PHILIP Warren Anderson was a giant among theoretical physicists in the second half of the last century. He passed away in Princeton, New Jersey, United States, on March 29, at the age of 96, while still active in research until his last breath. A statistical survey in 2006 named Anderson as the most creative living physicist.
He won the Nobel Prize in Physics in 1977 along with John Hasbrouck van Vleck and Nevill Francis Mott. He was also directly or indirectly responsible for half a dozen other Nobel Prizes. His career started in the 1950s, and his foundational discoveries transformed the then obscure field known as solid state physics (also known derisively as “squalid state physics”) to perhaps the most prominently active research area in subsequent decades. Even the name “condensed matter physics” is due to him.
Anderson’s theories of the condensed matter around us are relevant to and have far-reaching consequences for widely disparate phenomena such as the origin of the mass of elementary particles (electrons, quarks, and so on), the unusual “glitches” in pulsars (rotating neutron stars), the working of the brain, the complexities of financial markets, the colour of white paint, the origin of the rigidity of solids and the magnetic properties of rust.
Anderson was born in Indianapolis, Indiana, U.S., on December 13, 1923. He grew up on a farm in Urbana, Illinois. He came from a “family of secure but impecunious Midwestern academics” on both sides. His father was a professor of plant pathology at the University of Illinois, Urbana.
Anderson was both an undergraduate and a graduate student at Harvard University, where he worked for his PhD with van Vleck. He joined Bell Telephone Laboratories (Bell Labs) in 1949, where he would be for the next 35 years. Bell Labs, formally the R&D laboratories of a telephone company, had a constellation of world-class theorists and was a place where Anderson “learned most of all, the Bell mode of close experiment—theory teamwork”.
He spent 1953 in Japan as the first Fulbright scholar there and acquired a lifelong admiration for Japanese culture, arts and architecture, besides learning the board game GO (which he played throughout his life and of which he became a first Dan master). Starting in 1967, he divided his time between Bell Labs and academic institutions. He was with Cambridge University, United Kingdom, until 1975 and then with Princeton University, where he became the full-time Joseph Henry Professor of Physics in 1984 after leaving Bell Labs. He retired to emeritus status in 1996.
The reality of emergence
Anderson’s increasing awareness of the subject matter of science resulted in his path-breaking paper “More is different” ( Science , 1972). It woke all of us up to the reality of emergence, at a stage when “real” science was equated with reductionism although emergence has always been a known reality in science. It reminded us that “[a]t each stage (of complexity) entirely new laws, concepts and generalisations are necessary, requiring inspiration and creativity to just as great a degree as the previous one…. The main fallacy in this… [reductionist] thinking is that… the reductionist hypothesis does not imply by any means a ‘constructionist’ one.… The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity.” The last bit is a reference to the common belief that once the basic laws of nature are known, the rest is “just” a relatively straightforward, if painstaking, matter of putting things together according to these.
Condensed matter physics
Condensed matter physics (in both its quantum, or hard, and its classical, or soft, parts) describes a variety of natural phenomena and is readily accessible to controlled experiment. In this sense, it is very close to the wellspring of modern science as understood by Francis Bacon (1561-1620), one of its founding spirits. Bacon emphasised the importance of experiment over contemplation and over scriptural authority. He also felt that science should aim at practical inventions for the improvement of all human life. Anderson’s inspiration is Baconian, as he had often said. He started with experiment, then made a hypothesis and an appropriate theoretical model; interestingly, his inspiration in solving the model and in predicting its consequences is its underlying natural reality, the interconnected nature of which he had a profound knowledge.
From the amazing range of Anderson’s creative spirit, which was active in physics for nearly 70 years, we mention below just a few of his contributions, one each to the fields of disordered systems, magnetism and superconductivity. The examples we chose to write about form the basis of modern condensed matter physics and its present frontiers.
Disordered systems
We are all familiar with waves. According to quantum theory, the electron is a wave. It is known that a wave can interfere with itself. In a conducting disordered medium (such as an electrical wire), electrons move, diffusing from end to end. Anderson discovered in 1957 that under some conditions these waves simply cannot move. He was awarded the Nobel Prize for this discovery a full 20 years after he published a paper on it. The physics community did not pay much attention to this work; nor did many physicists believe in it. Mott, almost alone among them, saw that it provided the conceptual underpinning for the existence of an entire class of materials, namely, solid but amorphous semiconductors (not to mention insulating glasses and transformer oil), and that a number of applications could be developed. Mott also realised that this could lead to a new kind of metal-insulator transition (cessation of electrical conduction due to Anderson localisation), which he called the Anderson transition, and a new kind of insulator, the Anderson insulator. This effect is not specific to electron waves but is common to all waves in random media, for example, light waves, sound waves and even Rossby waves (ocean waves with a wavelength on the scale of a hundred kilometres). In 1979, Anderson, along with Elihu Abrahams, Don Licciardello and one of us (TVR) showed that electrical conductivity harbours telltale premonitory signs of localisation that can be accurately measured. This area of research continues to be an active field in basic science with profound technological implications for microelectronics and future quantum computers.
Magnetism
There are many magnetic systems that are intrinsically “frustrated”. In these, the magnetic interactions between some pairs of nearest neighbour atoms (which can be thought of here as tiny magnets with a certain strength, or as “magnetic moments”) are such that their magnetic moments tend to line up parallel to each other. For some other pairs (often involving the same magnetic moments), the more stable state would be for the magnetic moments to be mutually anti -parallel. So, a particular magnetic moment is intrinsically “frustrated”; some of its nearest neighbours “would like it” to point this way, while others “would like it” to point that way. It was commonly believed that just as a melt of disordered atoms or molecules freezes into a glass smoothly on cooling (motions become more and more viscous and then unobservable, at least on the scale of our lifetime), these “spin glasses” would also freeze continuously into the energetically most favourable configuration decided by the nature of the magnetic interactions of an atom with those in its vicinity. In 1975, Samuel Frederick Edwards and Anderson proposed a model for these systems; their novel analysis—which showed that there is actually a sharp transition into the spin glass state characterised by a precisely defined freezing criterion (and many other bizarre features that were confirmed experimentally)—revolutionised the field.
Further research showed that there are far-reaching parallels with many kinds of statistical systems that consist of a large number of interconnected parts. These could be interconnected neurons in the brain or a large number of cities situated at different distances from one another that a salesman is expected to visit and the associated question of the optimisation of travel time . Methods of combinatorial optimisation inspired directly by Anderson’s study have even spawned and invigorated areas of research outside physics.
Superconductivity
It was discovered in 1911 that at low temperatures a large number of metals and alloys lose all resistance to the flow of electrical current through them (superconductivity). Nearly half a century later, after many failed attempts by some of the greatest physicists of the time, John Bardeen, Leon Cooper and Robert Schrieffer (BCS) proposed a credible theory that accounted for the facts. There was, within the community, acceptance, relief and, equally, scepticism. Anderson clarified many of the basic issues, and this opened fertile directions of research with far-reaching implications. We mention only one here. In his study of BCS superconductivity, Anderson discovered in 1963 that basic principles of physics require that there are massive excitations concomitant with superconducting order. As it turns out, this is the same phenomenon by which all elementary particles in the universe are supposed to acquire mass, namely, the Anderson-Higgs mechanism of mass generation in elementary particles (Peter W. Higgs and Francois Englert won the Nobel Prize for this in 2013).
Following Georg Bednorz and Alex Muller’s remarkable Nobel Prize-winning discovery in 1986 of high temperature superconductivity in certain cuprates, Anderson opened a new direction in the field of superconductivity: the resonating valence bond (RVB) theory of high temperature superconductivity. In this approach, superconductivity can arise even when there is only repulsion between electrons (and that too strong); this is to be contrasted with the BCS theory, which relies on an effective attraction between electron pairs. Interestingly, Anderson first presented this theory at a conference in Bangalore (now Bengaluru) in December 1986. According to Anderson, the work of two renowned Indian chemists, P. Ganguly and C.N.R. Rao, on lanthanum cuprate, about which he learned in detail in Bangalore, was part of the inspiration for the RVB theory. One of us (GB) joined Anderson in this game as a close collaborator from January 1987.
In an article published in Nature in 2005, Anderson re-emphasised that while the creators of the quantum revolution in physics felt that the quantum domain was atomic and subatomic (with classical physics being the right description of the world at the macroscopic scales readily accessible to humans), Fritz London alone among the quantum pioneers saw clearly that superconductivity and superfluidity were quantum effects on a macroscopic scale. This is a timely reappraisal because recent theoretical and experimental discoveries have revealed to us novel kinds of quantum matter. Their strange (and potentially revolutionary) macroscopic properties at room temperatures are related to properties of quantum states of electrons at the level of atoms. This was one of Anderson’s abiding concerns: macroscopic quantum phenomena in condensed matter physics.
Anderson immeasurably deepened the concept of broken symmetry, which he emphasised as an example of emergence. The behaviour of constituents of a certain piece of matter is governed by certain laws of motion; these laws have certain symmetries. Often, physical states are realised that break these underlying symmetries. Among other things, Anderson showed that characteristic rigidities follow when symmetry is broken (for example, it hurts when you kick a stone). In some cases, quantum mechanics restores the symmetry, but this happens typically at astronomical time scales. Broken symmetry is itself emergent. For instance, it does not make any sense to think of an atom as a solid, but a collection of atoms can have such a property. Similarly, we cannot think of an atom of lead as a superconductor. But when a collection of them is cooled below a certain temperature, the piece of lead becomes a superconductor, an emergent broken symmetry state.
While looking at Anderson’s contributions to physics, the very first fact that draws one’s attention is this: They are all motivated by an experimental fact and a desire to understand it in a fundamental way. The process of understanding leads to new models, fundamental principles and, often, paradigms. This was a crucial aspect of Anderson’s way of doing physics: the engagement he had with experiments, both data and detail. He was not merely aware of the relevant experimental facts but understood the tangled network of connections between several of them. Some of these were obvious, others not. This heightened awareness gave him a unique security in the world his mind inhabited. This also meant that he was quite idiosyncratic in what he valued in people and in physics.
He was quite independent minded, often contrarian, and was not excessively weighed down by the mathematical subtleties or difficulties of this theoretical approach or that. The following paragraph from Anderson’s Nobel lecture captures his stance in science: “One of my strongest stylistic prejudices in science is that many of the facts Nature confronts us with are so implausible given the simplicities of non-relativistic quantum mechanics and statistical mechanics, that the mere demonstration of a reasonable mechanism leaves no doubt of the correct explanation. This is so especially if it also correctly predicts unexpected facts…. Very often such a simplified model throws more light on the real workings of Nature than any number of ab initio calculations of individual situations, which even where correct often contain so much detail as to conceal rather than reveal reality. It can be a disadvantage rather than an advantage to be able to compute or to measure too accurately, since often what one measures or computes is irrelevant in terms of mechanism. After all, the perfect computation simply reproduces Nature, does not explain her….”
Conscience keeper
As a thinking citizen, Anderson often took forthright public positions that brought him into confrontation with the “authorities”. For example, he was against the “Star Wars” initiative of the U.S. government (1983) and wrote against it; the public interchange between him and the then Secretary of State, George P. Schultz, can be found in Anderson’s book More and Different: Notes from a Thoughtful Curmudgeon (World Scientific, Singapore, 2011).
As a scientist, Anderson was a conscience keeper of his field. He identified truly important developments and helped them grow. He could be very critical as well. In his article in Scientific American (November 1994) on Anderson titled “Gruff Guru of Condensed-Matter Physics”, the author John Horgan notes: “Robert Schrieffer, a Nobel laureate in physics, who has often butted heads with Anderson, admires his blunt style. Anderson ‘has played a uniquely provocative role to make sure that people get things right’, Schrieffer says. But he adds, ‘Anderson can be undiplomatic.’”
Friends of Anderson recall that he could be impetuous at times in a very funny way. V.N. Muthukumar, a long-time associate of Anderson (known to all as Phil), recalls his first meeting with him: “Phil took me along to the cafeteria at the Institute for Advanced Study in Princeton (one of his favourite luncheon places) for lunch. I parked my car, and we were making our way to the cafeteria when Phil turned suddenly and walked up to a pick-up truck parked nearby. Showing great purpose and determination, he tore a bumper sticker off the truck (it was one of those ‘Guns don’t kill people; People kill people’ NRA stickers). I was transfixed and had an appalling vision of a truck driver with rippling muscles charging at Phil.…” (Luckily, this did not happen.)
Anderson had many close collaborators and associates originating from the Indian subcontinent: T.V. Ramakrishnan, G. Baskaran, Sajeev John, C.M. Varma, B.S. Shastry, H.R. Krishnamurthy, S. Chakravarty, Anil Khurana, Sanjoy K. Sarker, S.L. Sondhi, R.N. Bhatt, G. Srinivasan, V.N. Muthukumar, K.A. Muttalib, M. Randeria and Nandini Trivedi, among others. He was an Honorary Fellow of the Indian Academy of Sciences from 1997.
In a book containing selected papers of his ( A Career in Theoretical Physics , World Scientific, 2nd Edition, 2004), Anderson remarks: “The contribution of physics is the method of dealing correctly both with the substrate from which emergence takes place, and with the emergent phenomenon itself.… Ever newer insights into the nature of the world around us will continuously arise from this style of doing science.” Anderson was the best, and arguably the last, exemplar of this way of doing physics.
G. Baskaran is with the Institute of Mathematical Sciences, Chennai, and the Indian Institute of Technology Madras.
T.V. Ramakrishnan, FRS, is with the Indian Institute of Science, Bengaluru.
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