I was born in 1933, in New York City to Frederick and Eva Weinberg. My early inclination toward science received encouragement from my father and, by the time I was 15 or 16, my interests had focused on theoretical physics.
I received my undergraduate degree from Cornell in 1954, and then went for a year of graduate study to the Institute for Theoretical Physics in Copenhagen (now the Niels Bohr Institute). There, with the help of David Frisch and Gunnar Källén, I began to do research in physics. I then returned to the U.S. to complete my graduate studies at Princeton. My Ph.D thesis, with Sam Treiman as adviser, was on the application of renormalization theory to the effects of strong interactions in weak interaction processes.
After receiving my PhD in 1957, I worked at Columbia and then, from 1959 to 1966, at Berkeley. My research during this period was on a wide variety of topics—high energy behavior of Feynman graphs, secondclass weak interaction currents, broken symmetries, scattering theory, muon physics, etc.—topics chosen in many cases because I was trying to teach myself some area of physics. My active interest in astrophysics dates from 1961–1962; I wrote some papers on the cosmic population of neutrinos and then began to write a book, Gravitation and Cosmology, which was eventually completed in 1971. Late in 1965, I began my work on current algebra and the application to the strong interactions of the idea of spontaneous symmetry breaking.
From 1966 to 1969, on leave from Berkeley, I was Loeb Lecturer at Harvard and then visiting professor at M.I.T. In 1969, I accepted a professorship in the physics department at M.I.T., then chaired by Viki Weisskopf. It was while I was a visitor to M.I.T. in 1967 that my work on broken symmetries, current algebra, and renormalization theory turned in the direction of the unification of weak and electromagnetic interactions. In 1973, when Julian Schwinger left Harvard, I was offered and accepted his chair there as Higgins Professor of Physics together with an appointment as Senior Scientist at the Smithsonian Astrophysical Observatory.
My work during the 1970s has been mainly concerned with the implications of the unified theory of weak and electromagnetic interactions, with the development of the related theory of strong interactions known as quantum chromodynamics, and with steps toward the unification of all interactions.
In 1982, I moved to the physics and astronomy departments of the University of Texas at Austin, as Josey Regental Professor of Science. I met my wife, Louise, when we were undergraduates at Cornell, and we were married in 1954. She is now a professor of law. Our daughter, Elizabeth was born in Berkeley in 1963.
Weinberg Photo Album at end of entry.
Awards and Honors
Honorary Doctor of Science degrees, University of Chicago, Knox College, City University of New York, University of Rochester, Yale University
American Academy of Arts and Sciences, elected 1968
National Academy of Sciences, elected 1972
J. R. Oppenheimer Prize, 1973
Richtmeyer Lecturer of Am. Ass'n. of Physics Teachers, 1974
Scott Lecturer, Cavendish Laboratory, 1975
Dannie Heineman Prize for Mathematical Physics, 1977
Silliman Lecturer, Yale University, 1977
Am. Inst. of PhysicsU.S. Steel Foundation Science Writing Award, 1977, for authorship of The First Three Minutes (1977)
Lauritsen Lecturer, Cal. Tech., 1979
Bethe Lecturer, Cornell Univ., 1979
Elliott Cresson Medal (Franklin Institute), 1979
Nobel Prize in Physics, 1979
Awards and Honors since 1979
Honorary Doctoral degrees, Clark University, City University of New York, Dartmouth College, Weizmann Institute, Clark University, Washington College, Columbia University
Elected to American Philosophical Society, Royal Society of London (Foreign Honorary Member), Philosophical Society of Texas
Henry Lecturer, Princeton University, 1981
CherwellSimon Lecturer, University of Oxford, 1983
Bampton Lecturer, Columbia University, 1983
Einstein Lecturer, Israel Academy of Arts and Sciences, 1984
McDermott Lecturer, University of Dallas, 1985
Hilldale Lecturer, University of Wisconsin, 1985
Clark Lecturer, University of Texas at Dallas, 1986
Brickweede Lecturer, Johns Hopkins University, 1986
Dirac Lecturer, University of Cambridge, 1986
Klein Lecturer, University of Stockholm, 1989
James Madison Medal of Princeton University, 1991
National Medal of Science, 1991
From Nobel Lectures, Physics 19711980, Editor Stig Lundqvist, World Scientific Publishing Co., Singapore, 1992
This autobiography/biography was written at the time of the award and first published in the book series Les Prix Nobel. It was later edited and republished in Nobel Lectures.
Steve Weinberg died in Austin, Texas on July 23, 2021.
His discoveries deepened understanding of the basic forces at play in the universe, and he took general readers back to its dawn in his book “The First Three Minutes.”
By Dylan Loeb McClain
Steven Weinberg, a theoretical physicist who discovered that two of the universe’s forces are really the same, for which he was awarded the Nobel Prize, and who helped lay the foundation for the development of the Standard Model, a theory that classifies all known elementary particles in the universe, making it one of the most important breakthroughs in physics in the 20th century, died on Friday in a hospital in Austin, Texas. He was 88.
His daughter, Dr. Elizabeth Weinberg, confirmed the death but did not specify a cause.
Dr. Weinberg’s stature in physics would be hard to overstate.
In 2011, Dr. Brian Greene, a theoretical physicist at Columbia University, invited Dr. Weinberg to be the inaugural speaker at a new lecture series, titled “On the Shoulders of Giants,” organized by the World Science Festival at New York University. While introducing his guest, Dr. Greene related how, in the early 1980s, he was working at I.B.M. when he was invited to give a lecture at the University of Texas at Austin, where Dr. Weinberg was a professor. When he told his boss, John Cocke, a pioneer of computer science, that Dr. Weinberg would be at the talk, Dr. Cocke warned him, “You should know, there are Nobel laureates and then there are Nobel laureates.” Dr. Weinberg was in the second category.
Though he had the respect, almost awe, of his colleagues for his scientific abilities and insights, he also possessed a rare ability among scientists to communicate and explain abstruse scientific ideas to the public. He was a soughtafter speaker, and he wrote several popular books about science, notably “The First Three Minutes: A Modern View of the Origin of the Universe” (1977).
The work for which Dr. Weinberg was awarded the Nobel had a transformative impact on physics, in particular on the development of quantum mechanics, which tries to understand and explain what happens in the subatomic world.
There are four known forces in the universe: gravity; electromagnetism; the strong force, which binds the nuclei of atoms together; and the weak force, which causes radioactive decay. The first two forces have been known for centuries, but the other two were discovered only in the first two decades of the 20th century.
Over the next decades, physicists struggled to find a theory that would account for all the forces, or what Einstein called a theory of everything. Though there were significant discoveries, particularly of new particles with exotic names like quarks (the components of protons and neutrons in the nucleus) and leptons (which include electrons but also more esoteric particles called muons and taus), a unified theory or model remained elusive.
In 1967, Dr. Weinberg began using something called gauge theory to study the interactions in weak forces, which had not been successfully explained up to that point.
Gauge theory had been developed in the 19th century by James Clerk Maxwell, a British physicist, in his seminal work to explain electromagnetism. In the 1950s, it was used by Robert Mills and Chen Ning Yang, a Chinese American physicist, who later won the Nobel Prize, to understand strongforce interactions.
But Dr. Weinberg’s application of gauge theory to the weak force soon ran into a problem. Electromagnetism is a force that acts at large distances, but the weak force acts only at very short distances — smaller than the nucleus of an atom.
In electromagnetism, when two particles — say, electrons — collide, they exchange a massless neutral particle called a photon, which is also known as a gauge boson. If two particles collide because of the weak force, gauge theory requires — because of the short distances of the interaction — that the gauge bosons that are exchanged be massive and possibly electrically charged.
Fortunately, several years earlier, physicists had come up with a way to generate mass for gauge bosons called the Higgs Mechanism. It was named for Peter Higgs, a British physicist, and it predicted the existence of a previously unknown particle that is responsible for giving other particles their mass. The particle was given the name the Higgs boson, and its discovery, in 2012, brought Dr. Higgs and his colleague François Englert the 2013 Nobel Prize.
Using this new idea, Dr. Weinberg was able to create a model in which weak interactions produced massive, at least by atomic standards, gauge boson particles. He called them W and Z bosons.
His theory also predicted that in some collisions — for example, between two electrically neutral particles like a neutron and a neutrino — a neutral current, as opposed to a charged one, would be created, indicating that there had been an exchange of a Z boson.
Dr. Weinberg theorized that there was a link between the photon and the W and Z bosons, suggesting that they were created by the same force. The conclusion was that, at very high energy levels, the electromagnetic and weak forces were one and the same. It was a step on the path to the unified theory that physicists had been searching for.
Dr. Weinberg published his findings in 1967 in a groundbreaking paper, “A Model of Leptons,” in the journal Physical Review Letters. The article is one of the most cited research papers in history.
Working separately, Dr. Abdus Salam, a Pakistani theoretical physicist, came to the same conclusions as Dr. Weinberg. Their model became known as the WeinbergSalam Theory. It was revolutionary, not only for proposing the unification of the electromagnetic and weak forces, but also for creating a classification system of masses and charges for all fundamental particles, thereby forming the basis of the Standard Model, which includes all the forces except gravity.
The existence of neutral current was confirmed experimentally in 1973, while it took another decade for the W and Z bosons to be verified, by Carlo Rubbia and Simon van der Meer at the CERN supercollider in Switzerland near Geneva. That work earned Dr. Rubbia and Dr. van der Meer the 1984 Nobel Prize.
Dr. Weinberg and Dr. Sheldon Lee Glashow spoke to reporters after learning that they would share the 1979 Nobel. Working separately, Dr. Abdus Salam, a Pakistani theoretical physicist, also shared in the prize. Credit...Associated Press Photo Dr. Weinberg, Dr. Salam and Dr. Sheldon Lee Glashow, an old high school classmate of Dr. Weinberg’s who had resolved a critical problem with the WeinbergSalam model, were jointly awarded the 1979 Nobel Prize “for their contributions to the theory of the unified weak and electromagnetic interaction between elementary particles.”
After learning that Dr. Weinberg had died, John Carlos Baez, a theoretical physicist at the University of California, Riverside, wrote on Twitter: “For all the talk of unification, there are few examples. Newton unified terrestrial and celestial gravity — apples and planets. Maxwell unified electricity and magnetism. Weinberg, Glashow and Salam unified electromagnetism and the weak force.”
Dr. Weinberg’s prodigious output went well beyond his contributions to the Standard Model. In the mid1960s, after the discovery of cosmic background radiation, the heat signature left over from the Big Bang at the beginning of the universe, Dr. Weinberg began studying cosmology, leading to his book “Gravitation and Cosmology” in 1972.
Soon after, he was invited to give a talk on the subject at the undergraduate science center at Harvard. During the lecture, Dr. Weinberg described the evolution of the universe in the first three minutes after the Big Bang, when things had cooled down enough for atomic nuclei to bond together. He then commented, “After that, nothing of any interest would happen in the history of the universe.” Image Dr. Weinberg reached a wide general readership with this 1977 book explaining the explosive evolution of the universe in its first three minutes. Dr. Weinberg reached a wide general readership with this 1977 book explaining the explosive evolution of the universe in its first three minutes.
The quip led a book publisher to engage Dr. Weinberg to write “The First Three Minutes,” which gained a wide readership and made cosmology a respectable field for physicists. In the book he described the earth as “a tiny part of an overwhelmingly hostile universe” and famously, and grimly, concluded, “The more the universe seems comprehensible, the more it also seems pointless.”
He wrote many other books, including one on the history of science, “To Explain the World: The Discovery of Modern Science” (2015), and three volumes totaling 1,500 pages, on quantum field theory, which merges classical physics, special relativity and quantum mechanics. The series is widely regarded as the definitive text on the subject.
Dr. Willy Fischler, a theoretical physicist whom Dr. Weinberg recruited for the faculty of the University of Texas, Austin, in 1982, said that Dr. Weinberg’s greatest work may have been in the development of effective field theory, which provides a mathematical method to use in relatively lowenergy experiments to detect the effects of higher energy particles that can’t be seen or measured directly. Dr. Fischler called him the father of effective field theory.
Steven Weinberg was born in New York City on May 3, 1933, the only child of Frederick and Eva (Israel) Weinberg. His father was a court stenographer, his mother a homemaker.
As he told the Nobel Institute in a 2001 interview, he first became interested in science when a cousin of his who had been given a chemistry set passed it along to him. The cousin had decided to take up boxing instead. “Perhaps he should have stayed in science,” Dr. Weinberg said.
He went to the Bronx High School of Science, where Sheldon Lee Glashow was among his classmates and friends. After graduating from Cornell University in 1954, he spent a year at the Institute for Theoretical Physics in Copenhagen, which was later renamed the Niels Bohr Institute, after the Nobel laureate. Dr. Weinberg returned to the United States in 1955 to work on his Ph.D. at Princeton University under Sam Treiman, a noted theoretical physicist.
Dr. Weinberg worked at Columbia University until 1959 and then at the University of California, Berkeley, until 1966, when he became a lecturer at Harvard and a visiting professor at nearby M.I.T. until 1969. M.I.T. then hired him, but he moved back to Harvard in 1973 to become the Higgins professor of physics, succeeding Julian Schwinger, who had won the Nobel Prize in 1965 for his contributions to the understanding of particle physics. Dr. Weinberg was also named the senior scientist at the Smithsonian Astrophysical Observatory, which is also in Cambridge, Mass., along with Harvard and M.I.T.
Dr. Weinberg married Louise Goldwasser in 1954; they had met as undergraduates at Cornell. In 1980, Ms. Weinberg joined the University of Texas, Austin, as a law professor. For the next two years, she and Dr. Weinberg commuted back and forth from Cambridge as Dr. Weinberg wrapped up his work at Harvard. He joined his wife in Texas in 1982, becoming a professor of physics and astronomy, as he had been at Harvard.
As part of his move, Dr. Weinberg was allowed to create a highlevel theoretical physics research group at the University of Texas and to recruit professors for it. It has grown to include eight full professors and five assistant professors and is considered one of the leading centers of physics research in the United States.
Dr. Fischler, who continues to work with the theory group, said of Dr. Weinberg, “He had a knack to consider the important problems, but not only what was important, but what was solvable.”
Dr. Weinberg, who never retired, continued to teach until the spring this year.
He received many awards and accolades besides the Nobel, including the National Medal of Science in 1991 and the Benjamin Franklin Medal for Distinguished Achievement in Science in 2004. He was elected to the American Academy of Arts and Sciences and the Royal Society in Britain. Last year, he received a $3 million award for his contributions to fundamental physics from the Breakthrough Prize Foundation, founded by Mark Zuckerberg of Facebook, Sergey Brin of Google and Jack Ma of Alibaba, among others.
In addition to his daughter, a medical doctor, he is survived by his wife and a granddaughter.
Dr. Weinberg opposed religion, believing that it undermined efforts to seek and discover truth. In “The First Three Minutes” he wrote, “Anything that we scientists can do to weaken the hold of religion should be done and may in the end be our greatest contribution to civilization.” In his interview with the Nobel Institute, he was asked him about his oftenquoted line near the end of “The First Three Minutes” — “The more that the universe seems comprehensible, the more it also seems pointless.”
“What I meant by that statement is that there is no point to be discovered in nature itself; there is no cosmic plan for us,” he said. “We are not actors in a drama that has been written with us playing the starring role. There are laws — we are discovering those laws — but they are impersonal, they are cold.”
He added: “It is not an entirely happy view of human life. I think it is a tragic view, but that is not new to physicists. A tragic view of life has been expressed by so many poets — that we are here without purpose, trying to identify something that we care about.”
Correction: July 26, 2021 An earlier version of this obituary referred incorrectly to a lecture series, titled "On the Shoulders of Giants," in which Dr. Weinberg was the inaugural speaker. It was held in 2011, not 2015, and the event, sponsored by the World Science Festival, took place at New York University, not Columbia University.
"Hi, Mel,
I remember Ben Forsyth very well. There was an exam for the New York State Scholarship that we both took. I came in second in the Bronx. Ben came in first. This I have never forgiven."
He sat for portraits with me on three occasions, and used the images on some of his book jackets, including To Explain the World and the second edition of Lectures on Quantum Mechanics. When I took this photograph, we were in his home, where I had set up a backdrop and lights.
“Stop that,” he said. “Get out of there.”
“Excuse me?” I asked, worried that I had somehow offended him.
“Stop that,” he said again. He was talking to his cats, who had climbed into my camera bag. He didn’t use that cloying voice most people assume for their petshe was talking to them in the same way he'd address you or me.
After this shoot, he poured me a tiny glass of sherry (or possibly port) and we talked about Newton’s OPTICKS.
Some Reminiscences of Steven Weinberg
I was extremely lucky to have started my PhD in 1981, just before Steve joined UT. Coming from Guatemala, UT was the only place I could have hoped to be accepted in the US for my PhD, thanks to an initiative started by Robert Little to support Central American physicists. I knew the high energy and relativity groups were already very strong at UT and I was very pleased to have been accepted with the help of Robert Little and Mel Oakes that I had met in a school in Guatemala a few years before.
After finishing the ‘big seven’ courses, I managed to get the courage to ask Steve to be my PhD supervisor. After some hesitation, he asked me to read his more recent paper and discuss it with him after a week. An impossible task, but I did my best to get an idea about that paper. Luckily for me, Steve was very busy and after that week, he asked me to talk with his postdoc, Joe Lykken, (now deputy director of Fermilab) who was already working with him. Joe assigned me a project which was an extension of his work with Steve, and I managed to pass my qualifying exam even though I was extremely nervous since the previous student of Steve had failed and left the field.
After the qualifying exam, I became a member of ‘Weinberg’s group’ and we met every week for the legendary brown bag lunches in his office. Each time, one or two members of the group reported on some original work in progress or some review of recent papers. The atmosphere was tense for a PhD student, but we learned a lot from Steve’s continuous interruptions to get to understand each subject in his own way. This experience, together with the interactions with all of Steve’s visitors and the new hires, such as Willy Fischler and Joe Polchinski (and the other theorists who were already at UT, such as Cecil and Bryce DeWitt, Philip Candelas, Claudio Teitelboim, George Sudarshan, Duane Dicus, John Wheeler and the great group of postdocs and fellow students), made the PhD experience exceptionally rich.
During that time, String Theory came to prominence, and Steve and the whole group moved to work in this direction. They were very exciting times and we felt UT was one of the top places in the world for the subject. This allowed me to finish a good PhD thesis under Steve’s supervision, although much of my work I did with fellow students such a s Cliff Burgess and Anamaría Font. Joe Polchinski was one of my examiners and, being the first time he had to examine a thesis, he came with many questions to ask me after my standard presentation. Luckily for me, Steve stopped Joe and told him that the thesis was good and we should finish fast and reserve any questions for later. I was very much relieved.
Steve helped me then to move on my career. It was because of his special recommendation that I was given a nice postdoc at CERN after UT and also for the many later jobs I got. The fact that I was a student of Steve's played a crucial role with my professorship at Cambridge and even my ten years as director of the Abdus Salam International Centre for Theoretical Physics (ICTP). For this, I will always be in his debt.
During all these years, I have remained in touch with him and we met on several occasions. Just to mention a few:
After finishing my PhD, I asked Steve if he would be willing to donate his collection of scientific journals to the Guatemalan national university to which he kindly agreed. We needed only to get someone to pay for the transportation. Abdus Salam immediately agreed and arranged for ICTP to cover the expenses. I used to call this the last WeinbergSalam collaboration.
For my 60th year conference, Steve recorded a 5 minutes video to talk about me and wish me a happy birthday. This video is now one of my greatest treasures. Also, on the occasion of the 50th anniversary of his Nobel prize paper (17 October 2017) I organized a special colloquium at ICTP that Steve kindly accepted to give: ‘Reminiscences of the Standard Model’
https://www.youtube.com/watch?v=mX2R8nJhLQ
Since Steve had constantly rejected all attempts to have a conference in his honour, I took this opportunity to give a 15 minutes introduction to the main scientific contributions of Steve. This, of course, did not do him justice, but at least illustrates that while an introduction of 15 minutes is enough to summarise a normal scientist's achievements, for Steve, this was impossible.
A few years ago, after some email exchanges he told me he was talking with a used car dealer and realized that his last name was Quevedo, Steve was curious if this last name was common in Spanish speaking countries and asked me about it. I don’t remember how I answered, but always wondered what was Steve doing talking with a used car dealer!
Even though I was Steve’s student we did not collaborate on scientific papers. He usually preferred to work by himself. Howeve,r due to the sad death of Joe Polchinski, we joined Raphael Bousso to write a scientific biography of Joe for the National Academy. I appreciated a very human aspect of Steve while writing this article.
https://inspirehep.net/literature/1778922
The last time I met Steve in person was in February 2018, when I went to UT and gave a colloquium. He kindly introduced me (he needed only 12 minutes of course). Here is a photograph that Harry Swinney kindly took on that occasion:
His many contributions to science, including his outstanding textbooks and popular science books, are well documented, as well as his famous quotes on many aspects of science and related subjects. Here I would like to finish by sharing a couple of Steve’s quotes that may be less known:
During the question period after his colloquium at ICTP, someone asked him how has he managed to get so much done in his career to which he replied: "Very simple, I don’t go to church and I don’t ski, so I have plenty of free time." Finally, we were having a conversation once on religion, and he emphasized that you do not need to be religious to have high moral standards and said: "I know many atheists that have very high moral standards, for instance myself!"
It has been my greatest honour to somehow have my career and my life associated with such an incredible human being as Steve Weinberg; it is impossible for me to exaggerate how much admiration I have for him.
Some Reminiscences of Steven Weinberg
My thesis advisor at UT Austin was George Sudarshan. But later the core part of my thesis work was vetted by Steve Weinberg and friendly postdocs of his group. When I finished I had an offer for a postdoc back in India but the formal process was going to take long. I approached Steve and he readily accepted me as a Research Associate.
To be facetious I would say George at one point was famous for his theory of tachyons and Weinberg gave the precise prescription to make massless bosons as well as chiral fermions massive, creating tardyons amenable to renormalisation. Between these two great physicists and their groups much of my thesis work unfolded.
One memory I have is of getting into the elevator on the 4th floor ( the ground floor) of the RLM building one morning and Weinberg. Just when it was starting a tall young Texan college man walked in – in my colorful imagination he is even wearing the cowboy hat – and in a really jovial loud drawl said “Good Morning Professor Weinberg”, this was early 1980’s and Weinberg joining was a big news in the papers or the student had probably heard him give a talk as well. Weinberg held his satchel wordlessly and looked straight at the elevator door. The young student got off at one of the early levels where the classrooms used to be and the elevator mostly became empty. As we approached 9th floor the other faculty member told him something like, Steve that was Texan hospitality for you. Weinberg said “Yea, I guess he was trying to be friendly to me, but I am not used to friendliness”.
I attended about six semesters of Weinberg’s high power courses. From Fall 82 to Spring 84 what later became volumes I and II of QFT, could not attend the volume III on SUSY but again attended the course on String Theory during the calendar year 1986. These were highly charged classes with all the details worked out in great detail on the board. I had chosen a seat somewhere front left of the class and held it regularly. During the pleasant spring time of Austin, Weinberg wanted to let the fresh air in. On more than one occasion he grumbled about the modern central air conditioning. He would come with an Allen key in his jacket pocket and go over to a window near the podium and push it open. His classes were in the TuesdayThursday11 am slot and regularly went on till 12:45, at which point he would vanish as the class was trying to finish copying out the last lines on the board. But if you asked any question during the class he answered it in the most friendly way.
The handwritten notes would come at regular intervals. They were the cryptic writeup of the calculations but would be unintelligible to someone who did not know the context. I once asked him in class why he would not include also a little punchline to the derivation in the notes. He laughed and said, for that you have to come to the class. The QFT notes looked evolved over some time, but when the string theory course started, and it was a subject in high ferment then, Steve’s notes came with the same rigour and the same detail.
Below are page of Weinberg's 1982 lecture notes on Quantum Field Theory made available by Anamaria Font and Urjit Yajnic, students in the class.
In my later PhD years as I struggled to find and solve my thesis problems Mark Rubin, Steve Blau and Andy Albrecht made nice friends and my thesis was definitely helped by them. At this point I picked up enough courage and started joining the brown bag lunch seminars that would happen in Weinberg’s office on Tuesdays. I made two presentations for two of the problems that reached publication quality. It was very intimidating standing within a few feet of Weinberg and the whole group of a dozen or so physicists of high accomplishments in that office and trying to convince them you had done something interesting. On the second occasion which was a smaller piece but precisely defined work, Weinberg began asking questions in disbelief. And I had no facility to answer. But Polchinski was sitting in the back of the group and he started nodding at me. I picked up enough courage and then later Polchinski also joined in to let Weinberg know there was some precedent for the unusual effect I was talking about. After that session got over I went over to Sudarshan’s office (all the way the other end of the hall) for some work. And while I was there we suddenly heard the booming voice coming down the hall “George, George ...” and Weinberg walked in. They were supposed to go for some meeting together and then he saw me. And he immediately said “Oh, you should not mind [the way I was asking questions], just that when I am trying to understand something I get like that.” This was the most disarming apology if we may call it so, and for the remainder of my time there I lived in “who’s afraid of Steve Weinberg” mode, well to the extent I could, because the next time I had to give a talk in front of him I was just as awkward.
In 1983 Salam visited and gave a colloquium in which he announced the miracle of D=11 supergravity as a potential theory of gravity and tongue in cheek, announced that 11 was not a special number to any of the major religions. Weinberg in his introduction said something like the zeal with which Salam takes up themes would makes the rest of us feel guilty if we did not join in.
There are a few interesting memories of the time as an Associate during 1986 when one got invited to join the Theory Group at the Faculty Club for lunch. I once remember looking around our rather cramped round table to note that Weinberg was the only American, all others were from Chile, Sri Lanka, Romania, Sweden, Belgium, UK, Japan, Britain, ... and of course me. On one of those occasions he surprised Teitelboim with a rhetorical question “So how do you think a dictator feels when he stands at his balcony in the morning [looking at the people below]”, referring of course to the situation in Chile.
Someone once asked him why in late 60’s early 70’s he did not take up to work on the proof of renormalisation of the Electroweak theory himself. And his response was that he was busy with several other things, including his involvement with the SALT treaty preparation for which he was travelling frequently to Washington DC.
When in early 1987 my offer from Tata Institute of Fundamental Research arrived I planned to move back to India. I first went to John Wheeler who had been a very kind mentor to me. He tried dissuading me in his characteristic style saying, “Oh I know so and so who went back to Iran and then he got sent to the war front with Iraq and when we asked him how that was, he said, oh those Iraqis, they can’t shoot straight”. Yes the world did look very bleak from those lofty towers but I was somehow set upon returning to India to bring back the excellent science I had learnt. I then went to Weinberg and he bluntly asked “Are you sure you want to go”? I should mention at this point that once Weinberg took someone under his wing, wings were bound to grow on you and he was willing to wait and maintain some level of support till that happened. But I had made up my mind. And then I said, will you remember me? He had after all heard me out on my thesis topics and had also signed my thesis as a member of the defence committee. And he immediately pointed to his shelf and said, “Yes of course I have your thesis right there along with those of my students.”
By mid90’s email communication became possible and I mailed him on several occasions, sometimes sending my papers. His reply would definitely come, sometimes very quickly, especially from someone as busy as him. At a critical juncture in late 1990’s as a midcareer faculty trying still to decide what should my next project be, I asked him exactly that. Pat came his reply : “Dear Urjit If I had a problem that I could assign to someone I should rather give it to a graduate student or a young physicist here.” Fair enough I was a grown up boy and I did not have to lean on him, but I was persistent, and I reverted specifying the two broad directions one somewhat formal the other phenomenological, that I was trying to decide between. And equally promptly he replied putting his finger on my second option, supersymmetric model building.
I take this opportunity to record my sadness at having lost a mentor and lifelong inspiration at least some years sooner than most of us had thought. I was extremely fortunate to have joined UT Austin at such a unique time. When I look back, the mentors and great teachers I had there, despite the wide variety of specific contributions they became famous for, there was a common ethos that always attempted to create an elegant and lucid mathematical framework, yet be uncompromisingly attached to the guidance of Nature. In Hindustani music (North Indian classical music), a gharana is a system of social organisation in the Indian subcontinent, linking musicians or dancers by lineage or apprenticeship, and more importantly by adherence to a particular musical style. In theoretical physics I have subsequently seen the undercurrents of many different attitudes and styles. The unique legacy that I and my contemporaries carry may well be called the Texas gharana.
Some Reminiscences of Secretaries
Steve's classnotes were usually brought to the classroom by Weinberg's secretary
Adele
Traverso. She had a demeanor that fended off any agencies likely to waste even a second of her boss' time. The other notable secretaries who were the lifelines of our offices were Eliane Dunn in CPT and Zelda Davis who was Wheeler's secretary  she used to "look after" us somewhat clueless graduate students well.
And then there was Janee M. Richardson Trybyszewski who ran the whole department. She had to invade our room down in the second level dungeon once after there were reports it was being used as a temporary residence. I kept working at my desk while she investigated. No it was not me.
Steven Weinberg, a theorist who unified two fundamental forces and shaped the way physicists and the public thought about the universe, died July 23 in Austin at 88.
“Steve was one of the last figures from this heroic era of particle physics that culminated in the development of the Standard Model,” said Scott Aaronson, a theoretical computer scientist at the University of Texas at Austin, where Weinberg was a professor for forty years.
If he achieved mythic status through physics, it was from humble beginnings. Steven Weinberg was born in New York City to Frederick and Eva Weinberg, a court stenographer and homemaker respectively. Weinberg’s interest in science was cultivated at the Bronx High School of Science, where he was—famously—classmates with Glashow, who would also go on to attend Cornell.
After Cornell, Weinberg married Louise Goldwasser, and the newlyweds spent a year in Copenhagen. He then went back to America and finished his PhD with Sam Treiman at Princeton on weak decays and renormalization, the mathematical technique for wrangling annoying infinities. Over the next decade, he bounced from Columbia to Berkeley before landing in Cambridge, MA, where he held appointments at MIT and Harvard.
In the early 1960s, Glashow and Salam attempted to unify electromagnetism and the weak force by proposing massive W and Z bosons as force carriers. But giving the W and Z mass made the theory nonrenormalizable. Weinberg took the idea of spontaneous symmetry breaking and in three brisk pages showed how the mechanism could lead the W and Z to appear massive at lower energies. One of the most impactful papers in particle physics, “A Model of Leptons” went mostly unnoticed: for two years after it was published in Physical Review Letters, it garnered only two citations.
“Why doesn't anybody quote his paper between 1967 and 1970? The reason is nobody could do that calculation,” said Helen Quinn, a professor emerita at SLAC. Weinberg knew that his model was “probably renormalizable,” but it wasn’t until a 1970 paper by Gerard t’Hooft that the dam burst and citations flooded in. When Quinn and her coauthors did the first oneloop calculation for Weinberg’s theory, “he was so happy he invited us to sherry at his house,” she said.
As a theorist, Weinberg was not particularly focused on model building. “It is ironic that his Nobel Prize was for a specific model, because he was really interested in the general picture and not in the specific models, no matter how beautiful,” Howard Georgi, a Harvard physicist, wrote in an email to APS News.
“He told me why once: Models are almost always wrong. But if you have general arguments that follow from general principles, that has a chance of being correct in the long run,” said John Preskill, a physicist at Caltech and one of Weinberg’s students.
Quinn recalls an argument between Julian Schwinger and Weinberg during a student’s thesis defense. “Julian's position was effectively that that theory is best which is flexible enough to accommodate all new data and be adapted to it,” she said. “Steve's position was that that theory is best which is very well defined, and thus can be tested and ruled out.”
Some of Weinberg’s colleagues argue that his real seminal contribution to particle physics was not electroweak unification but articulating how to think about effective quantum field theories (EQFTs). Though EQFTs had been in use for decades, Weinberg’s insight was that physics lurking at much higher energies would appear in terms suppressed by heavy masses. This perspective shaped the hunt for unknown particles and “underlies almost everything we do from LHC physics to string theory to dark matter,” Georgi wrote.
Beyond particle physics, Weinberg also made contributions to astrophysics and cosmology, in particular by reintroducing the cosmological constant as a problem—prior to the discovery of dark energy—and working on matterantimatter asymmetry in the early universe. He expounded on his view that the very small and very large were connected in The First Three Minutes, a popular science text, which both introduced the public to cosmic microwave background radiation for the first time and inspired a generation of practicing physicists to hone their cosmological queries.
In 1981, Weinberg followed his wife Louise to UT Austin, where she was already a professor at the law school. He established a theoretical physics department where his Tuesday precolloquium lunches became de rigeur. “The discussion was basically led by him,” said Willy Fischler, a theorist at UT Austin. “Often, it was about history, poetry, and literature.”
Despite his laurels and seniority, Weinberg continued teaching. This fall, he was set to teach a course on thermodynamics and statistical mechanics. “I was amazed. I mean Steve is 88, and he's going to teach a course that he has never taught,” said Fischler.
Colleagues noted Weinberg’s intensity and testified to his singlemindedness when attacking a physics problem. “He wasn't going to come to your office and say, ‘How are you doing? How was your weekend?’ He wasn't that kind of person,” said Sonia Paban, a theoretical physicist at UT Austin.
Weinberg was known for his solitary style, and he was frequently a sole author. When working from home, Weinberg kept a TV on his desk and enjoyed listening to old movies in the background to feel less isolated. But earlier in his career, Weinberg frequently collaborated with physicists like Quinn, Glashow, and Benjamin Lee.
When Quinn and Roberto Peccei published their approach to the strong CP problem, they did not predict an axion. “Weinberg actually called me up and asked me, ‘Did you notice that your theory has this property that there's a pseudoGoldstone boson?’ And I said, ‘Well, no, I didn't. But you're absolutely right. Obviously, it does.’ And he said, ‘Well, in that case, I'll publish it myself.’” Quinn said. “So what he was doing was giving me the opportunity to be a coauthor of the paper with the axion.”
Others also spoke to Weinberg’s sense of fairness. Paban recalls an incident when a visiting Nobel laureate dismissed a question by a student during a colloquium. “The speaker looked at [the student] and said, ‘I see you don't understand’ and he proceeded,” she said. “Steve raised his hand and said, ‘I don't understand that—and don't give me that answer.’”
For Weinberg, the pursuit of understanding was not an idle matter. “Our mistake is not that we take our theories too seriously, but that we do not take them seriously enough,” he wrote in The First Three Minutes.
“Steve said, ‘I think we don't take our theories seriously enough, because it's so hard to believe that the squiggles that you make on a piece of paper are actually the way nature works.’” Preskill said. “In his case, and in a few spectacular examples, they were indeed.”
The author is a science writer based in Bellport, New York.
Our job in physics is to see things simply, to understand a great many complicated phenomena in a unified way, in terms of a few simple principles. At times, our efforts are illuminated by a brilliant experiment, such as the 1973 discovery of neutral current neutrino reactions. But, even in the dark times between experimental breakthroughs, there always continues a steady evolution of theoretical ideas, leading almost imperceptibly to changes in previous beliefs. In this talk, I want to discuss the development of two lines of thought in theoretical physics. One of them is the slow growth in our understanding of symmetry and, in particular, broken or hidden symmetry. The other is the old struggle to come to terms with the infinities in quantum field theories. To a remarkable degree, our present detailed theories of elementary particle interactions can be understood deductively, as consequences of symmetry principles and of a principle of renormalizability which is invoked to deal with the infinities. I will also briefly describe how the convergence of these lines of thought led to my own work on the unification of weak and electromagnetic interactions. For the most part, my talk will center on my own gradual education in these matters because that is one subject on which I can speak with some confidence. With rather less confidence, I will also try to look ahead and suggest what role these lines of thought may play in the physics of the future.
Symmetry principles made their appearance in twentieth century physics in 1905 with Einstein’s identification of the invariance group of space and time. With this as a precedent, symmetries took on a character in physicists’ minds as a priori principles of universal validity, expressions of the simplicity of nature at its deepest level. So it was painfully difficult in the 1930s to realize that there are internal symmetries, such as isospin conservation, [1] having nothing to do with space and time, symmetries which are far from selfevident, and that only govern what are now called the strong interactions. The 1950s saw the discovery of another internal symmetry  the conservation of strangeness [2] —which is not obeyed by the weak interactions, and even one of the supposedly sacred symmetries of spacetime—parity—was also found to be violated by weak interactions. [3] Instead of moving toward unity, physicists were learning that different interactions are apparently governed by quite different symmetries. Matters became yet more confusing with the recognition in the early 1960s of a symmetry group—the “eightfold way” —which is not even an exact symmetry of the strong interactions. [4]
These are all “global” symmetries, for which the symmetry transformations do not depend on position in space and time. It had been recognized [5] in the 1920s that quantum electrodynamics has another symmetry of a far more powerful kind, a “local” symmetry under transformations in which the electron field suffers a phase change that can vary freely from point to point in spacetime, and the electromagnetic vector potential undergoes a corresponding gauge transformation. Today, this would be called a U(1) gauge symmetry, because a simple phase change can be thought of as multiplication by a 1 x 1 unitary matrix. The extension to more complicated groups was made by Yang and Mills [6] in 1954 in a seminal paper in which they showed how to construct an SU(2) gauge theory of strong interactions. (The name “SU(2)” means that the group of symmetry transformations consists of 2 x 2 unitary matrices that are “special,” in that they have determinant unity). But here, again, it seemed that the symmetry, if real at all, would have to be approximate because, at least on a naive level, gauge invariance requires that vector bosons like the photon would have to be massless, and it seemed obvious that the strong interactions are not mediated by massless particles. The old question remained: if symmetry principles are an expression of the simplicity of nature at its deepest level, then how can there be such a thing as an approximate symmetry? Is nature only approximately simple?
Some time in 1960 or early 1961, I learned of an idea which had originated earlier in solid state physics and had been brought into particle physics by those like Heisenberg, Nambu, and Goldstone, who had worked in both areas. It was the idea of “broken symmetry,” that the Hamiltonian and commutation relations of a quantum theory could possess an exact symmetry, and that the physical states might nevertheless not provide neat representations of the symmetry. In particular, a symmetry of the Hamiltonian might turn out to be not a symmetry of the vacuum.
As theorists sometimes do, I fell in love with this idea. But, as often happens with love affairs, at first I was rather confused about its implications. I thought (as turned out, wrongly) that the approximate symmetries— parity, isospin, strangeness, the eightfold way— might really be exact a priori symmetry principles, and that the observed violations of these symmetries might somehow be brought about by spontaneous symmetry breaking. It was, therefore, rather disturbing for me to hear of a result of Goldstone, [7] that, in at least one simple case, the spontaneous breakdown of a continuous symmetry like isospin would necessarily entail the existence of a massless spin zero particle  what would today be called a “Goldstone boson.” It seemed obvious that there could not exist any new type of massless particle of this sort which would not already have been discovered.
I had long discussions of this problems with Goldstone at Madison in the summer of 1961, and then, with Salam while I was his guest at Imperial College in 196l–1962. The three of us soon were able to show that Goldstone bosons must, in fact, occur whenever a symmetry like isospin or strangeness is spontaneously broken and that their masses then remain zero to all orders of perturbation theory. I remember being so discouraged by these zero masses that when we wrote our joint paper on the subject, [8] I added an epigraph to the paper to underscore the futility of supposing that anything could be explained in terms of a noninvariant vacuum state: it was Lear’s retort to Cordelia, “Nothing will come of nothing: speak again.” Of course, The Physical Review protected the purity of the physics literature, and removed the quote. Considering the future of the noninvariant vacuum in theoretical physics, it was just as well.
There was actually an exception to this proof pointed out soon afterwards by Higgs, Kibble, and others. [9] They showed that if the broken symmetry is a local, gauge symmetry like electromagnetic gauge invariance then, although the Goldstone bosons exist formally and are in some sense real, they can be eliminated by a gauge transformation, so that they do not appear as physical particles. The missing Goldstone bosons appear instead as helicity zero states of the vector particles, which thereby acquire a mass.
I think that, at the time, physicists who heard about this exception generally regarded it as a technicality. This may have been because of a new development in theoretical physics which suddenly seemed to change the role of Goldstone bosons from that of unwanted intruders to that of welcome friends.
In 1964, Adler and Weisberger [10] independently derived sum rules which gave the ratio gA/gV of axialvector to vector coupling constants in beta decay in terms of pionnucleon cross sections. One way of looking at their calculation, (perhaps the most common way at the time), was as an analogue to the old dipole sum rule in atomic physics: a complete set of hadronic states is inserted in the commutation relations of the axial vector currents. This is the approach memorialized in the name of “current algebra.” [11] But there was another way of looking at the AdlerWeisberger sum rule. One could suppose that the strong interactions have an approximate symmetry, based on the group SU(2) x SU(2), and that this symmetry is spontaneously broken, giving rise among other things to the nucleon masses. The pion is then identified as (approximately) a Goldstone boson, with small nonzero mass, an idea that goes back to Nambu. [12] Although the SU(2) X SU(2) symmetry is spontaneously broken, it still has a great deal of predictive power, but its predictions take the form of approximate formulas, which give the matrix elements for low energy pionic reactions. In this approach, the AdlerWeisberger sum rule is obtained by using the predicted pion nucleon scattering lengths in conjunction with a wellknown sum rule [13] which, years earlier, had been derived from the dispersion relations for pionnucleon scattering.
In these calculations, one is really using not only the fact that the strong interactions have a spontaneously broken approximate SU(2) X SU(2) symmetry, but also that the currents of this symmetry group are, up to an overall constant, to be identified with the vector and axial vector currents
of beta decay. (With this assumption gA/gV gets into the picture through the GoldbergerTreiman relation, [14] which gives gA/gV in terms of the pion decay constant and the pion nucleon coupling.) Here, in this relation between the currents of the symmetries of the strong interactions and the physical currents of beta decay, there was a tantalizing hint of a deep connection between the weak interactions and the strong interactions. But this connection was not really understood for almost a decade.
I spent the years 196567 happily developing the implications of spontaneous symmetry breaking for the strong interactions. [15] It was this work that led to my 1967 paper on weak and electromagnetic unification. But before I come to that I have to go back in history and pick up one other line of thought having to do with the problem of infinities in quantum field theory.
I believe that it was Oppenheimer and Waller in 1930 [16] who independently first noted that quantum field theory, when pushed beyond the lowest approximation, yields ultraviolet divergent results for radiative self energies. Professor Waller told me last night that when he described this result to Pauli, Pauli did not believe it. It must have seemed that these infinities would be a disaster for the quantum field theory that had just been developed by Heisenberg and Pauli in 1929–1930. And indeed, these infinities did lead to a sense of discouragement about quantum field theory, and many attempts were made in the 1930s and early 1940s to find alternatives. The problem was solved (at least for quantum electrodynamics) after the war, by Feynman, Schwinger, and Tomonaga [17] and Dyson [19]. It was found that all infinities disappear if one identifies the observed finite values of the electron mass and charge, not with the parameters m and e appearing in the Lagrangian, but with the electron mass and charge that are calculated from m and e, when one takes into account the fact that the electron and photon are always surrounded with clouds of virtual photons and electronpositron pairs [18]. Suddenly all sorts of calculations became possible and gave results in spectacular agreement with experiment.
But even after this success, opinions differed as to the significance of the ultraviolet divergences in quantum field theory. Many thought—and some still do think—that what had been done was just to sweep the real problems under the rug. And it soon became clear that there was only a limited class of socalled “renormalizable” theories in which the infinities could be eliminated by absorbing them into a redefinition, or a “renormalization,” of a finite number of physical parameters. (Roughly speaking, in renormalizable theories, no coupling constants can have the dimensions of negative powers of mass. But every time we add a field or a spacetime derivative to an interaction, we reduce the dimensionality of the associated coupling constant. So only a few simple types of interaction can be renormalizable.) In particular, the existing Fermi theory of weak interactions clearly was not renormalizable. (The Fermi coupling constant has the dimensions of [mass]2.) The sense of discouragement about quantum field theory persisted into the 1950s and 1960s.
I learned about renormalization theory as a graduate student, mostly by reading Dyson’s papers. [19] From the beginning, it seemed to me to be a wonderful thing that very few quantum field theories are renormalizable. Limitations of this sort are, after all, what we most want, not mathematical methods which can make sense of an infinite variety of physically irrelevant theories, but methods which carry constraints, because these constraints may point the way toward the one true theory. In particular, I was impressed by the fact that quantum electrodynamics could, in a sense, be derived from symmetry principles and the constraints of renormalizability; the only Lorentz invariant and gauge invariant renormalizable Lagrangian for photons and electrons is precisely the original Dirac Lagrangian of QED. Of course, that is not the way Dirac came to his theory. He had the benefit of the information gleaned in centuries of experimentation on electromagnetism and, in order to fix the final form of his theory, he relied on ideas of simplicity (specifically, on what is sometimes called minimal electromagnetic coupling). But we have to look ahead to try to make theories of phenomena which have not been so well studied experimentally, and we may not be able to trust purely formal ideas of simplicity. I thought that renormalizability might be the key criterion, which also, in a more general context, would impose a precise kind of simplicity on our theories and help us to pick out the one true physical theory out of the infinite variety of conceivable quantum field theories. As I will explain later, I would say this a bit differently today, but I am more convinced than ever that the use of renormalizability as a constraint on our theories of the observed interactions is a good strategy. Filled with enthusiasm for renormalization theory, I wrote my PhD thesis under Sam Treiman in 1957 on the use of a limited version of renormalizability to set constraints on the weak interactions, [20] and a little later, I worked out a rather tough little theorem [21] which completed the proof by Dyson [19] and Salam [22] that ultraviolet divergences really do cancel out to all orders in nominally renormalizable theories. But none of this seemed to help with the important problem of how to make a renormalizable theory of weak interactions.
Now, back to 1967. I had been considering the implications of the broken SU(2) x SU(2) symmetry of the strong interactions, and I thought of trying out the idea that perhaps the SU(2) x SU(2) symmetry was a “local,” not merely a “global,” symmetry. That is, the strong interactions might be described by something like a YangMills theory, but, in addition to the vector Ú mesons of the YangMills theory, there would also be axial vector Al mesons. To give the Ú meson a mass, it was necessary to insert a common Ú and Al mass term in the Lagrangian, and the spontaneous breakdown of the SU(2) x SU(2) symmetry would then split the Ú and Al by something like the Higgs mechanism, but since the theory would not be gauge invariant the pions would remain as physical Goldstone bosons. This theory gave an intriguing result, that the A1/Ú mass ratio should be √2 and in trying to understand this result without relying on perturbation theory, I discovered certain sum rules, the “spectral function sum rules,” [23] which turned out to have variety of other uses. But the SU(2) x SU(2) theory was not gauge invariant, and hence it could not be renormalizable, [24] so I was not too enthusiastic about it. [25] Of course, if I did not insert the A1Ú mass term in the Lagrangian, then the theory would be gauge invariant and renormalizable, and the Al would be massive. But then there would be no pions and the Ú mesons would be massless, in obvious contradiction (to say the least) with observation.
At some point in the fall of 1967, I think, while driving to my office at M.I.T., it occurred to me that I had been applying the right ideas to the wrong problem. It is not the Ú mesons that are massless: it is the photon. And its partner is not the Al, but the massive intermediate boson, which since the time of Yukawa had been suspected to be the mediator of the weak interactions. The weak and electromagnetic interactions could then be described [26] in a unified way in terms of an exact but spontaneously broken gauge symmetry. [Of course, not necessarily SU(2) X SU(2)]. And this theory would be renormalizable like quantum electrodynamics because it is gauge invariant like quantum electrodynamics.
It was not difficult to develop a concrete model which embodied these ideas. I had little confidence then in my understanding of strong interactions, so I decided to concentrate on leptons. There are two lefthanded electrontype leptons, the Óe and eL and one righthanded, electrontype lepton, the eR so I started with the group U(2) X U(1): all unitary 2 x 2 matrices acting on the lefthanded etype leptons, together with all unitary 1 X 1 matrices acting on the righthanded etype lepton. Breaking up U(2) into unimodular transformations and phase transformations, one could say that the group was SU(2) X U( 1) X U( 1). But then one of the U(l)‘s could be identified with ordinary lepton number and since lepton number appears to be conserved and there is no massless vector particle coupled to it, I decided to exclude it from the group. This left the fourparameter group SU(2) x U( 1). The spontaneous breakdown of SU(2) x U( 1) to the U(1) of ordinary electromagnetic gauge invariance would give masses to three of the four vector gauge bosons: the charged bosons W±, and a neutral boson that I called the Z0. The fourth boson would automatically remain massless, and could be identified as the photon. Knowing the strength of the ordinary charged current weak interactions like beta decay which are mediated by W±, the mass of the W± was then determined as about 40 GeV/sin(ı) where (ı) is the ÁZ0 mixing angle.
To go further, one had to make some hypothesis about the mechanism for the breakdown of SU (2) x U (1). The only kind of field in a renormalizable SU(2) X U(1) theory whose vacuum expectation values could give the electron a mass is a spin zero SU(2) doublet (º+, º0 ), so for simplicity I assumed that these were the only scalar fields in the theory. The mass of the Z0 was then determined as about 80 GeV/sin (2ı). This fixed the strength of the neutral current weak interactions. Indeed, just as in QED, once one decides on the menu of fields in the theory, all details of the theory are completely determined by symmetry principles and renormalizability, with just a few free parameters: the lepton charge and masses, the Fermi coupling constant of beta decay, the mixing angle ı, and the mass of the scalar particle. (It was of crucial importance to impose the constraint of renormalizability; otherwise, weak interactions would receive contributions from SU(2)xU(I)  invariant fourfermion couplings as well as from vector boson exchange, and the theory would lose most of its predictive power.) The naturalness of the whole theory is welldemonstrated by the fact that much the same theory was independently developed [27] by Salam in 1968.
The next question now was renormalizability. The Feynman rules for YangMills theories with unbroken gauge symmetries had been worked out [28] by deWitt, Faddeev and Popov and others, and it was known that such theories are renormalizable. But in 1967, I did not know how to prove that this renormalizability was not spoiled by the spontaneous symmetry breaking. I worked on the problem on and off for several years, partly in collaboration with students, [29] but I made little progress. With hindsight, my main difficulty was that, in quantizing the vector fields, I adopted a gauge now known as the unitarity gauge [30]: this gauge has several wonderful advantages, it exhibits the true particle spectrum of the theory, but it has the disadvantage of making renormalizability totally obscure.
Finally, in 1971, ‘t Hooft [31] showed in a beautiful paper how the problem could be solved. He invented a gauge, like the “Feynman gauge” in QED, in which the Feynman rules manifestly lead to only a finite number of types of ultraviolet divergence. It was also necessary to show that these infinities satisfied essentially the same constraints as the Lagrangian itself, so that they could be absorbed into a redefinition of the parameters of the theory. (This was plausible, but not easy to prove, because a gauge invariant theory can be quantized only after one has picked a specific gauge, so it is not obvious that the ultraviolet divergences satisfy the same gauge invariance constraints as the Lagrangian itself.) The proof was subsequently completed [32] by Lee and ZinnJustin and by ‘t Hooft and Veltman. More recently, Becchi, Rouet and Stora [33] have invented an ingenious method for carrying out this sort of proof by using a global supersymmetry of gauge theories which is preserved even when we choose a specific gauge.
I have to admit that, when I first saw ‘t Hooft’s paper in 1971, I was not convinced that he had found the way to prove renormalizability. The trouble was not with ‘t Hooft, but with me: I was simply not familiar enough with the path integral formalism on which ‘t Hooft’s work was based, and I wanted to see a derivation of the Feynman rules in ‘t Hooft’s gauge from canonical quantization. That was soon supplied (for a limited class of gauge theories) by a paper of Ben Lee, [34] and after Lee’s paper, I was ready to regard the renormalizability of the unified theory as essentially proved.
By this time, many theoretical physicists were becoming convinced of the general approach that Salam and I had adopted: that is, the weak and electromagnetic interactions are governed by some group of exact local gauge symmetries; this group is spontaneously broken to U(l), giving mass to all the vector bosons except the photon; and the theory is renormalizable. What was not so clear was that our specific simple model was the one chosen by nature. That, of course, was a matter for experiment to decide.
It was obvious even back in 1967 that the best way to test the theory would be by searching for neutral current weak interactions, mediated by the neutral intermediate vector boson, the Z0. Of course, the possibility of neutral currents was nothing new. There had been speculations [35] about possible neutral currents as far back as 1937 by Gamow and Teller, Kemmer, and Wentzel, and again in 1958 by Bludman and LeiteLopes. Attempts at a unified weak and electromagnetic theory had been made
[36] by Glashow and Salam and Ward in the early 1960’s, and these had neutral currents with many of the features that Salam and I encountered in developing the 196768 theory. But, since one of the predictions of our theory was a value for the mass of the Z0, it made a definite prediction of the strength of the neutral currents. More important, now we had a comprehensive quantum field theory of the weak and electromagnetic interactions that was physically and mathematically satisfactory in the same sense as was quantum electrodynamics—a theory that treated photons and intermediate vector bosons on the same footing, that was based on an exact symmetry principle, and that allowed one to carry calculations to any desired degree of accuracy. To test this theory, it had now become urgent to settle the question of the existence of the neutral currents.
Late in 1971, I carried out a study of the experimental possibilities. [37] The results were striking. Previous experiments had set upper bounds on the rates of neutral current processes which were rather low, and many people had received the impression that neutral currents were pretty well ruled out, but I found that, in fact, the 196768 theory predicted quite low rates, low enough, in fact, to have escaped clear detection up to that time. For instance, experiments [38] a few years earlier had found an upper bound of 0.12 ± 0.06 on the ratio of a neutral current process, the elastic scattering of muon neutrinos by protons, to the corresponding charged current process, in which a muon is produced. I found a predicted ratio of 0.15 to 0.25, depending on the value of the Z0  Á mixing angle ı. So there was every reason to look a little harder.
As everyone knows, neutral currents were finally discovered [39] in 1973. There followed years of careful experimental study on the detailed properties of the neutral currents. It would take me too far from my subject to survey these experiments, [40] so I will just say that they have
confirmed the 196768 theory with steadily improving precision for neutrinonucleon and neutrino electron neutral current reactions, and since the remarkable SLACYale experiment [41] last year, for the electronnucleon neutral current as well.
This is all very nice. But I must say that I would not have been too disturbed if it had turned out that the correct theory was based on some other spontaneously broken gauge group, with very different neutral currents. One possibility was a clever SU(2) theory proposed in 1972 by Georgi and Glashow, [42] which has no neutral currents at all. The important thing to me was the idea of an exact spontaneously broken gauge symmetry, which connects the weak and electromagnetic interactions, and allows these interactions to be renormalizable. Of this, I was convinced, if only because it fitted my conception of the way that nature ought to be.
There were two other relevant theoretical developments in the early 1970s, before the discovery of neutral currents, that I must mention here. One is the important work of Glashow, Iliopoulos, and Maiani on the charmed quark. [43] Their work provided a solution to what, otherwise, would have been a serious problem, that of neutral strangeness changing currents. I leave this topic for Professor Glashow’s talk. The other theoretical development has to do specifically with the strong interactions, but it will take us back to one of the themes of my talk, the theme of symmetry.
In 1973, Politzer and Gross and Wilczek discovered [44] a remarkable property of YangMills theories which they called “asymptotic freedom” —the effective coupling constant [45] decreases to zero as the characteristic energy of a process goes to infinity. It seemed that this might explain the experimental fact that the nucleon behaves in highenergy, deep inelastic, electron scattering as if it consists of essentially free quarks. [46] But there was a problem. In order to give masses to the vector bosons in a gauge theory of strong interactions, one would want to include strongly interacting scalar fields, and these would generally destroy asymptotic freedom. Another difficulty, one that particularly bothered me, was that, in a unified theory of weak and electromagnetic interactions, the fundamental weak coupling is of the same order as the electronic charge, e, so the effects of virtual intermediate vector bosons would introduce much too large violations of parity and strangeness conservation, of order 1/137, into the strong interactions of the scalars with each other and with the quarks. [47] At some point in the spring of 1973, it occurred to me (and independently to Gross and Wilczek) that one could do away with strongly interacting scalar fields altogether, allowing the strong interaction gauge symmetry to remain unbroken so that the vector bosons, or “gluons”, are massless, and relying on the increase of the strong forces with increasing distance to explain why quarks as well as the massless gluons are not seen in the laboratory. [48] Assuming no strongly interacting scalars, three “colors” of quarks (as indicated by earlier work of several authors [49]), and an SU(3) gauge group, one then had a specific theory of strong interactions, the theory now generally known as quantum chromodynamics.
Experiments since then have increasingly confirmed QCD as the correct theory of strong interactions. What concerns me here, though, is its impact on our understanding of symmetry principles. Once again, the constraints of gauge invariance and renormalizability proved enormously powerful. These constraints force the Lagrangian to be so simple that the strong interactions in QCD must conserve strangeness, charge conjugation, and (apart from problems [50] having to do with instantons) parity. One does not have to assume these symmetries as a priori principles; there is simply no way that the Lagrangian can be complicated enough to violate them. With one additional assumption, that the u and d quarks have relatively small masses, the strong interactions must also satisfy the approximate SU(2) X SU(2) symmetry of current algebra, which, when spontaneously broken, leaves us with isospin. If the s quark mass is also not too large, then one gets the whole eightfold way as an approximate symmetry of the strong interactions. And the breaking of the SU(3)xSU(3) symmetry by quark masses has just the (3,3)+(3,3) form required to account for the pionpion scattering lengths [15] and GellMannOkubo mass formulas. Furthermore, with weak and electromagnetic interactions also described by a gauge theory, the weak currents are necessarily just the currents associated with these strong interaction symmetries. In other words, pretty much the whole pattern of approximate symmetries of strong, weak, and electromagnetic interactions that puzzled us so much in the 1950s and 1960s now stands explained as a simple consequence of strong, weak, and electromagnetic gauge invariance, plus renormalizability. Internal symmetry is now at the point where spacetime symmetry was in Einstein’s day. All the approximate internal symmetries are explained dynamically. On a fundamental level, there are no approximate or partial symmetries; there are only exact symmetries which govern all interactions.
I now want to look ahead a bit, and comment on the possible future development of the ideas of symmetry and renormalizability.
We are still confronted with the question whether the scalar particles that are responsible for the spontaneous breakdown of the electroweak gauge symmetry SU(2) X U(1) are really elementary. If they are, then spin zero semiweakly decaying “Higgs bosons” should be found at energies comparable with those needed to produce the intermediate vector bosons. On the other hand, it may be that the scalars are composites. [51] The Higgs bosons would then be indistinct broad states at very high mass, analogous to the possible swave enhancement in ππ scattering. There would probably also exist lighter, more slowly decaying, scalar particles of a rather different type, known as pseudoGoldstone bosons. [52] And there would have to exist a new class of “extra strong” interactions [53] to provide the binding force, extra strong in the sense that asymptotic freedom sets in not at a few hundred MeV, as in QCD, but at a few hundred GeV. This “extra strong” force would be felt by new families of fermions, and would give these fermions masses of the order of several hundred GeV. We shall see.
Of the four (now three) types of interactions, only gravity has resisted incorporation into a renormalizable quantum field theory. This may just mean that we are not being clever enough in our mathematical treatment of general relativity. But there is another possibility that seems to me quite plausible. The constant of gravity defines a unit of energy known as the Planck energy, about 1019 GeV. This is the energy at which gravitation becomes effectively a strong interaction, so that at this energy, one can no longer ignore its ultraviolet divergences. It may be that there is a whole world of new physics with unsuspected degrees of freedom at these enormous energies, and that general relativity does not provide an adequate framework for understanding the physics of these superhigh energy degrees of freedom. When we explore gravitation or other ordinary phenomena, with particle masses and energies no greater than a TeV or so, we may be learning only about an “effective” field theory; that is, one in which superheavy degrees of freedom do not explicitly appear, but the coupling parameters implicitly represent sums over these hidden degrees of freedom.
To see if this makes sense, let us suppose it is true, and ask what kinds of interactions we would expect on this basis to find at ordinary energy. By “integrating out” the superhigh energy degrees of freedom in a fundamental theory, we generally encounter a very complicated effective field theory—so complicated, in fact, that it contains all interactions allowed by symmetry principles. But where dimensional analysis tells us that a coupling constant is a certain power of some mass, that mass is likely to be a typical superheavy mass, such as 1019 GeV. The infinite variety of nonrenormalizable interactions in the effective theory have coupling constants with the dimensionality of negative powers of mass, so their effects are suppressed at ordinary energies by powers of energy divided by superheavy masses. Thus, the only interactions that we can detect at ordinary energies are those that are renormalizable in the usual sense, plus any nonrenormalizable interactions that produce effects which, although tiny, are somehow exotic enough to be seen.
One way that a very weak interaction could be detected is for it to be coherent and of long range, so that it can add up and have macroscopic effects. It has been shown [54] that the only particles whose exchange could produce such forces are massless particles of spin 0, 1, or 2. And furthermore, Lorentz’s invariance alone is enough to show that the longrange interactions produced by any particle of mass zero and spin 2 must be governed by general relativity. [55] Thus, from this point of view, we should not be too surprised that gravitation is the only interaction discovered so far that does not seem to be described by a renormalizable field theory  it is almost the only superweak interaction that could have been detected. And we should not be surprised to find that gravity is well described by general relativity at macroscopic scales, even if we do not think that general relativity applies at 1019 GeV.
Nonrenormalizable effective interactions may also be detected if they violate otherwise exact conservation laws. The leading candidates for violation are baryon and lepton conservation. It is a remarkable consequence of the SU(3) and SU(2) x U( 1) gauge symmetries of strong, weak, and electromagnetic interactions, that all renormalizable interactions among known particles automatically conserve baryon and lepton number. Thus, the fact that ordinary matter seems pretty stable, that proton decay has not been seen, should not lead us to the conclusion that baryon and lepton conservation are fundamental conservation laws. To the accuracy with which they have been verified, baryon and lepton conservation can be explained as dynamical consequences of other symmetries, in the same way that strangeness conservation has been explained within QCD. But superheavy particles may exist, and these particles may have unusual SU(3) or SU(2) x SU(1) transformation properties, and in this case, there is no reason why their interactions should conserve baryon or lepton number. I doubt that they would. Indeed, the fact that the universe seems to contain an excess of baryons over antibaryons should lead us to suspect that baryon nonconserving processes have actually occurred. If effects of a tiny nonconservation of baryon or lepton number such as proton decay or neutrino masses are discovered experimentally, we will then be left with gauge symmetries as the only true internal symmetries of nature, a conclusion that I would regard as most satisfactory.
The idea of a new scale of superheavy masses has arisen in another way. [56] If any sort of “grand unification” of strong and electroweak gauge couplings is to be possible, then one would expect all of the SU(3) and SU(2) x U(1) gauge coupling constants to be of comparable magnitude. (In particular, if SU(3) and SU(2) x U(1) are subgroups of a larger simple group, then the ratios of the squared couplings are fixed as rational numbers of order unity.[57]) But this appears in contradiction with the obvious fact that the strong interactions are stronger than the weak and electromagnetic interactions. In 1974, Georgi, Quinn and I suggested that the grand unification scale, at which the couplings are comparable, is at an enormous energy, and that the reason that the strong coupling is so much larger than the electroweak couplings at ordinary energies is that QCD is asymptotically free, so that its effective coupling constant rises slowly as the energy drops from the grand unification scale to ordinary values. The change of the strong couplings is very slow (like 1/√ln E) so the grand unification scale must be enormous. We found that for a fairly large class of theories, the grand unification scale comes out to be in the neighborhood of 1016 GeV, an energy not all that different from the Planck energy of 1019 GeV. The nucleon lifetime is very difficult to estimate accurately, but we gave a representative value of 1032 years, which may be accessible experimentally in a few years. (These estimates have been improved in more detailed calculations by several authors.) [58] We also calculated a value for the mixing parameter of about 0.2, not far from the present experimental of 0.23±0.01. It will be an important task for future experiments on neutral currents to improve the precision with which is known to see if it really agrees with this prediction.
In a grand unified theory, in order for elementary scalar particles to be available to produce the spontaneous breakdown of the electroweak gauge symmetry at a few hundred GeV, it is necessary for such particles to escape getting superlarge masses from the spontaneous breakdown of the grand unified gauge group. There is nothing impossible in this, but I have not been able to think of any reason why it should happen. (The problem may be related to the old mystery of why quantum corrections do not produce an enormous cosmological constant; in both cases, one is concerned with an anomalously small “superrenormalizable” term in the effective Lagrangian which has to be adjusted to be zero. In the case of the cosmological constant, the adjustment must be precise to some fifty decimal places.) With elementary scalars of small or zero bare mass, enormous ratios of symmetry breaking scales can arise quite naturally [59]. On the other hand, if there are no elementary scalars which escape getting superlarge masses from the breakdown of the grand unified gauge group then as I have already mentioned, there must be extra strong forces to bind the composite Goldstone and Higgs bosons that are associated with the spontaneous breakdown of SU(2) x U(1). Such forces can occur rather naturally in grand unified theories. To take one example, suppose that the grand gauge group breaks, not into SU(3) x SU(2) x U(l), but into SU(4) x SU(3) x SU(2) x U(1). Since SU(4) is a bigger group than SU(3), its coupling constant rises with decreasing energy more rapidly than the QCD coupling, so the SU(4) force becomes strong at a much higher energy than the few hundred MeV at which the QCD force becomes strong. Ordinary quarks and leptons would be neutral under SU(4), so they would not feel this force, but other fermions might carry SU(4) quantum numbers, and so get rather large masses. One can even imagine a sequence of increasingly large subgroups of the grand gauge group, which would fill in the vast energy range up to 1015 or 1019 GeV with particle masses that are produced by these successively stronger interactions.
If there are elementary scalars whose vacuum expectation values are responsible for the masses of ordinary quarks and leptons, then these masses can be affected in order α by radiative corrections involving the superheavy vector bosons of the grand gauge group, and it will probably be impossible to explain the value of quantities like me/mu a complete grand unified theory. On the other hand, if there are no such elementary scalars, then almost all the details of the grand unified theory are forgotten by the effective field theory that describes physics at ordinary energies, and it ought to be possible to calculate quark and lepton masses purely in terms of processes at accessible energies. Unfortunately, no one so far has been able to see how, in this way, anything resembling the observed pattern of masses could arise. [60]
Putting aside all these uncertainties, suppose that there is a truly fundamental theory, characterized by an energy scale of order 1016 to 1019 GeV, at which strong, electroweak, and gravitational interactions are all united. It might be a conventional renormalizable quantum field theory but at the moment, if we include gravity, we do not see how this is possible. (I leave the topic of supersymmetry and supergravity for Professor Salam’s talk.) But if it is not renormalizable, what then determines the infinite set of coupling constants that are needed to absorb all the ultraviolet divergences of the theory?
I think the answer must lie in the fact that the quantum field theory, which was born just fifty years ago from the marriage of quantum mechanics with relativity, is a beautiful but not very robust child. As Landau and Kallen recognized long ago, quantum field theory at superhigh energies is susceptible to all sorts of diseases—tachyons, ghosts, etc. and it needs special medicine to survive. One way that a quantum field theory can avoid these diseases is to be renormalizable and asymptotically free, but there are other possibilities. For instance, even an infinite set of coupling constants may approach a nonzero fixed point as the energy at which they are measured goes to infinity. However, to require this behavior generally imposes so many constraints on the couplings that there are only a finite number of free parameters left[6 1] —just as for theories that are renormalizable in the usual sense. Thus, one way or another, I think that quantum field theory is going to go on being very stubborn, refusing to allow us to describe all but a small number of possible worlds, among which, we hope, is ours.
I suppose that I tend to be optimistic about the future of physics. And nothing makes me more optimistic than the discovery of broken symmetries. In the seventh book of the Republic, Plato describes prisoners who are chained in a cave and can see only shadows that things outside cast on the cave wall. When released from the cave, at first their eyes hurt, and, for a while, they think that the shadows they saw in the cave are more real than the objects they now see. But eventually their vision clears, and they can understand how beautiful the real world is. We are in such a cave, imprisoned by the limitations on the sorts of experiments we can do. In particular, we can study matter only at relatively low temperatures, where symmetries are likely to be spontaneously broken, so that nature does not appear very simple or unified. We have not been able to get out of this cave, but by looking long and hard at the shadows on the cave wall, we can at least make out the shapes of symmetries, which though broken, are exact principles governing all phenomena, expressions of the beauty of the world outside.
***
It has only been possible here to give references to a very small part of the literature on the subjects discussed in this talk. Additional references can be found in the following reviews:.
Abers, E.S. and Lee, B.W., Gauge Theories (Physics Reports 9C, No. 1, 1973).
Taylor, J.C., Gauge Theories of Weak Interactions (Cambridge Univ. Press, 1976).
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39. The first published discovery of neutral currents was at the Gargamelle Bubble Chamber at CERN: Hasert, F. J. et al., Phys. Lett. 468, 121, 138 (1973). Also see Musset, P. Jour. de Physique 11 /12 T34 (1973). Muonless events were seen at about the same time by the HPWF group at Fermilab, but when publication of their paper was delayed, they took the opportunity to rebuild their detector, and then did not at first find the same neutral current signal. The HPWF group published evidence for neutral currents in Benvenuti, A. et al., Phys. Rev. Lett. 52, 800 (1974).
40. For a survey of the data see Baltay, C. Proceedings of the 19th International Conference on High Energy Physics, Tokyo, 1978. For theoretical analyses, see Abbott, L. F. and Barnett, R. M. Phys. Rev. D19, 3230 (1979); Langacker, P., Kim, J. E., Levine, M., Williams, H. H. and Sidhu, D. P. Neutrino Conference ‘79; and earlier references cited therein.
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52. Weinberg, S. ref 51, The possibility of pseudoGoldstone bosons was originally noted in a different context by Weinberg, S. Phys. Rev. Lett. 29, 1698 (1972).
53. Weinberg, S. ref. 51. Models involving such interactions have also been discussed by Susskind, L. ref. 51.
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56. Georgi, H., Quinn, H. and Weinberg, S. Phys. Rev. Lett. 33, 45 1 (1974).
57. An example of a simple gauge group for weak and electromagnetic interactions (for which sin 2 ı =1/4, was given by S. Weinberg, Phys. Rev. D5, 1962 (1972). There are a number of specific models of weak, electromagnetic, and strong interactions based on simple gauge groups, including those of Pati, J. C. and Salam, A. Phys. Rev. D10, 275 (1974); Georgi, H. and Glashow, S. L. Phys. Rev. Lett. 32, 438 (1974); Georgi, H. in Particles and Fields (American Institute of Physics, 1975); Fritzsch, H. and Minkowski, P. Ann. Phys. 93, 193 (1975); Georgi, H. and Nanopoulos, D. V. Phys. Lett. 82B, 392 (1979); Gürsey, F. Ramond, P. and Sikivie, P. Phys. Lett. B60, 177 (1975); Gürsey, F. and Sikivie, P. Phys. Rev. Lett. 36, 775 (1976); Ramond, P. Nucl. Phys, B110, 214 (1976); etc; all these violate baryon and lepton conservation, because they have quarks and leptons in the same multiplet; see Pati, J. C. and Salam, A. Phys. Rev. Lett. 31, 661 (1973); Phys. Rev. D8, 1240 (1973).
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Thanks to the Nobel Foundation for permission to publish this talk on this website.
© The Nobel Foundation 1979
Louise Weinberg is holder of the Bates Chair and Professor of Law at the University of Texas School of Law. Weinberg teaches and writes in Constitutional Law and Federal Courts. She received her undergraduate degree summa cum laude from Cornell, was elected to Phi Beta Kappa, holds two Harvard Law degrees, and clerked for Judge Wyzanski. She practiced in Boston as an associate in litigation with Bingham Dana & Gould, now Bingham McCutchen. She has taught at Harvard, Brandeis, and Stanford, and has received the Texas Exes' Excellence in Teaching Award. She is a member of the American Law Institute, and currently serves as an invited Adviser to the projected ALI Restatement (Third) of Conflict of Laws. A frequently invited public speaker, she has served as a Forum Fellow of the World International Forum, Davos. Professor Weinberg was Chair in 2013–2014 of the Association of American Law Schools Section on Conflict of Laws, and has chaired three different AALS Sections, thrice chairing the Section on Federal Courts, twice chairing the Section on Conflict of Laws, and chairing the Section on Admiralty. Recently she appeared in the Public Broadcasting System's fourpart series, The Supreme Court.
In the field of Constitutional Law, Weinberg's writings include Luther v. Borden, A TaneyCourt Mystery Solved (forthcoming 2017); A General Theory of Governance: Due Process and Lawmaking Power, William & Mary Law Review (2013); Unlikely Beginnings of Modern Constitutional Thought, University of Pennsylvania Journal of Constitutional Law (2012); The McReynolds Mystery Solved, University of Denver Law Review (2011); An Almost Archeological Dig: Substantive Due Process, An Early View, Constitutional Commentary (2010); Dred Scott and the Crisis of 1860, Symposium, ChicagoKent Law Review (2007); Our Marbury, Virginia Law Review (2003); and When Courts Decide Elections: The Constitutionality of Bush v. Gore, Symposium, Boston University Law Review (2002).
In the field of Federal Courts, Weinberg is author of Federal Courts: Judicial Federalism and Judicial Power (1994). Her recent work in the field includes Back to the Future: The New General Common Law, Symposium, Journal of Maritime Law and Commerce (2004); Of Sovereignty and Union: The Legends of Alden, Notre Dame Law Review (2001); and The Article III Box, Symposium, Texas Law Review (2000).
In the field of Conflict of Laws, Weinberg is coauthor of The Conflict of Laws (2002). Her work in this field includes A Radical Transformation for Conflicts Restatements, Symposium, Illinois Law Review (2015, pub. 2016 ); What We Don't Talk About When We Talk About Extraterritoriality, Symposium, Cornell Law Review (2015); and Theory Wars in the Conflict of Laws, Michigan Law Review (2005).
In the field of Legal Theory and Jurisprudence, Weinberg's writings include Of Theory and Theodicy: The Problem of Immoral Law, in Law and Justice in a Multistate World (2002) and Choosing Law, Giving Justice, Symposium, Louisiana Law Review (2000).
Weinberg is author of such classic articles as Federal Common Law, Northwestern Law Review (1989) and The New Judicial Federalism, Stanford Law Review (1977), and such provocative essays as Holmes' Failure, Michigan Law Review (1997) and Against Comity, Georgetown Law Journal (1991). She is a contributor to legal encyclopedias for the Oxford and Yale University Presses. Her pieces for the general public have appeared in The American Scholar, The Public Interest, and Daedalus.
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