A giant of physics

“PROPHETIC” is the word that most aptly describes Yoichiro Nambu’s work in theoretical physics, which spanned more than half a century. Considered one of the “giants” of physics, Nambu’s ideas played a key role in the development of one of the great accomplishments of 20th century physics: the “standard model” of particle physics. And among others, he laid the foundations for what might turn out to be a “theory of everything”, string theory. Nambu passed away on July 5 in Osaka. He was awarded the Nobel Prize in Physics in 2008 “for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics” ( Frontline , December 5, 2008).

Nature presents one with a rich diversity and hierarchy of “matter” and “forces”. Remarkably, this diversity has rather simple origins. All visible matter is made up of a few varieties of “fundamental particles” which exert forces on each other obeying simple laws. These fundamental particles come in several classes: quarks, leptons and force carriers. Quarks are particles that bind together and form neutrons and protons; the latter bind together into the nuclei of atoms by what is called the “strong force”. Leptons include electrons, neutrinos and their cousins. Electrons and protons are the main players in electromagnetic forces, which are responsible for most of the diversity in nature. Quarks and leptons are also subject to the “weak force”, which gives rise to radioactivity. Finally, there is gravity: this makes things fall to the ground, makes the planets go around the sun and holds stars together in galaxies. These various forces result from exchange of “force carriers”. For example, the photon is the force carrier for electromagnetic forces. A remarkable combination of theoretical ideas and experiments in the past century has led to a simple, cogent description of three of the fundamental forces: electromagnetism, weak forces and strong forces. This is what is called the standard model of particle physics.

The early years

When Nambu graduated from the University of Tokyo in 1943, Japan was in the midst of the Second World War, but Japanese physics was extremely vibrant. Among other things, a group of superb Japanese physicists was developing the framework of quantum field theory. This spark came from the work of Hideki Yukawa, who in the 1930s laid down the foundations of modern particle physics with his prediction that the force between nucleons inside a nucleus is caused by a particle (today called the pion) that unlike the photon had a mass. Yukawa showed that this results in a force which dies out quickly as one increases the distance between the nucleons, as opposed to electromagnetic forces, caused by a massless photon, which die out rather slowly. Yukawa was Japan’s first Nobel laureate, in 1949. Soon afterwards, Japan became a powerhouse of particle physics and quantum field theory. In 1965, Sin-Itiro Tomonaga got the Nobel Prize (shared with Richard Feynman and Julian Schwinger) for his work on the quantum field theory of electromagnetism. These authors worked out a set of “quantum rules” for meaningful calculations for electric and magnetic fields in an atom.

After the War, Nambu worked in Tomonaga’s group. In 1948, he joined a select group of theoretical physicists at the newly formed department at Osaka City University. He spent a short three years there, but those were the formative years of his life. “I had never felt and enjoyed so much the sense of freedom,” he said. Much of his early work dealt with quantum field theory. One influential paper dealt with the derivation of the precise force laws in nuclear physics. In the process, he derived the equation that describes how particles can bind with each other. This equation was later independently derived by Hans Bethe and Edwin Salpeter and is now commonly known as the Bethe-Salpeter equation.

Nambu always felt that his work in physics was guided by a philosophy that was uniquely his own. He was deeply influenced by the philosophy of Shoichi Sakata and Mituo Taketani, during his years in Osaka. Sakata was yet another prominent theoretical physicist in Japan at that time. He later became well known for the Sakata model, which was a precursor to the quark model of nuclear constituents. Sakata was influenced by Marxist philosophy and together with Taketani developed a “three-stage methodology” in physics. As Nambu recalled later, Taketani used to visit the young group of theorists at Osaka and “spoke against our preoccupation with theoretical ideas, emphasised to pay attention to experimental physics. I believe that this advice has come to make a big influence on my attitude towards physics.” Together with colleagues Kazuhiko Nishijima and Hironari Miyazawa, he immersed himself in understanding the properties of the newly discovered elementary particles called mesons.

In 1952, J.R. Oppenheimer invited Nambu to spend a couple of years at the Institute for Advanced Study in Princeton, New Jersey, United States. By his own account, this was not a very fruitful period. After a brief summer at Caltech, he finally came to the University of Chicago at the invitation of Marvin Goldberger. There he immersed himself in a remarkably stimulating intellectual atmosphere which epitomised Enrico Fermi’s style of “physics without boundaries”. There was no “particle physics” or “physics of metals” or “nuclear physics”: everything was discussed in a unified manner. Soon Nambu made a landmark achievement in the history of 20th century physics: the discovery that vacuum can break symmetries spontaneously. He came up with this idea while working in a rather different area of physics: superconductivity.

Spontaneous symmetry breaking: Prehistory Symmetries are ubiquitous in nature and often provide a guiding principle in physics. An example is “rotational symmetry”. Imagine yourself to be in deep space, so far away from any star or galaxy that all you see in any direction is really empty space. Things look completely identical in all directions. It can be said that the space around you has rotation symmetry. Of course, this is only approximate since there are stars and galaxies around that break this symmetry explicitly . The symmetry is broken because there are objects around, hence explicit .

There are other situations, however, where a symmetry is broken spontaneously. One example is a magnet. The molecules inside a magnet are themselves little magnets called dipoles, and the force laws between them dictate that each dipole try to align itself parallel to the neighbouring one. This means that at low temperatures almost all of them roughly point in the same direction, producing a net magnetic field. Clearly, this does not have rotational symmetry. The laws tell all dipoles to point in the same direction but do not tell them which common direction. Rotation symmetry is broken spontaneously . Nevertheless, the fact that the underlying laws respect rotational symmetry has a consequence: if we gently disturb one of the dipoles from its perfectly aligned position, the result is a wave that propagates through the magnet. Such a wave has a very low energy and is called a spin wave.

Superconductivity

Nambu took the concept of spontaneous symmetry breaking to an entirely new level. He came up with this idea while trying to understand the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity. Superconductors are materials that conduct electric currents without any resistance whatsoever. Superconductors also repel external magnetic fields. This is called the Meissner effect. Inside a superconductor, electromagnetic fields are short-ranged rather than long-ranged: as if the photon has acquired a mass, pretty much like Yukawa’s mesons. However, a massive photon appeared to contradict everything that was known about electromagnetism.

It was Nambu in 1959, and independently Philip Anderson (who received the Nobel Prize in 1977), who understood what was going on. They showed that the superconducting state broke a symmetry spontaneously, or more accurately a local symmetry of electromagnetism lay hidden. This symmetry is unlike the rotational symmetry which is broken in magnets or crystals. It is a symmetry associated with the fact that electric charge is conserved. Nambu (and Anderson) realised several key facts about this phenomenon. First, if one ignored the electromagnetic force between the electrons, this symmetry breaking would result in very low energy waves, pretty much like spin waves in a magnet. In quantum theory, waves become particles as well; this would be a massless particle. Second, electromagnetic forces hide the symmetry and make this would-be massless particle (the photon) massive. Third, this results in a unique energetic state in a superconductor: this state was experimentally discovered more than 20 years later.

This mechanism of generating masses for force carriers (like the photon in a superconductor) was understood in full generality by three independent groups: Peter Higgs; Francois Englert and Robert Brout; and Gerald Guralnik, C. Richard Hagen and Tom Kibble. Nowadays this is called the “Higgs mechanism”. It became the key to formulating the standard model of particle physics by Steven Weinberg and Abdus Salam, building on the earlier work of Sheldon Lee Glashow, and resulted in the current understanding of electromagnetic and weak forces. The analogue of the special massive state in a superconductor is the Higgs particle, discovered at the European Organisation for Nuclear Research (CERN) in 2014.

This effortless excursion across traditional boundaries of physics characterised Nambu’s work throughout his career.

Vacuum of the world What came next was astounding. Soon after finishing his work on superconductivity, Nambu returned to particle physics. The first thing he noticed was that the equation describing the excitations in a superconductor was very similar to the Dirac equation, which describes nucleons. The energy gap in a superconductor translates to the mass of nucleons.

The charge symmetry which is spontaneously broken in a superconductor also has an analogue: chiral symmetry . If the energy gap in a superconductor is a result of spontaneous symmetry breaking of charge symmetry, could it be that the mass of a nucleon is a result of spontaneous symmetry breaking of chiral symmetry? This is exactly what Nambu proposed in a short paper in 1960, soon followed by two papers with Giovanni Jona-Lasinio.

This was the revolutionary step. In all previous examples, spontaneous symmetry breaking happened in situations where there were constituents (the molecular dipoles in a magnet, for example) and the underlying laws did not permit them to arrange themselves maintaining the symmetry. Nambu, however, proposed that there are situations where spontaneous symmetry breaking can happen in the vacuum of the world .

In physics, vacuum is the name given to “nothing”. How can a symmetry be broken, even spontaneously, when there is nothing around? The radical nature of this idea was best described by Anderson: “To me—and perhaps more to his fellow particle theorists—this seemed like a fantastic stretch of imagination. The vacuum, to us, was and always had been a vacuum—it had, since Einstein got rid of the aether, been the epitome of emptiness,… I, at least, had my mind encumbered with the idea that if there was a condensate, there was something there… This is why it took a Nambu to break the first symmetry.”

Nambu was proposing that the masses of elementary particles have an origin, something one can calculate! The revolutionary nature of this idea can be hardly overstated. Soon after the papers of Nambu and Jona-Lasinio, Jeffrey Goldstone came up with a simpler model that also illustrated the phenomenon of spontaneous symmetry breaking.

Theory of strong forces

It is now known for certain that nucleons acquire masses because of spontaneous breakdown of chiral symmetry. However, the final realisation of this idea had to wait until another momentous work of Nambu. The idea that all hadrons (particles which experience strong forces) are made of quarks was proposed by Murray Gell-Mann, and independently by George Zweig, in 1964. However, soon the idea ran into serious trouble.

All particles in nature can be classified into two classes: boson s (named after Satyendra Nath Bose) and fermion s (named after Fermi). They have rather different behaviours: two identical fermions do not like to be on top of each other, while identical bosons do. All particles also have another property called spin. It is a law of nature that fermions have half integer spins, like ½, 3/2,...while bosons have integer spin, like 0,1,2,.... Now, the quarks that make up nucleons have spin ½. However, it appeared that if quarks are indeed the constituents of all hadrons, they cannot be fermions at the same time! To resolve this contradiction, Nambu and his colleague Moo-Young Han proposed that quarks possess an attribute which is now called colour . Each kind of quark comes in three colours. Two quarks may appear identical (and therefore cannot be on top of each other) if one ignores their colour. However, once one recognises that their colours are different, they cease to be identical, and the usual “exclusion” of fermions does not apply. Independent of Han and Nambu’s work, O. Greenberg had come up with another resolution: he postulated that quarks were not really fermions but something called “para-fermions”, which have unconventional properties that are just right to solve the problem.

However, it was Nambu’s proposal that turned out to be more fruitful. This is because he made another remarkable proposal: colour is like another kind of electric charge. A quark not only produced an ordinary electric field but a new kind of generalised electric field. This new kind of electric field causes a new kind of force between quarks. It is this force, he claimed, that is the basic strong force which holds the quarks together inside a nucleon. This proposal of a colour gauge theory turned out to be essentially correct and is now known as quantum chromodynamics (QCD). However, it was only after the discovery of “asymptotic freedom” for the generalised electric field in 1973 by David Gross, Frank Wilczek, and David Politzer that QCD became a candidate theory of the strong interactions.

Asymptotic freedom is a property of the theory that at very short distances, say the size of a proton (10 ^-15 metres), the interaction is negligible and the quarks (constituents of the proton) experience no force between them. This explained the observed scaling properties of the strong interactions at high energies (which probe short distances). However, as one tries to pull the constituent quarks apart, the force between them grows stronger and stronger so that they cannot break away free, that is, they remain confined! It took many more years and extensive computer calculations to establish quark confinement. Thus, QCD explains the existence of the nucleons that compose the nucleus of atom as composites of quarks that cannot be seen.

String theory, which is recognised today as the most promising framework of fundamental physics including gravity, had its origins in making sense of strongly interacting elementary particles in the days before the discovery of asymptotic freedom. To make a very long story short, Nambu, Holger Bech Nielsen and Leonard Susskind proposed that many mathematical formulae of the day could be explained by the hypothesis that the underlying physical objects were strings (one-dimensional objects) rather than point particles. This was a radical departure from the “Newtonian” viewpoint that elementary laws of nature are formulated in terms of particles or point-like constituents.

Nambu (and independently Tetsuo Goto) also provided a simple dynamical principle with a large local symmetry for consistent string propagation. His famous paper on the string model entitled “Duality and Hadrodynamics” was submitted to the Copenhagen High Energy Physics Symposium in 1970.

In a letter dated September 4, 1986, to one of us (Spenta R. Wadia), Nambu said: “Just for your information, the following is the background story about the paper. In August 1970, there was a symposium to be held in Copenhagen just before a High Energy Physics Conference in Kiev, and I was planning to attend both. But before leaving for Europe, I set out to California with my family so that they could stay with our friends during my absence. Unfortunately, our car broke down as we were crossing the Great Salt Lake Desert, and we were stranded in a tiny settlement called Wendover for the three days. Having missed the flight and the meeting schedules, I cancelled the trip in disgust and had a vacation in California instead. The manuscript, however, had been sent out to Copenhagen, and survived.

“I must have been in a rather depressed mood at that time. After my 1968 paper I struggled to cure the various deficiencies of the dual string model, but no convincing solution was in sight.”

A unique style

It is quite common for scientists to become excessively attached to their own creations. In contrast, Nambu was remarkably open-minded. To him, all his work was like putting in a few pieces in a giant jigsaw puzzle: he never thought that he had discovered the “ultimate truth”.

In the fall of 1978, when one of us (Wadia), just out of graduate school, joined Nambu’s group at the University of Chicago, obsessed with Kenneth Wilson’s formulation of QCD on a lattice and, like many others in those days, wanting to solve the theory and demonstrate quark confinement. Once during a heated discussion with a colleague, there was a gentle tap on the shoulder and a soft voice (Nambu) asked: “How do you know this is the correct theory of the strong interaction?” He always had a healthy scepticism about currently accepted theories.

This deep sense of modesty was a part of his personality as well. To the entire community of physicists, he was this shy, unassuming man often difficult to understand coming up with one original idea after another. There was a sense of play in the way he did science. Maybe that is why his ideas were sometimes incomprehensible when they first appeared.

As his graduate student, one of us (Sumit R. Das) would discuss physics and other things with him almost every other day. Those discussions covered a wide range of physics: Nambu strongly believed in “physics without boundaries”. At that time, he was trying to find patterns in the spectrum of masses of elementary particles. Standing in front of the blackboard, he would write down various empirical equations relating the masses and juggle around the various terms to see whether they fit his intuition from other fields of physics: superconductivity, superfluidity and nuclear physics. A long time ago, he had discovered the mechanism by which particles get their masses. Now he wanted to know why those masses are what they are. It is not yet known whether any of his ideas from that time are correct. Maybe the couple of papers he wrote then will be one of those prescient papers. Maybe not. But, he was surely enjoying himself and he certainly infected us with the sheer joy of doing physics.

Nambu visited the Indian Institute of Science, Bengaluru, in 1983 as a guest of E.C.G. Sudarshan and also visited the Kolar underground laboratory of the Tata Institute of Fundamental Research (TIFR). During that visit, one of us (Wadia) asked him whether Sudarshan should have been awarded the Nobel Prize for his work with Robert Marshak on the V-A law of weak interactions. His answer: “If the neutral current got the Nobel Prize, the charged current should also have got it.”

Nambu’s legacy, “physics without boundaries”, must have had a subconscious influence on some of us in India involved in setting up the International Centre for Theoretical Sciences (ICTS), part of the TIFR in Bengaluru, where “science is without boundaries”.

We end this article with a quote from Nambu’s speech at the Nobel presentation ceremony at the University of Chicago on December 10, 2008, which clearly shows his view of nature: “Nowadays, the principle of spontaneous symmetry breaking is the key concept in understanding why the world is so complex as it is, in spite of the many symmetry properties in the basic laws that are supposed to govern it. The basic laws are very simple, yet this world is not boring; that is, I think, an ideal combination.”

Sumit R. Das is University Research Professor and Chair of the Physics Department at the University of Kentucky, U.S., and was a graduate student of Nambu at the University of Chicago. Spenta R. Wadia is Emeritus Professor and founding director of the International Centre for Theoretical Sciences of the TIFR in Bengaluru and spent his postdoctoral years with Nambu at the University of Chicago.