opted instead for a private Quaker college. During that time, Howard University made a bold move by poaching a handful of Black physics professors from prominent, predominantly white institutions, and this inspired Gates to move from the University of Maryland. During his time at Howard University, Gates and his colleague Hitoshi Nishino were researching a special symmetry called supersymmetry. Supersymmetry is a theory that attempts to connect the fermions, such as electrons, of our world to the force carriers, such as photons. Although in our experience we see both these fermions and bosons, as the force carriers are called, Gates and Nishino were thinking about a class of particles that we don’t typically experience, known as anyons. Anyons only exist in two-dimensional systems, and they emerge from matter particles, but they enable the violation of a fundamental law that matter can only have integer or half-integer spins. Gates and Nishino’s work was aimed at developing a theory that linked the supersymmetric relationship between fermions and bosons to anyons. Recall that all observed matter has either integer or half-integer quantum spin.1 For example, the electron, a main building block for molecules, has half-integer spin. Gates and Nishino wrote a beautiful set of equations that made these anyons supersymmetric and discovered a surprising feature that the equations were conformally invariant—we won’t go into the details here, but it’s a symmetry that related the microcosm to the macrocosm.2 The result was published in a respectable physics journal and enjoyed a modest number of citations.
In the subsequent eleven years, a theory developed from string theory called M-theory, which attempts to unify all forces, underwent a conceptual revolution—it encoded a property called holography. A holographic theory is one where gravity is encoded in another theory, operating in one fewer dimension, without gravity. For example, gravitational physics in our three spatial dimensions could be holographically encoded in a two-dimensional theory with no gravity. This work was famously christened the ABJM theory, named after the authors, and was, and is, considered one of the most important results in theoretical physics in decades. The four authors much later discovered that the exact supersymmetric and conformal invariant equations that Gates and Nishino derived had a holographic description in M-theory. Many physicists, including me, were not, and still are not, aware of the original equations of Gates and Nishino. To be fair, the authors of ABJM actually cited the Gates-Nishino work, yet it still did not rise to the acclaim that it may have deserved. After all, the equations that ABJM used were the same that Gates and Nishino had derived eleven years earlier. Why did the community not call this theory Gates-Nishino-ABJM? Why did the community not notice the importance of the original Gates-Nishino work?
SCENE 2
After a few months into my second postdoc, I stopped going to my office to work. The dozen or so postdocs in the theory group were very interactive. However, time after time, I found my attempts to interact with my peers were not reciprocated, and were even ignored. One day a good friend, Brian Keating, who was a postdoc at Caltech, was visiting our group. Brian, who is white, pulled me aside and said, “I know what’s going on. I know why you’re not coming to your office. I overheard a conversation with some other postdocs, and they said that they want to punish you.” So, what did I do to them that would warrant punishment by shunning me? My friend volunteered the reason: “They feel that they had to work so hard to get to the top and you got in easily, through affirmative action.” I must admit harboring both disdain for and envy of my postdoctoral colleagues. Most of them grew up with privilege that I did not have and a sense of entitlement that the enterprise of science belonged to people like them. I also presumed that their relationship with physics was different from mine.
For me physics was literally a tool for survival. Reading physics books and solving problems kept me away from the streets of the Bronx. Physics paid my way into college and graduate school, and unlocked the shackles of a likely life of poverty in the Bronx. There were times when I would stay up all night playing with physics problems and equations. Yet, I remain thankful to Brian, because, after that day, I made sure that most of my publications and research over the next three years as a postdoc were independently administered and authored. I did not want to be further penalized by colleagues and peers since I could not change their perception of my not deserving admittance to their elite club. By doing independent work, I felt that it would address the perception of whatever shortcomings may inhibit my future employment. While it was useful to learn how to complete independent work, my strategy still did not erase the perception and treatment that I would receive from colleagues throughout my career.
Because I lacked a feeling of belonging in the group, and so that I could continue to be productive, I moved most of my calculational operations to a café across from Stanford’s computer science department and I worked by myself. In hindsight, this isolation was a blessing in disguise; it forced me to develop my outside-the-box thinking. At the time, the discovery of dark energy—a concept closely related to a parameter in the general theory of relativity known as the cosmological constant—prompted the entire group, including me, to rethink the very foundations of theoretical physics. And because I had just spent two productive years in London at Imperial College, where I had developed an improvisational and visual style of approaching problems coupled with Jungian dream analysis that Chris Isham had trained me in, I was very prepared for some outside-the-box thinking about the issue of dark e
nergy. Once I had developed a clear idea of what I wanted to pursue with those techniques, then I would unleash an arsenal of traditionally mathematical devices that I mastered to develop a model. I naturally kept this atypical research strategy to myself in fear of further stigma.
One morning after forcing myself to go to campus, I was struck by an insight that had come in one of those dreams I had told Isham about a year previously. The dream inspired me to focus on the particular properties of space-time called discrete transformations. You can see an example of a discrete transformation when you look in a mirror, which makes your left hand look like it is the right hand of your reflection. I had a sense that I was onto something important, so at my café office, and with a celebratory beer, I started doodling inchoate diagrams on a napkin. I had developed this strategy of free play by presenting many competing rough sketches from my mind’s eye of the physics I was developing, before committing to any mathematics. At that stage of my investigations, there were no equations, just different sketches that resembled Picasso-like drawings of the physics of accelerating space-times and their discrete transformations—their reflections.
One day not very long after, I noticed the head of our theoretical physics group, Michael Peskin, on a physics chat stroll with the golden-child postdoc of our group, the guy that all the postdocs wanted to be like. As Peskin and the golden boy walked by, I couldn’t hold myself back. I said nervously, “Michael, I think I got something interesting about some work on the cosmological constant.” Peskin engaged me, and I started blurting out what in hindsight were pretty zany ideas. The golden child smirked and said with a tone of dismissal, “You and your crazy ideas again.” In fact, golden boy was one of those whose rejection kept me from hanging out in the theory center. But Peskin saw something and said, “That’s interesting, why don’t you come to my office next week and tell me more about it.”
Fear of a Black Universe Page 7