The Institute played an important role in my life on two occasions—as a graduate student at Princeton University in the 1950s, and as a visiting Member in 1964.
1952–54: Five encounters with Einstein
As a graduate student in Princeton from 1952 to 1956, I went to the Institute to attend seminars. I visited Einstein in his office and in his home, and introduced Einstein at the last seminar he gave.
I saw Einstein three times to learn about the theory with a non-symmetric metric he was considering in order to unify gravity and electromagnetism. Meeting with Einstein was exhilarating and I felt awed in his presence; however, the meetings were not helpful for my understanding of his unified theory. If something was not clear, I was too much in awe of Einstein to press him for further explanation. As an example of my diffidence, one visit to Einstein was just before lunch. As it was winter, Einstein started to put on his heavy grey cloth coat before going out to walk home. I had an impulse to help him on with his coat, but did not because I felt this would be too intimate. I found it more helpful to meet with Bruria Kaufmann, Einstein’s scientific assistant; I felt at ease with her and was able to press her when I did not understand her explanations.
Years later, I heard that Robert Oppenheimer had told postdocs at the Institute not to bother Einstein. I don’t think that was doing Einstein a favor, because Oppenheimer’s admonition isolated Einstein even more than he was already because of his refusal to accept quantum mechanics.
My most memorable meeting with Einstein was in 1953. John Wheeler took his general relativity class to ask questions of Einstein and to have tea with him in his home on Mercer Street. We walked across Princeton as if we were going to a museum. We asked Einstein questions ranging from Mach’s principle and the expanding universe to his attitude toward quantum theory. He appeared very humble. He took our questions seriously and answered our questions fully, including a question about the future of his house. He answered straightforwardly: “This house will never become a place of pilgrimage where people come to see the bones of the saint.” I felt that Einstein had not accomplished all he had hoped to do and was ready to pass the torch to us. When Wheeler asked Einstein what advice he would give to these young men who aspire to become physicists, Einstein simply shrugged his shoulders and said, “Who am I to say.” The poem “Mercer Street” recalls this visit to Einstein in his home.
A spring afternoon
A line of nine walk though the town
A musty house, the shutters drawn
A sage lives within
His key turned the lock
For twenty years to unify
Electric field, magnetic field
Space-tine matter, too
A calm beyond time
A humble man received his guests
To talk, to feel the breath of youth
To hand them the key
The day turned to dusk
The parting time. Advice was sought
For these young men who start the path
He lost long ago
He shrugged. Scratched his head,
Discomforted, at sea, he sent
Them out with “Who am I to say?”
Cool air cleared their heads
The last time I saw Einstein was on April 14, 1954, when I introduced him at the last seminar he gave. We kept his planned talk quiet so the whole town of Princeton would not show up. Einstein talked about the difficulty of combining quantum mechanics with special relativity. I don’t remember my introduction, except that it was brief. If ever there was a person who needed no introduction it was Einstein.
1964: The Institute’s atmosphere for discovering color in quarks
Important developments in particle physics took place in 1964. Spontaneously broken symmetry pioneered by Yoichiro Nambu, and independently developed by Robert Brout and François Englert, and by Peter Higgs, as well as by Gerald Guralnik, Richard Hagen, and Tom Kibble, was proposed in 1964. This work led to what is now called the Higgs mechanism as a solution to a number of difficulties with the quantum field theory of elementary particles. The quark model and color also were introduced in that year. Indeed, the framework in which we think about particle physics was established in 1964. This recollection focuses on the quark model and color.
The increasing number of apparently elementary particles, first found in cosmic rays, and then produced in accelerators, required a framework to bring order to the new data. Murray Gell-Mann’s eightfold way, and similar work by Yuval Ne’eman, grouped the new particles in sets of eight (octets) and ten (decuplets) connected with the symmetry group, SU(3)flavor, that preserves the length of three-dimensional complex vectors.
Initially, the fundamental “flavor” triplet of SU(3) was not used to describe these particles. In 1964, George Zweig and Gell-Mann independently introduced this triplet as fundamental entities underlying the observed particles, and they called the fundamental triplet “aces” and “quarks” respectively. Zweig thought of his aces as concrete particles; by contrast, Gell-Mann initially thought of his quarks as mathematical objects to be used to construct the octets and decuplets. Their quark model placed the mesons in quark-antiquark states and the baryons in 3-quark states. They chose charges 2/3,−1/3,−1/3 for the flavor triplet in order to produce the requisite integer charges for the mesons and baryons. They chose spin-1/2 for the quarks in order to have the observed spins for the baryons. The low-lying mesons fit into an octet of pseudoscalar mesons (spin-zero particles that change sign under space inversion) and an octet plus a singlet of vector mesons (spin-one particles). Of more interest for what follows, the low-lying baryons were assigned to an octet of spin-1/2 particles, including the proton and neutron, and a decuplet of spin-3/2 particles. This decuplet included the △++ containing 3 up quarks with parallel spins. There was no reason, aside from the charge and spin assignments, for the quark and antiquark compositions of the baryons and mesons. This was the situation in September, 1964, when I arrived at the Institute for Advanced Study.
The Atmosphere at the Institute in 1964
My apartment and my office were both ready: I could hit the road running and start work immediately. Evenings I would join friends and play ping pong at a table in the Institute basement. I had a vicious topspin left-hand slam and discharged a lot of aggression at the ping-pong table.
People at the Institute were very excited about a paper by Feza Gürsey and Luigi Radicati.1 They unified the spin-1/2 positive parity nucleon octet and the spin-3/2 decuplet in the 56-dimensional representation of the larger group, SU(6), (the group that contains the product of the two possibilities of spin up and spin down times the three “flavors” colloquially called “up,” “down,” and “strange”). Benjamin W. Lee, who was also at the Institute, gave me a preprint of the paper he had just finished with Mirza A. Baqi Beg and Abraham Pais, both of whom had just moved to the Rockefeller Institute (shortly to be renamed “University”). In their paper, they calculated the ratio of the magnetic moments of the proton and neutron in the 56-dimensional representation of SU(6) with the result −3/2, which agreed with experiment to within 3 percent.2 From our present perspective, this result was too good, since quark-antiquark pairs and gluons, among other things, such as relativity, were ignored. Nonetheless, this result, together with the supermultiplet 56-dimensional representation of SU(6), convinced me that quarks were real and should be taken seriously as constituents of hadrons. I became an enthusiastic believer in quarks.
The quark model required the quarks to have spin 1/2. The spin-statistics theorem implied that they are fermions and must be in antisymmetric states under permutations. Surprisingly, the SU(6) model of Gürsey and Radicati placed the three quarks in the symmetric three-particle representation of the permutation group, the 56-dimensional representation of SU(6). This presented the paradox that the quarks seemed to behave as bosons instead as fermions as they should have.
With the background of the work on parastatistics I had done with Albert Messiah,3 I realized that this paradox would be resolved if the quarks obeyed parafermi statistics of order-3. I had arrived at the Institute knowing the solution to the paradox that the quarks in the 56-dimensional representation were in the symmetric permutation state, before I had even heard of the problem, because I had been playing around with other statistics just for the fun of it. The seemingly useless knowledge that quantum mechanics allows statistics other than bose or fermi became useful in the context of the quark model.
This was tantamount to introducing a new three-valued charge, now called “color.” However, to suggest that quarks carry an unseen three-valued color charge strained credulity. The parafermi statistics would be hidden. The wave function of the quarks including the parastatistics factor would be antisymmetric as required by the exclusion principle and the spin-statistics connection. However, when the parastatistics wave function was factored out, the remaining wave function would be symmetric in the “visible” space-spin-SU(3)flavor degrees of freedom, and the quarks would behave as bosons in these visible degrees of freedom, as they did in the 56-dimensional representation of Gürsey and Radicati.4
Since the paradox had arisen in the ground-state baryons, I worked out the consequences of the parafermi model for the excited states of the baryons as an independent test of this idea. I called this model the “symmetric quark model.” I used a simple shell model in which the quarks in the ground-state baryons are in states with zero orbital angular momentum, “s states,” and the first excitations have two quarks in s states and one in a “p” state with one unit of angular momentum.5 I tabulated the properties of these resonances, as well as some higher resonances.
I gave a copy of the preprint of my paper to Robert Oppenheimer, who, as Director of the Institute for Advanced Study, was my host. A week later I met him at an Eastern Physics Meeting at the University of Maryland, my home institution. When I asked him if he had read my paper, he replied, “Greenberg, it’s beautiful!” I was elated. After a pause, he completed his assessment of my paper by saying, “But I don’t believe a word of it!” Although I was not discouraged by his negative opinion, I did not have the presence of mind to ask what his objection was. Unfortunately, Oppenheimer died before data that confirmed color as well as my model of baryons had been obtained. Further confirmation of the three-valued charge, now called “color,” implied by parastatistics of order-3 came later.
Further Consequences of Color
The 3 of color appears in a simple way in the π0 →2γ decay represented by the anomalous triangle diagram with the π0 connected to one vertex of the triangle via the axial current and with a photon at each of the other vertices. Quarks circulate around the triangle; each color contributes equally to the decay matrix element so that the decay matrix element is multiplied by a factor of 3 and the decay rate is multiplied by a factor of 9 relative to the results for color-singlet quarks. The factor of 9 for the decay rate agrees with experiment. It is amusing that the same matrix element and decay rate follow from integer charged protons and neutrons circulating around the triangle. The color factor 3 also enters in the ratio of the cross sections σ(e+e–→hadrons)/σ(e+e–→μ+μ–). Again, the factor 3 is required to agree with data. For these two examples, the parastatistics model agrees in lowest order with the now-standard gauge theory of color, quantum chromodynamics (QCD). The parastatistics model cannot be gauged because of the twisted commutation relations and fails to agree with experiment and with QCD in higher orders. As its name suggests, color enters in a fundamental way in QCD and the successful predictions of QCD confirm the existence of the color degree of freedom. Harald Fritzsch, Gell-Mann, and Heinrich Leutwyler gave a summary of the advantages of the color model.6 Color also provides an explanation of “saturation”: why the lowest mass hadrons are made of just two combinations, 3 quarks for baryons and a quark-antiquark pair for mesons. Daniel Zwanziger and I showed that only the three-valued color charge can explain saturation.7
Oppenheimer was not alone in being skeptical of color as well as of quarks. Particles with the fractional charges of the quark model had not been observed, nor have they been observed to this day. Suggesting that quarks carry a hidden three-valued color charge seemed speculative beyond reason. Quarks and color were not accepted by the physics community until the discovery of “naked” charm in 1975.
Oppenheimer and the Institute
Oppenheimer arranged lunches on Tuesday, the day of the weekly seminars, to which he invited members of the permanent Faculty at the Institute as well as faculty from Princeton University and also some visiting Members at the Institute. He arranged for sandwiches and fruit at these informal lunches in his office. During the conversations about physics, people would write things on the blackboard in his office. I noticed that Oppenheimer was very active in these discussions, but he never wrote anything on the board.
Oppenheimer presided at the Tuesday seminar, usually given by an outside speaker. Sometimes Oppenheimer made comments that anticipated what the speaker was about to say. He would then turn around and look back at the audience to see how his comments were received.
Although Oppenheimer was generally kind to me, he could be cruel to other physicists. On one occasion, a faculty member at Rutgers sat in the first row of the seminar room. When Oppenheimer entered he said, “That is not for you” to this person, whereupon the Rutgers faculty member moved to a seat in the back of the room.
I interacted with several of the visiting Members; in particular Ben Lee, John Cornwall, and Peter Freund, who had suggestions to generalize the SU(6) model of Gürsey and Radicati, as well as Sam MacDowell and Korkut Bardaksi. I recruited Alex Dragt and Ching-Hung Woo for Maryland where they both became faculty members. The permanent Members I interacted most with were Freeman Dyson and Frank Yang.
The time I spent at the Institute was crucial for my development as a physicist. I did my most important work during that time and made lasting friendships with other colleagues. The atmosphere at the Institute, the frequent interaction with Members, the collegiality, and the seminars were highly conducive to doing original work. I think the culture of the Institute, then and now, is unparalleled for generating new ideas.