Notice: We are in the process of migrating Oral History Interview metadata to this new version of our website.
During this migration, the following fields associated with interviews may be incomplete: Institutions, Additional Persons, and Subjects. Our Browse Subjects feature is also affected by this migration.
Please contact [email protected] with any feedback.
Credit: First Post
This transcript may not be quoted, reproduced or redistributed in whole or in part by any means except with the written permission of the American Institute of Physics.
This transcript is based on a tape-recorded interview deposited at the Center for History of Physics of the American Institute of Physics. The AIP's interviews have generally been transcribed from tape, edited by the interviewer for clarity, and then further edited by the interviewee. If this interview is important to you, you should consult earlier versions of the transcript or listen to the original tape. For many interviews, the AIP retains substantial files with further information about the interviewee and the interview itself. Please contact us for information about accessing these materials.
Please bear in mind that: 1) This material is a transcript of the spoken word rather than a literary product; 2) An interview must be read with the awareness that different people's memories about an event will often differ, and that memories can change with time for many reasons including subsequent experiences, interactions with others, and one's feelings about an event. Disclaimer: This transcript was scanned from a typescript, introducing occasional spelling errors. The original typescript is available.
In footnotes or endnotes please cite AIP interviews like this:
Interview of Abhay Ashtekar by David Zierler on February 3, 2021,
Niels Bohr Library & Archives, American Institute of Physics,
College Park, MD USA,
For multiple citations, "AIP" is the preferred abbreviation for the location.
Abhay Ashtekar, Evan Hugh Professor of Physics and Director of the Institute for Gravitation and the Cosmos at Penn State, is interviewed by David Zierler. Ashtekar recounts his childhood in the Indian state of Maharashtra, and discusses his early fascination with physics and the universe. He describes his undergraduate interests in general relativity and the opportunities that led to his enrollment at the University of Texas to join the Center for Relativity. Ashtekar discusses the culture shock when he arrived in Austin and Bob Geroch’s mentorship in quantum gravity, and his decision to follow Geroch to Chicago. He describes his interactions with Chandrasekar and his graduate research on quantum field theory in curved space-times and the asymptotic nature of space-time. Ashtekar discusses his postdoctoral appointment at Oxford to work with Roger Penrose, and he explains the moral origins of his commitment to making his field visible and therefore richer in opportunity for junior scholars. He explains his reasons to return to Chicago for a second postdoc, his decision to join the faculty at Syracuse, and a formative visiting appointment he had in Paris. Ashtekar describes the attraction in joining the faculty at Penn State, and his increasing focus on loop quantum gravity and the intellectual origins of the Ashtekar variable. He explains these developments as part of the broader effort to merge quantum mechanics and general relativity and the implications this will have on our understanding of the Standard Model. Ashtekar surveys the field of loop quantum cosmology and its relation to both inflation and string theory, and he conveys the enjoyment he felt with the detection of gravitational waves. At the end of the interview, Ashtekar explains why he does not like the phrase “theory of everything,” he reflects on the lessons he has learned from the luminaries who have mentored him, and he explains why the field still does not fully understand quantum mechanics.
Okay, this is David Zierler, oral historian for the American Institute of Physics. It is February 3rd, 2021. I'm delighted to be here with Dr. Abhay Ashtekar. Abhay, it's great to see you. Thank you so much for joining me.
It's my pleasure. Thank you for inviting me.
Okay, so to start, would you please tell me your titles and institutional affiliations, and you'll notice I made that plural because I know you have more than one. (Ashtekar: Right.) My home appointment is at Penn State where I'm the Director of the Institute for Gravitation and the Cosmos, Evan Pugh Professor of Physics, and I also hold the Eberly Chair in the College of Science. My other appointment is at the Perimeter Institute in Canada where I hold a Distinguished Visiting Research Chair. I am also on Advisory Boards of several institutions world-wide.
Abhay, were you the inaugural Director of the Institute, or did it precede your tenure?
Yes, I was the inaugural director. The institute began when I moved to Penn State in 1993, so a long time ago! I was offered the Eberly Chair with the understanding that I would create a research center in Gravitation. We decided that the institute should not be frozen in time but should be an evolving entity, taking into account the opportunities that are offered by the intellectual growth of fields, interconnections that develop, and also the local opportunities in terms of faculty hired at Penn State. The institute itself does not have any faculty positions of its own but we look out for potential collaborations in areas across which we need to build bridges. And various departments have been very supportive of these ideas and Penn State has recruited a lot of faculty in the areas covered by the Institute.
Well, Abhay, I'd like to ask before we take it all the way back to the beginning, a very in the moment question, as we're all dealing with the pandemic. As a theoretical physicist, right, in what ways has the physical isolation of the past 10 months been useful for you, perhaps to work on equations that you might not otherwise have had time to, and in what ways has the lack of real, in-person interaction been difficult, both on an interpersonal level, but also on a scientific and collaborative level?
As you said, as theorists, it does give us more time to collaborate at distance by Zoom. This is something that we could have done a long time ago, but we didn't think of it. Now a days almost every of my mornings is taken by zoom meetings with people in Europe, and sometimes, India, China or Japan. It works quite well, especially if you have an iPad because you can write down equations and both people can work on the same whiteboard. But I have to confess that it has a negative side in that it does create a lot of eye strain so I cannot do it too long.
And there is a limitation because there is a real difference between Zoom and in-person interaction. There is synergy --a psychological space you enter-- when you are in front of a big blackboard, that is missing. In part, it could just be that my generation of people were used to blackboards, and maybe the next generation would be used to screens. But when I'm discussing with postdocs and students --we typically spend hours staring at the blackboard and thinking together-- and somehow, with zoom and Skype the interaction is not at the same level --the intensity of the interaction, or the depth in the interaction, is not the same. When thinking is mature, either in my mind or their mind, zoom meetings are very efficient for putting finishing touches. But for thinking from scratch and developing some new idea completely, it was much easier with a blackboard, several of us just staring at it together, sitting in the office and brainstorming.
Well, let's take it all the way back to the beginning. Now, let's go back to India. I'd like to start first with your parents. Tell me a little bit about them and where they're from.
They were from a state called Maharashtra, which is in the western part of India, the state in which Mumbai is located. My father was a civil servant in the state government, and my mother was primarily a homemaker, but she was also an author. She was not prolific, but she did write for magazines, short stories, and such things in the local language of the state of Maharashtra, which is Marathi. It's a big state. It's comparable to a European country in terms of population. Marathi literature is quite rich. We had many monthly literary magazines. I grew up reading them and also books – novels, poetry, and short stories.
You were born right after. What were your family's experiences during partition?
They were sufficiently far from the conflict because Maharashtra is quite far from the Indian border with Pakistan. And so, it was not a big turmoil. There were incidents, and my father, being a civil servant, oversaw law and order in sub-districts. The police, for example, could not take serious action against crowds unless they had a go-ahead from somebody like my father. So, there were some small incidents, but there wasn't anything major or trauma that my parents saw or faced.
And where did you grow up, Abhay?
I grew up in Maharashtra. The Indian Administrative Service was constituted using principles laid down by the British. The idea was that a civil servant should not stay in one place too long because then corruption occurs. So civil servants were frequently transferred from one place to another, sometimes because of promotion, but even if there was no promotion, there were periodic horizontal transfers. And so, I grew up in about seven different cities. They were not big cities. I was always a new kid in school, had to make new friends and academically prove myself, and so on. Relatively recently I realized that, in some ways, that phase of my life has played an important role later. I wasn't consciously aware of it but helped me not to be psychologically held back by completely new circumstances, or new people, new institutions and so on.
As a young boy, what memories stick out in your mind from your family's cultural, religious, or political practices?
In terms of religion, my family belongs to Jain religion, which is an extremely nonviolent religion. But they were, as one says in the United States, ‘secular Jains’ in the sense that while they did participate in religious ceremonies, they were not devout.
In terms of politics, the spectrum was narrow while I was growing up. I've memories of Gandhi and Nehru and of the tremendous sacrifices that the freedom fighters had made. Just incredible that they could do this through peaceful movements. They were beaten up and horses would ride into the crowds, they were jailed, and they still just persisted in their fight for freedom and independence without counter-violence. Even now, after all these years when I speak of it, I get goosebumps. That's the spirit which I was really exposed to and my friends and I were all very proud of this heritage as I grew up.
Later, the political system became corrupt. But when I was growing up, there was very much a sense of pride that we were the one country which managed to overthrow its colonial regime by nonviolent means, the country had shown the world a new way to deal with conflicts, and a sense that we're making a lot of progress. There was a lot of pride in that. So, this was the background in religion and politics. Then there was a third point also, you said?
Cultural. Any cultural practices?
Yeah. I was quite immersed in literature. One thing that I lacked, although I did not know at that time, was music. In many parts of India --I shouldn't say all parts of India because it doesn't generalize-- you were just not that involved in music. In other words, you just listened to music on the radio, and that was it. If you were very serious, you went to what they call, gharānā, which is a house of music, led by a famous musician, and then you practiced a particular instrument, or a couple of instruments, for many years to become a professional. I did not have music lessons or any real exposure to classical music. Later I came to realize that this was a serious gap. Only when I came abroad that was exposed to music and became then became very interested in classical Western music, particularly, Baroque, and also in classical Indian music. By now, music is an integral part of my life, which I listen to it while working, for relaxing and just to find peace. This is something that was missing in my upbringing.
There's something else that is kind of tangential to culture per se, but interesting as a turning point. When I was 12 to 13, I started reading a little bit of English literature. It suddenly became clear to me that the standards by which a literary work is deemed to be great can depend greatly on the specific language and culture around it. What I thought as great literary pieces in Marathi would seem to be derivative from an international perspective, and not so great. And it was a big revelation for me to realize that ‘great literature’ is not so universal. At some level, it is obvious, but this ‘culture dependence’ was not at all clear to me because until then I was exposed only to literature in Marathi. This was in stark contrast with science. Newton's laws are just Newton's laws. It didn't matter that he was English. They were regarded as fundamental all over the world, across cultures, taught everywhere. The contrast stood out particularly because I had just learned Newton's laws. It all came together, so to say. This universality of science, which transcends cultures and countries and languages, made a deep impression on me. And that is roughly when I got more and more drawn into science.
Did your teachers or your parents, did they recognize that you had special mathematical and scientific abilities, even from a young age?
My teachers did, and my parents also did, in the sense that they saw my performance on examinations, heard what teachers said, etc. So, while my parents did not judge my abilities directly, teachers did. From the very beginning, they encouraged me. But I've to say that till I was 18, I had not met anybody who was active in scientific research and publishing papers. I did not even know that research could be a career, something I could do for a living. I only knew that one could have a teaching career because in colleges there were professors. Nonetheless, I was very fortunate because even though they were not active researchers and did not know forefront science my professors were very encouraging. And that, I think, was very good for me.
There are two examples. First, when I was 16 –that is when students entered college in India -- students could take out only one book out of library at one time and they could keep it for up to two weeks. The principal of the College gave me his library card, so I could take out more books on his name and then return them. The second example was that rather early on, I mean compared to my contemporaries, I started learning quantum mechanics, mostly old quantum mechanics, the Bohr atom, photoelectric effect, and very simple things like that. My professors encouraged me enormously even though it was way ahead of our syllabus. So that played a major role in my early development.
And another thing that had a longer influence on me was that in school, as well as in college, there was a lot of freedom because it was the British educational system in which you did not have quizzes and tests all the time. In school as well as in college there was an exam in the middle of the year, and then there was the final exam. In between, there was a lot of freedom. I could then do other things during that time. Completely accidentally I came across popular books by George Gamow. I probably saw them in the library and then went to the bookstore and tried to order them. And it was very important for my development that I had read Gamow’s books like One Two Three … Infinity which introduced mathematical paradoxes and also early universe cosmology. Since Gamow had done pioneering work in nucleosynthesis in the early universe, he had good discussions of the evolution of temperature, matter density and so on in the early universe. I could make such forays to get acquainted with the then forefront ideas precisely because there was freedom. If I had constant pressure to prepare for the for a next quiz, I might not have been able to do that. So, these unusual circumstances helped me.
What kind of a high school did you go to?
In India, public high schools were free, and there were also private high schools. I went to a private school in which fees were nominal – say a few dollars a year at the then conversion rate. Until I was about 11 or so I was in a school in which the medium of instructions was Marathi. There was just one language class in English. But then, my father got transferred. We went to a new place. My parents thought it would be good for me to go to an English-medium school, to give me an edge, so to say, in my college career since all college classes were taught in English. And so, from about 12, I was in a school in which all classes were in English.
Between financial considerations, decisions on how close or not you wanted to stay to home, and based on your academic interest, what colleges were available that you were considering attending?
In India, at least in my days, nobody left home for school or first two years of college. It was like in Europe where people generally go to school and college in their hometown. My then-hometown, Kolhapur, is a small city -- which in India meant a few hundred thousand people -- that had Rajaram College which was already more than 100 years old. Since it was clear that it was the best college in town, I went there. But then, after a year or two in a college specializing in Science, you had to decide: Do you want to continue in pure science, or go to an Engineering school like one of the famous Indian Institutes of Technology (IIT), or to go to Medical school and become a doctor? It was taken for granted that students who were doing well would want to go to IIT or a good Medical college. So, I did appear for the IIT entrance exam, and I got in. I was about 17 and, in retrospect, that is when the first big turning point of my academic life came. I had to decide whether to continue in pure science or whether I would go to IIT. I should add that in those days IITs did not offer degrees is pure sciences, only in Engineering. IIT exam was a one-year before the regular Engineering exam. So, I had to take it at 17. For me, the great thing was that my parents put no pressure whereas a lot of parents, even today, exert pressure saying it would be crazy to turn down an offer from IIT and pursue pure science instead. Going to IIT was considered as a guaranteed gateway to success in life and you went to pure science only if you did not make it to either the Engineering or Medical pathways. My parents didn't put any pressure at all.
Is that because they saw that your inclinations were in research? Did they recognize that?
I don’t think that they understood the word ‘research’ in the way you and I understand it because they had not interacted with, or even seen, any active researcher. But they had respect for knowledge. That was deeply embedded in the Indian society. And, as Feynman observed, there is respect for knowledge also in the Israeli society. My parents’ reaction was the same for my sister who went to Medical school. At the time, while it was not unusual, it was not common thing for a girl to go to a Medical school. My parents just let us do what we thought was the best for us. I went back and forth in my mind, and then concluded that, well, if I did science, then I won't have to stick to one problem, so to say. Of-course at the time I did not know what exactly this choice meant – I thought it was like writing many theses because I had heard that one writes a thesis for one’s Ph.D. It was the vague allure of ‘freedom to choose’ as opposed to work on a regular 9-5 job that led me to choose pure science.
Now, the Indian system modeled after the British system means that you declare a focus as a freshman in college. You had to decide what you're going to do at the very beginning.
Yes. In the Indian system, as a freshman, you had to decide whether you wanted to go to Arts or Sciences or Commerce --which would be ‘business’ in the US. If you were in Science, after the first year you had the possibility to go to IITs, and after your second year, you could go to a regular Engineering college or a Medical college.
And so when did you focus on physics?
I focused on physics after I decided not to go to IIT. Initially I wasn't sure, and I pursed both physics and mathematics. But I did decide that I would not complete my last two years of college in Kolhapur, but I would go to the Institute of Science in Bombay University. It used to be called The Royal Institute of Science by the British, but after they left, the adjective ‘Royal’ was dropped. At that time, it was considered to be the best place in Bombay for sciences. And so, at 18, I left Kolhapur, and I went to Bombay.
Was this because professors or you yourself realized that you needed a higher institute of study to satisfy your intellectual curiosity?
There were some professors who were great at giving good advice. The Rajaram College that I was in, was a government college. Some of my professors were familiar with the Institute of Science because it was also a government college. I also gathered information from informal contacts. Of course, there was no internet or even a phone at home. So, information gathering was all by mail. It was a different world. It was, in a way, much more relaxed. I found out that Bombay had frontier institutions like the Tata Institute for Fundamental Research and the Bhabha Atomic Energy Center. So, there was a feeling that you would have more opportunities, even though you did not know exactly what those opportunities were.
As an undergraduate, Abhay, did you have exposure both to the world of theory and experimentation?
Yes. All throughout my undergraduate years, we had both theory and experiment, and the first two years also in chemistry and biology, and then, in subsequent years, only in physics.
And for you intellectually, was it always theory that you wanted to focus on?
Yeah, and I wasn't very good in experiments. It's not that I was worse than other students, but I did not have any special talent, whereas in theory, I felt that I could read books and learn things that were way ahead of what was taught in the class. In experiment, there's nothing I could do on my own and in the lab we only had prefabricated, precooked experiments.
What level of exposure did you have to General Relativity as an undergraduate?
Very little, only qualitative exposure as in Gamow’s books and a few slightly more advanced ones. But I was interested. So, for example, I remember going to bookstores and browse both in Kolhapur, but also in Bombay. Bookstores in Bombay were much bigger, and I found some books in Relativity, particularly the Brandeis lectures on Relativity which had very good lectures by some leading relativists. And so, I would go through these books; not that I understood the detailed calculations, but qualitative ideas would sink in.
But there was one thing that did happen related to General Relativity. This is a slight digression, but it leads to the next topic. When I was in Bombay, I had a National Science Talent Scholarship. I was incredibly lucky because the very year I went to Bombay, some leading physicists in the Tata Institute of Fundamental Research decided that they would get to know the undergraduates, improve the syllabus and so on. So, they asked those of us who had a Natural Science Talent Scholarship to come to the Tata Institute once a week. That was one of those complete surprises. But this is the kind of opportunities that open-up in a place like Bombay. And so, there were about five or six of us, who went to Tata Institute once a week. The Feynman lectures in physics were available in an Indian edition, which was affordable for us. So, they thought that we should go through these books. About half the time they would ask us questions on what we understood and half the time we could ask them questions. The Feynman lectures came with a book of problems and we could check the final answers at the back of that book. There was one problem in which I first got the same answer as the book, but then later that night I realized that I had made a mistake. When I corrected it, I got a different answer. The difference was just a numerical factor, but the origin was conceptual. So being a brash young man, I wrote to Feynman explaining what happened. And then, much to my surprise he actually wrote back. And I kept the letter for a very long time. I probably still have it. He said "The book was wrong. You're right." But then, he also had a phrase, something like, "You know the subject well enough to rely on yourself," basically telling me not to keep bothering him with such trivialities in the future! But his reply was a big boost for me, as you can imagine. And people at the Tata Institute were also impressed by that.
Now I can come back to the question about General Relativity. The two professors who met us regularly, B. M. Udgoankar and Yash Pal were nuclear and cosmic ray physicists, and they introduced us to an astrophysicist, S. M. Chitre who knew general relativity. So, I started also talking to him and stopping by his office with "Could I ask you a few questions?" kind of thing. Based on what I had read in elementary books, I decided to try to calculate what would have happened in the early universe if Newton’s constant was time varying. It was not at all deep, but Professor Chitre took interest, and wrote nice comments on my writeup. And that is how I started discussing just a little bit about the cosmological aspects of General Relativity with him. That turned out to be extremely helpful when I applied to graduate schools in the United States.
Was it your own desire? Were professors telling you that you would be best served by pursuing a graduate degree in the United States?
I should backtrack a little. In India one received bachelor's degree at 20. So typically, Indian students received their master’s degree at 22 and then applied graduate school in the US. I was 20 and the question was whether I should go abroad, or whether I should perhaps go to the Tata Institute graduate school. They kindly arranged an interview for me, which was, in retrospect, pretty unusual because they normally accepted students who were ready to do their Ph.D. But at the end of the interview, they realized that there were many gaps in my background. Since the Tata Institute did not have remedial courses, I was told by Professor Udgaonkar "Well, you could join if you like, but it would be better to go to a regular university, which also has more courses than just the focused graduate-level courses that the Tata Institute was offering."
Luckily, I had gone to USIS, the United States Information Service in the Bombay consulate. Because there was no internet or anything, the only way to find information about the US universities was through the brochures that USIS from various graduate school. There, I found that the University of Texas at Austin had a Center for Relativity and at that time it was the largest relativity group in the world. There were some 8 faculty members in Relativity, and the most celebrated names were there, Jürgen Ehlers, Roy Kerr, Ray Sachs, Englebert Schucking, Alfred Schild, and so on. So, I decided to apply there. Usually, they didn't accept students from India with only a bachelor’s degree. But since I had these letters from Udgaonkar and Chitre, I guess they decided to give me a chance.
Had you ever left India before this?
No, I'd almost never left Maharashtra, my state! I had gone once for a trip to just a little bit south of Maharashtra, but I never went outside.
What year did you arrive in Texas?
[laugh] What year? It was 1969.
1969. And what were your impressions? What did it feel like to get there? A different world?
Oh, boy! A completely different world. I later realized that the culture shock would have been much bigger if I was not completely drowned in my studies. Because I had so much catching up to do that I had to work hard, I mean, extremely, extremely hard. Therefore, in some sense, I was oblivious to what was happening around me. I was going to the department, attending courses, doing homework, reading, catching up, and making sure I understood things by going to office hours and asking questions, and also doing my TA duty. It was good that I was so occupied because whenever I did look up, I saw some there were very, very strange things. Because I lived within walking distance from the university, there were a lot of fraternities around me. And on the weekends, they would have all kinds of parties, which were quite exotic. Early on, I think it was the end of my first semester, there was a party in which all the boys rode in on horses. The girls stood in the balconies of the sororities, and the boys picked them up on their horses from the balconies. To me, it was like a Bollywood movie. [laugh] I could hardly believe it. The horses were neighing, and there was horse dung all over the place, and so on. I was just completely taken back, I mean, "Is this the real world, or I'm on a Bollywood set?" So, there were interesting things like that.
I also should say that there was some racism. When I arrived, I sensed it very clearly that if you were not white, they didn't want to rent you an apartment. So, I had some trouble getting housing, but once I did find an apartment, the owners were very, very nice. It was a white couple, and he was a captain in army. They were very nice people.
Were you in the program for long enough to have a graduate advisor?
Yeah. At the beginning of my second year, Bob Geroch had joined the faculty at University of Texas. And so, I started working with Bob, I mean, it was just informally working with him.
And what was Bob working on at that point?
Bob is a General Relativist. At that time, he was working on existence of spinorial structures on manifolds and applications of spinors to General Relativity. Bob had done a postdoc with Roger Penrose, and then, he was also in Syracuse. He had an amazing career because was hired as an Associate Professorship with tenure in Austin after being a postdoc only for three years. At that time, I had already started reading a little bit about Quantum Gravity. It seems ridiculous at this stage because I was just learning Quantum Mechanics, and General Relativity at the same time!
I was sitting-in on a C*-Algebra course. And there's a very famous construction which goes by the name Gelfand-Naimark-Segal construction, or the GNS construction, which basically tells you that if you are given a C*-algebra and if you've given a positive linear functional on it, which in physics language is the vacuum expectation value function, then you can build a representation. You can create a Hilbert space and operators on it that realize the given C*-algebra.
I told Bob about this construction and suggested that maybe one use it for Quantum Gravity. I remember giving a talk informally to just our Relativity group about how one might use this C*-Algebra technique for a harmonic and recover the full Hilbert space of quantum states knowing just the operators. To me, this route was impressive because of the way we're taught Quantum Mechanics. You start with the Hilbert space of states, and then you define the position and momentum operators on it. Whereas here, what was fundamental was the observables, and then, the states are recovered using the positive linear functional. I realized later that in Quantum Field Theory this reversal is essential because there are inequivalent representations of the Heisenberg commutation relations. In Quantum Mechanics, it's not essential because the representations are usually equivalent to each other for systems with a finite number of degrees of freedom.
That's what I was doing with Bob. But then, Bob stayed in Texas just for one year. He got an offer of, I think, a full professorship, from the University of Chicago. And he asked if I wanted to apply to Chicago. So, I applied to Chicago. And that's how I went to Chicago, and that's where I got my degree.
Clearly, you and Bob were working so well together, he wanted you to join him in Chicago?
Right. But I think ‘working well together’ would be an overstatement. I think he just thought that I had potential to do good work, so I was worth spending some time on! He was just a fabulous, fabulous graduate advisor, right? I remember once telling him something, and then a few hours later I was walking along the main avenue in front of the university, the main drag as they called it, and Bob's wife was driving. He asked his wife to stop the car and ran out and tell me, “By the way, one can do the following thing”, which was the next step that I could take. I was very surprised that a professor would do this, jump out of the car just to continue a chain of thought with a student. I was very, very impressed by that.
In Chicago, he lived quite far away from the University. He didn't want to live in Hyde Park; he lived in a suburb. Once a week or so, he would have a pizza dinner in Hyde Park with students and postdocs. In those days, everything was communicated through pre-prints. There was no Internet! So, he would bring the latest pre-prints and just say "Read the title and the abstract." And then, we were supposed to try to guess what was in the paper; how the main result may have been proved. What did they do? How did they do it, so to say? It's a very ambitious thing, right? Of course, we were supposed to just sketch the main ideas.
In retrospect, this idea of figuring out things from scratch, so to say, made a very deep impression and had a deep influence on my way of thinking. There's a tremendous advantage because when you think of from scratch, you see that there are other directions in which the ideas could also be developed. But you're also much slower than just reading the papers because these good people who wrote them had spent considerable time proving things. Even today, I think I'd be much better served by just reading something, but I tend to try to figure it out from scratch. I tell my students that they have to strike a balance. I am not well-balanced in this respect. Often it is much faster just to read a paper than trying to figure it out. Gary Horowitz was another student Bob had, and I think Bob instilled the same kind of spirit in him.
When you moved to Chicago, as you say, Texas was such a big group. Was your sense that Bob being hired to Chicago was that Chicago was looking to enlarge their group?
Yes. It was really because of Chandra -- this is Chandrasekhar, often referred to as the preeminent astrophysicist of the 20th century. As you probably know, every 10 years or so he liked to change his field. Sometime in the '60s, he decided that his next area would be General Relativity. There is an interesting story here. To see firsthand what was happening at the forefront of the subject, Chandra wanted to go to a major conference in Warsaw on General Relativity. And so, he asked for a travel grant from NSF, and they asked him, "Are you invited to speak?" He said, "No." "Well then, have you worked in this field?" He said, “No”. They were hoping to find one of the routine reasons to fund his conference travel. But then, finally they realized that Chandra was thinking of entering this area in a serious way and made an exception and provided the funds. The conference had a deep influence on him. In the late '60s or in the early 70s, he made his final decision to enter the field. And so, one summer, he invited three young relativists who were known to be very, very good --Brandon Carter, George Ellis and Bob Geroch-- to give him a crash course in modern General Relativity. Each of them would give a lecture a day, and Chandra would take notes and call them, sometimes at night, for clarifications. And then the faculty offer was made to Bob. So, the group was smaller than in Austin; there were just three faculty at the time: Chandrashekhar, Bob Geroch, and Jim Ipser an astrophysicist, who subsequently moved to Florida.
Was Bob Wald there at that point?
No, he was not.
Perhaps as a window into Bob's style as a graduate advisor, how closely was your thesis research related to what he was doing at the time?
Not really. I mean, what we did together, which is a bit strange for a graduate student, was to write a review paper on Quantum Gravity. That helped me enormously in terms of writing skills. But the thesis project itself was something quite different.
And what was it? What did you work on for your thesis?
It's both an interesting and a complicated story. My thesis was about using these *-algebra methods to arrive at a new way of looking at Quantum Field Theory in Curved Space-Times. During my last year as a graduate student, Hawking had discovered that black holes can evaporate quantum mechanically. Even though I was just a graduate student, I was asked to give a series of talks on quantum field theory in curved space-times and the Hawking effect. As an aside, to my total shock Chandra came to every of those talks! My thesis was inspired by that material. It was approved by the committee and the paper was submitted to a journal --I don't remember which one-- and came back with a referee report. But instead of quickly replying to referee’s comments, I kept working on new problems that seemed much more interesting. And so, I never replied to the journal. But the University of Chicago had a rule that the thesis should be a single-authored paper, which is published. But that paper was not published. Two years later, I won the gravity foundation prize and that made the then Associate Head of the Department concerned that it may appear unseemly that the University had not yet granted me my Ph.D. So, he persuaded my Ph.D. committee to allow me to use another, already published paper as my thesis paper. So, when you ask me about my thesis, it was a little bit difficult to answer: which one am I talking about? My final, official thesis was inspired by some work that Bob had done, but my research was carried out completely independently. It was about the Asymptotic Structure of Space-Time.
And where did you see your research fitting into the broader theoretical questions of the time?
Well, at that time, as you probably know, by and large, most people in the physics community did not really pay much attention to General Relativity.
This was a low point, you're saying.
Well, it had been a low point all along. It was not that it was up, and then, it went down. It never really caught on in the mainstream physics community. In the '70s there were very interesting, seminal advances. The singularity theorems proved by Penrose, Hawking, Geroch and others, and the paper for which Roger received his Nobel Prize this year, were published. And we all thought that these were truly fundamental advances that were telling us something deep about Nature. But most people in the broader physics community didn't pay much attention to those papers.
Because it was all about Particle Physics at this point.
It was all about Particle Physics or Condensed Matter Physics, and at that time, Biological Physics was also emerging. And even some leading people literally didn't believe in black holes!
They accepted them as mathematical solutions but thought that they don't really exist in nature. To answer your question: In terms of consensus in the broader physics community, general relativity was still at a low point. But the few of us who were students and postdocs in Chicago, and then, at Oxford, as I'll explain in a second, we felt strongly that all these advances were going to change the future of physics.
So, our attitude in research was very gung-ho, but it did not translate to jobs. I graduated in the mid-70s and up until the end of '70s, was a very low point for jobs. There was literally just one new faculty position every two years in the United States in any research university. On the one hand, we had great, great enthusiasm: Isn't this beautiful? Isn't this deep? Doesn't this have to do with fundamental structure of our universe? And then, on the other hand, there were no jobs. So, it was a very tense period. It is only in retrospect that you realize how tense it was.
Abhay, I'll test your memory. Who was on your thesis committee?
Bob Geroch was the Chair, and then, Chandra and Jim Ipser were on my committee and Peter Freund who was a Particle Physicist was the outside member. I'll tell you an interesting story about Peter also. Peter was a very outgoing person. He was an opera singer in addition to being well-known Particle Physicist. During my first meeting of the Ph.D. committee, he asked, "What are you planning to work on?” I said, “I would like to work on Quantum Gravity.” And Peter said, “Oh, then you know that the problem is solved.” I was taken aback (and so was Bob). Peter was referring to the then recent work of Faddeev and Popov on a technique for handling the gauge freedom in non-Abelian gauger theories and general relativity. Of course, the problem of quantum gravity is far from being solved even today! So already at that time, there was a kind of a difficulty in cross-communication. What a Particle Physicist would think of as central problems in Quantum Gravity and what a Relativist would think of as central problems in Quantum Gravity were already at odds with each other. But, fortunately, people like Bob came to my rescue to say that, "Well, but we don't think it's solved because the central issues have to do with space-time geometry and we don't know what the quantum nature of space-time geometry is," and so on. It was interesting, though.
Now, the academic job market was rough at this point for faculty positions, but what about for postdocs? Did you have good opportunities to choose from?
Right. When I graduated from Chicago, I had some five or six offers; I don't remember exactly. There were, maybe, 10 postdoc positions in the field. Chandra told me that there was just no question as to which offer I should accept: I had to go to Oxford to work with Penrose, because Chandra had such a high regard for Penrose. Once he flew to England just to get something clarified from Penrose. He spent a day there and flew back.
Abhay, I wonder if coming from India to Texas, and then from Chicago to England if that was less of a culture shock for you, actually?
Yes, it was less of a culture shock because you get used to so many different things that way. But in some ways, the answer is ‘yes and no’, because in Chicago I did not find any discrimination; in England, I did. And the reason is because Indians were considered as the black minority, right? It turned out that two of us from Chicago went to Oxford that year. In a way I had a more "prestigious" position, being with Roger. My friend was in Particle Physics who had a nice but a regular postdoc position. But he got accommodation right away; no problem because he was a postdoc with the right skin color. I had to struggle to find accommodation in Oxford. I don't at all mean to say that my colleagues were discriminating in any way. Absolutely not. Everybody was extremely nice. But in the larger society, there was discrimination.
Now, had you met Roger in the States before meeting him in Oxford?
No, I had not met him in the States.
And what was he working on when you met him?
He was working on the so-called nonlinear gravitons. I should just take a couple of minutes to explain that. Basically, Einstein's equations are very complicated, right? And so of course, we're not anywhere near finding a general solution of Einstein's equation using, say, Green's functions, or any such method. You can find a lot of very interesting solutions if you assume symmetries. But Roger was coming from a novel perspective; first spinors and then twistors. He thought that perhaps the way to understand General Relativity more deeply would be to focus on the spin structure. Zero rest-mass particles have helicities. You've got left-handed and the right-handed particles. Left-handed photons, for example --that is, photons with helicity plus one-- are described by self-dual Maxwell fields, and the right-handed ones --with helicity minus one-- by anti-self-dual Maxwell fields. So, Roger thought that one should first look for self-dual solution and anti-self-dual solutions of Einstein's equations.
Now, in the real physical space-time -- Lorentzian space-time -- self-dual solutions are complex. So, they don't really have direct interpretation in the classical world. In the Maxwell case, you can obtain real solutions by adding self-dual and anti-self-dual solutions. But in General Relativity, because of non-linearity, you cannot add self-dual and anti-self-dual metrics and get a real solution. Still, there were reasons coming from Yang-Mill's theory to focus on self-dual and anti-self-dual solutions.
Using a twistor theory point of view, Roger found that there is a way to obtain all anti-self-dual and all self-dual solutions of Einstein's equations. These are complex space-time; their metrics are not real. Still this method of finding all self-dual or anti-self-dual solutions without assuming any symmetry was a mathematical breakthrough because it neatly bridged algebraic geometry and the theory of nonlinear differential equations. The bridge is called the Penrose transform. And then, independently, Ted Newman in Pittsburgh was working on similar ideas. Penrose and Newman had worked together for many, many years earlier. And Ted had also found a way of obtaining all self-dual and all anti-self-dual solutions. Roger was very interested in understanding the relation between the two ideas. During my first year at Oxford, the connection was made clear, with the help of the celebrated mathematician Michel Atiyah who was also in Oxford at that time. It was an exciting time!
So, I became very interested in these ideas about self-duality and developed a solid understanding of the underlying mathematical and conceptual structures. During the two years in Oxford, I understood more or less all of Twistor theory as it was then. Because of the similarity with Maxwell’s theory, Roger called the self-dual solutions to Einstein's equations ‘nonlinear gravitons’ emphasizing the non-linearity of Einstein’s equations.
I did not do original research on twistor theory or nonlinear gravitons. But these ideas were critical later when I found the new variables for General Relativity. But in Oxford I was just following what was happening in Twistor theory. My research work was on Quantum Field Theory in Curved Space-time that I talked about, which was motivated by Hawking's work, but also by these ideas about C*-Algebras that I mentioned. And I was able to pinpoint the new structure that is needed to do Quantum Field Theory in Curved Space-Time. In technical language, it's called a complex structure on the space of solutions of classical field equations. Basically, you have a classical phase space, or the space of solutions to a field equation equipped with a Poisson-bracket --or a symplectic structure-- and you have to supplement it with an additional mathematical structure to go to Quantum Theory. In fact, this is what we do, without explicitly saying so, when we decompose fields to the positive and negative frequency parts in the standard, flat space Quantum Field Theory. But in general curved space-times we don't have a way to carry out this decomposition. We cannot take Fourier transforms on curved manifolds. Therefore, we cannot talk about positive negative frequency solutions in such a simple way. One needs a new structure.
And then, I found out that if you have a time-independent space-time –or, a stationary space-time-- then there's a canonical such structure, and therefore, there's a canonical Quantum Theory. Roger was very interested in this, he encouraged me a lot, and he is the one who forwarded the paper to the Royal Society. These ideas have become kind of commonplace now. Bob Wald used them in his short book on Quantum Field Theory in Curved Space-times and it was spread in the community through this exposition.
On an interpersonal level, what was Roger like to work with?
Roger, he's such a nice person to interact with! I mean, it's just is a pleasure to be around him. No question about it. Same was true with Bob Geroch, but in a different way. At one stage, Chandra told me that Bob Geroch was the fastest person that he had seen except for John Von Neumann.
Fastest, you mean the fastest thinker?
Yes, Chandra said that Bob was the most brilliant and the fastest thinker he had met since John Von Neumann. Roger, I won't say displayed the same kind of brilliance, but he has the incredible depth. And he is a little bit of a dreamer; in fact, I should say a lot of a dreamer. He is the best dreamer that I ever met. He sees some structures, and then his mind works around them in ways that other people's mind would not. He gropes around in the dark and find new structures before they come to light. And then when they come to light, everybody says, "Oh, wow!" When he did his nonlinear graviton work, it was like that.
Roger, at that time had been divorced. His children lived in London and would come once a week to Oxford. Roger would often go out to dinner with them and invite us postdocs who wanted to go. Very often, we went to a pizza place and had hours’ long discussions. I've been extremely fortunate in having these three mentors, first, Bob Geroch, then Chandra, then Roger.
It's amazing. I mean, it's—
It's totally amazing. I always feel that I'm just so fortunate. But I learned different things from them. From Bob Geroch, I learned the importance of clarity --clean thinking, that goes to the heart of the problem. But with Roger, it was different --it was always a little bit mysterious, a little bit vague; he didn't have the sharp reasoning Bob had. As Bob would say, there is an uncertainty principle between clarity and depth! Just by watching Roger, I learned something by osmosis about trying to grope in the dark and find some shapes before they come to light, as I said before.
And with Chandra, more than scientific things, I really learned what the moral fiber of a scientist is. What should one be doing? What is the true motivation behind doing science? I was really fortunate in that Chandra took some interest in me even though I did not work with him. We did discuss science, but we would talk about other things as well. Occasionally, he invited me at his house, and sometimes he'd start telling anecdotes until it was late, I mean, late for him because he got up at 4 o'clock in the morning every day! He had an incredible memory. He could tell us about, say, what happened in say May 1935. I don't remember what happened last May! So, it was quite amazing.
I think here are two things that most people know about Chandra. First, his interactions with Eddington. Over many years Eddington put him down. In the end Chandra was completely right and Eddington was completely wrong. But Chandra neither gave up, nor pursued confrontations. He just kept doing good work. That requires tremendous strength, right? If a random person says that you should have this type of attitude, you'd say, yeah, in principle, yes. But if you see somebody who has done it, and you've seen them with your own eyes continuing to work like a normal human being, you realize in a deep way that it is possible.
The second thing Chandra did was tremendous public service. I don't know exactly for how many years now, -- certainly more than 20 years, maybe 30 years -- he was the Chief Editor of Astrophysical Journal. And the journal was really not very prestigious before he took over. By the time he left, it became the journal in astrophysics, right? And during that time, he made a deal with his wife that, while he was in charge of this journal, he would work in the journal office for close to eight hours during the day, then go home, have dinner, and work eight hours first at night and then early in the morning on his research. So, he worked 16 hours a day for, I don't know, more than 20 years! And one could ask: what did he get out of that journal? Nothing concrete, really. He did it out of a sense of duty. Nobody else could do it. With his own research and stewardship of the journal, he elevated the level of the entire field. That's what I mean by moral fiber.
That really did influence me greatly in the decisions I took much later in my career. It was all at a sub-conscious level. It's only later I realized what the roots were. There's one thing that I felt very strongly when I was in the postdoc stage. As I was telling you, a lot of us felt that we were in this tunnel, and we couldn't see the light at the end of the tunnel because there were no faculty jobs in General Relativity. Period. At that time, I felt very strongly that this happened mainly because a generation of relativists lacked the necessary sense of commitment to the field. Earlier, there was the generation of John Wheeler and Peter Bergmann and so on, who were very active, very visible. And because of their efforts General Relativity was understood as being a reasonable field to hire new faculty in. John Wheeler created these positions, not just in Princeton, but in Caltech, in Maryland, in Utah, and so on. And Peter Bergmann did the same. However, the next generation, including Bob Geroch's, did not have the same sense of commitment to the field.
So, I made a decision early on that greatly influenced my later career: If at all I got a job in a research university and settled down, I would owe it to my field to spend time and energy into making it more visible, on par with the level of the intellectual advances that were occurring. In other words, I felt that the field was deep; it had great potential. It was making deep advances, and it should get its due credit. Relativists should get faculty positions. They should get grants and visibility. Recognition should be commensurate with the intellectual quality of contributions.
Abhay, you've also worked to make the field accessible to a broader audience. I wonder if that's part of it as well?
It's very much so. Also, as Director of our Institute, I have made a lot of outreach efforts. I often go to India and China to talk to younger students, give courses in summer schools. Also, as the President of the International Society for General Relativity, I initiated a large number of initiatives to raise the profile of the field. And then, I also accepted the position of an Editor in Chief for General Relativity and Gravitation. It is not a brilliant journal, but because it is the organ of the society, I felt an obligation to do that. So yeah, I'd done a lot of those things.
Abhay, during your Oxford years, how much interaction did you have with Stephen Hawking?
I was asked to go to Cambridge a few times to give talks. At that time, Stephen could still speak, although it was not easy to understand him unless one really focused on what he was saying. I could understand him. He was very interested in the review paper on Quantum Gravity that I had written with Bob Geroch and so he asked me questions about several sections in that paper. And then, he --and also Gary Gibbons-- were interested in this way of looking at Quantum Field Theory in Curved Space-Time in terms of complex structures I mentioned. There was quite some interaction with Stephen about that. And finally, in Oxford, I also changed the direction of my research a little bit. I started working much more on gravitational waves and asymptotic structure of space-time. And I had some interactions with Stephen about asymptotics. There was one comment he made which turned out to be quite important for my work later.
What opportunity did you have next after Oxford?
It turned out that I went back to Chicago as a postdoc. There were still no jobs in the United States --faculty-level jobs. I was married to a French mathematician and therefore tried to get a position in France. I managed to get a visiting associate professorship. I spent two years in France. And then, I got the faculty position at Syracuse. I stayed in Syracuse for a long time. While at Syracuse, I was offered a Chair in Paris. This was in '83. So maybe, I should talk about that a little bit about those experiences. Because I had spent the two years between '78 and '80 in France, some of the French academics came to know me. And some Particle Physicists very much wanted to have, in the university, a presence of what they called Modern General Relativity, Modern Gravity Theory. They had had a Professorship in General Relativity that was held by a former student of de Broglie, who died prematurely. It had been dormant for a long time. They opened it up, did the search, and they offered me the job. Given this background, I felt it was a great honor.
So, I went to Paris. In Chicago and Oxford, I was used to discussing physics and mathematics with others for several hours every day. But in Paris, this changed because, first of all, the city is spread out, and second, because people in Relativity were primarily interested in astrophysical issues and by then I was interested more in mathematical and conceptual issues of Quantum Gravity. And so, left largely to myself, I put together the ‘self-duality’ ideas that I picked up in Oxford, but generalized them in such a way that they were applicable to just good old real General Relativity rather than the complexified theories that Roger (and Ted Newman) had developed. In other words, I obtained a new description of General Relativity in which the space-time metric becomes a secondary variable. We'll talk about that, if you like, a little bit later, but let me just finish about the Paris.
The problem was basically that in Paris, the academic system was extremely bureaucratic. I don't know if it has changed substantially. I went there thinking that since they wanted me to introduce Modern Gravitation in the university, I would be giving graduate-level courses in Gravitation and training research students and postdocs. But instead, they asked me to give courses, in French of course, to large classes of first-year undergraduates. It required a lot of preparation and organization, but the work involved was completely unrelated to advanced gravitational physics.
Also, effects of the '68 student revolution in Paris were still visible. Students could be very unruly. They would throw chalks at some professors; sometimes, they would throw little bags of flour in front of the blackboard! The campus was extremely dirty. I was totally shocked. I wasn't doing what I thought was expected of me, which was to introduce Modern Gravitation Theory in the graduate curriculum, and perhaps, get students and postdocs, and start working with them. And so, I resigned from Paris, and I went back to Syracuse. Luis Michel, a senior particle physicist then at Institut des Hautes Etude Scientifique near Paris later told me that I was only the third person to in the 20th century resign from a physics Professorship in Paris; he was the second!
I spent several years in Syracuse. And then I received an offer of an endowed Chair from Penn State with the expectation of creating a new Center for Gravitational Physics. In Syracuse I also had a Chair, but the Penn State offer was more attractive to me because the mathematics department was significantly stronger than the one at Syracuse and Penn State also has a strong Astronomy and Astrophysics department, whereas we didn't have any real astronomers or astrophysicists at all in Syracuse. So, I came here to Penn State and started the Center.
And then, a few years later, I got an offer to become the Director of the Albert Einstein Institute or the Max Planck Institute for Gravitational Physics near Potsdam. I took that offer very seriously. I basically told my administrative colleagues at Penn State that I was leaving, put the house on the market, and so on.
But then, two things happened. One was that because this was a Directorship at a Max Planck Institute, I was invited to visit --as they say, to ‘negotiate’-- about what it would take to move me. And they were very generous and very kind, and all my colleagues there were very, very nice. They bent over backwards to offer me significant resources and even making some sacrifices for themselves. I was very moved. But the society outside academia was something else. This was around 2000 – a decade after reunification of Germany-- and the Institute is in the Brandenburg state, in the eastern part of Germany. The state had many neo-Nazis at the time. My mother-in-law is German, therefore, my wife speaks German fluently, and so when we visited, she could understand what the local people were saying. I couldn't understand very much. I would go to a grocery store and there would be some drunken people sitting outside, and when I came out, and they would laugh at me. They said things like: "Oh, look at him. He's blacker than a charcoal." I did not understand them, but my wife did.
And then three more serious incidents happened during that trip. I was once returning to Potsdam from Berlin. The S-bahn was nearly empty since it was about 9 o'clock at night. Suddenly, some skinheads came into my compartment. And in those days, those skinheads were typically burly, and they had big Alsatian dogs with them. I was very uncomfortable but couldn't leave because they and their dogs were blocking the door. And at that time our son, who was with us on the trip, was still a baby. I felt that I didn’t want my son to grow up feeling trapped like that. I could probably adopt a high stand and ignore crude comments and insults. Our son was going to know German; he was going to understand them; and I didn't want him to face what had I had faced.
The next thing that happened was that while we were in Potsdam, there was news about a restaurant in the Brandenburg state, which was owned by a Sikh family of Indian origin. They had been running it for a while. Some skinheads came there on motor bikes and just destroyed the restaurant and beat up the people, including the owners. And finally, news came out in the local paper that some police officer in Potsdam was arrested because they found all kinds of Nazi stuff in his apartment. And so, although I knew the Institute would be excellent for science, I turned down the offer and decided to stay at Penn State. Soon after, there was an article in Der Spiegel written by a high-level administrator at the Max Planck Society, denouncing the Neo-Nazi activities, that highlighted my decision and the reason behind it. In retrospect, I think I might have accepted the offer if we didn't have to bring up a young child there.
These matters are now very relevant to the United States, given the current atmosphere in our society here. I completely understand the sentiments of the black physicists about the way they're treated in the society, not because I have anywhere near the direct experience that they've had, but because I have seen the hints of it, first had, and even that was enough to put me off.
Abhay, I'm curious as you're thinking about your career options and moving from institution to institution, job titles and ways you might identify yourself? There's Cosmology, there's General Relativity, there's Astrophysics, there's Astronomy. What were the terms that were most efficacious for you as you were looking for faculty opportunities?
Well, General Relativity, Cosmology, Black holes, but also Geometry and Physics, because I'm also deeply interested in Geometry. So, there's also this mathematics part, various issues, Symplectic Geometry and Geometric Quantization.
And a very broad question. I mean, you operate in such a theoretical research world. What, over the course of your career, may have been some advances, observationally or experimentally that may have been valuable to you?
Well, so I've made a big transition starting about 15 years ago. Until then, I was primarily a mathematical physicist, as you were saying. But I made this transition saying that Loop Quantum Gravity, about which we'll talk little bit more later—
is far from being finished. But on the other hand, it has matured enough that one can think about applications. And so, I started learning Observational Cosmology. As you say, and it was a major, major transition because the way of thinking and so on is quite different. I talked to Observational Cosmologists very often and worked with them at Penn State and elsewhere. I gave talks to cosmology groups as well; about what Loop Quantum Gravity could contribute in terms of predictions for observations. Our last PRL was about exactly that, about how it can alleviate the anomalies in the Cosmic Microwave Background. Given any one anomaly, the tension between theory and observations is only at two or three sigma level; but if we take two together, then the implication is that we live in quite an exceptional universe according to standard inflation. Can the situation change if we bring in Planck scale physics? At first, it would seem that it won’t, because Planck scale physics refers to the very small and the anomalies refer to the largest observable scales. But we showed in the recent PRL and the follow up paper that in Loop Quantum Gravity, there is an unforeseen interplay between the ultraviolet and the infrared and therefore anomalies can be alleviated.
So, I've been talking with the cosmologists quite a lot. And all along, I had kept in touch with the Gravitational Wave community. It's just that they didn't have any observations for the longest time. It now turns out that my early work in Gravitational Waves --that I started thinking about already in Oxford and started writing papers on soon after I arrived at Syracuse-- is quite relevant to the current observations. Of course, I'm not capable of understanding in detail all the phenomenological aspects, or of using the intricate data analysis software they use. So, what I had to do was to come up with ideas from the mathematical physics side and collaborate with people --my students and postdocs, and also my former students who are faculty members elsewhere who thoroughly understand data analysis. How do we transform the deep theoretical insights into observations, and how can we improve our phenomenological understanding by combining observations with these insights? So, in the last 15 years, I have been more and more involved with observations both on the cosmology side and gravitational waves side. I would say I have been devoting 40% or 50% of my time to these applications rather than mathematical physics.
Let's set the stage for the Ashtekar variable. So, my question there is, in the mid-1980s, what is the overall gap in the research in the field that you're motivated to try to understand through the creation of these variables? What's missing, essentially?
As I mentioned before, as a graduate student, I wrote a review paper on Quantum Gravity with Bob Geroch. Therefore, I had a reasonable grasp of the landscape -- not that I knew every detail, but I had a good grasp of the overall picture. And coming from Gravity, rather than from Particle Physics, I was much more attracted towards non-perturbative methods. These methods were the ones that were advocated by Dirac, Bergman; and then, Arnowitt, Deser, and Misner; Wheeler and DeWitt, and other people.
Now, what do I mean by non-perturbative methods? Well, in perturbation theory, what one does is like what Feynman did in QED. One linearizes Einstein’s equations, thereby ignoring the interactions. The linearized fields propagate in Minkowski space. Nonlinearities are incorporated by successive iterations, more and more corrections. There are abstract arguments to say that if you could sum up for this perturbation theory, then, you would get General Relativity.
Those coming from Gravity background had a different take. Penrose, for example, liked to say that, if you first steamrolled General Relativity into flatness, and then tried to make the resulting corpse alive again by waving the magic band of Perturbative Quantum Field Theory, it's unlikely that you will succeed. One should not really linearize in the first place. So, coming from General Relativity background I was interested in non-perturbative methods.
In the non-perturbative landscape, there was a Hamiltonian framework that dealt with exact general relativity without any linearization which was generally considered as a starting point for Quantum Gravity. This was taken up by John Wheeler and led to the famous Wheeler-DeWitt equation where the quantum state is represented by a wave function of three-dimensional geometries. For a particle the dynamical trajectory can be thought of as evolution of its position x and quantum states can be represented as functions of x. So Similarly, the four-dimensional space-time can be thought of as a trajectory representing evolution of three-dimensional geometries, since at each instant you have a three-dimensional geometry. A four-dimensional geometry results from stacking them together. Following the example of a particle, quantum states should be represented by wave functions of these 3-geometries. This was John Wheeler’s idea. He called general relativity ‘geometrodyanics’ –dynamical theory of 3-geometries.
Following Einstein, a 3-geometry was represented by a spatial, positive definite metric on a 3-dimensional manifold. The Hamiltonian formulation was based on these metrics. Conceptually, the procedure is very natural. But the equations are very, very complicated. They're highly nonpolynomial in the metric, and this feature create a huge difficulty in using the Hamiltonian framework to obtain a well-defined Quantum Theory.
In this non-perturbative landscape, my idea was to look for something that might tremendously simplify these equations. Thus, first focus on non-perturbative approaches that deal with nonlinear Einstein's equations directly and then ask if we can simplify the equations sufficiently to pass on to Quantum Gravity.
Did you know at the time that it would be as significant as it was? In other words, was it like a Eureka moment where you really understood what you hit on, or was this a more gradual process?
Both. So let me explain what I mean. In a loose sense, one can interpret Penrose’s non-linear graviton construction (or mathematically equivalent versions thereof constructed by Newman and Plebanski) as saying that the self-dual sector of General Relativity is exactly integrable. Therefore, it is natural to hope that the complicated equations of the geometrodynamical Hamiltonian formulation that people had been using may simplify of one uses self-dual (or anti-self-dual) fields. I was thinking along these lines for a while. In that sense, the realization was gradual. But the Eureka moment, if you like, was a key departure from the constructions of Penrose, Newmann and Plebanski. These constructions referred only to complex space-times –not to the physical, Lorenzian space-times of real general relativity. The qualitatively new idea was that one should stick to real solutions of Einstein's equations, or dynamical trajectories on the real phase space of General Relativity, and regard self-dual variables simply as complex coordinates on this real phase space that provide brand new tools to simplify Einstein’s equations.
Let me give an elementary example. Let us consider a harmonic oscillator. The phase space consists of x and p, and we just live with that. But we could also introduce a complex variable z = x +ip and z* = x – ip and then do everything in terms of z and z*. These complex variables simplify both classical and quantum dynamics, although the simplification is modest for a harmonic oscillator. Even though you're using complex variables, you're still talking about a real simple harmonic oscillator. You're not talking about a complex simple harmonic oscillator. It's the same physical object. You're just giving a complex description for that object.
What I realized is that you can similarly take the real phase space of General Relativity and use self-dual and anti-self-dual variables. So, z of the harmonic oscillator would be like self-dual variables in general relativity. You're still talking about Real General Relativity. Whereas in Penrose’s Twistorial approach and in the Newman and Plebanski approaches one is talking about complex General Relativity. So that ‘aha moment’ was that we can talk about Real General Relativity, but just in terms of complex variables. And for General Relativity, as I will explain, the simplification of equations is enormous.
There's a second independent motivation, which to me was equally strong. People like Steven Weinberg have often said that the emphasis on the space-time metric and its geometry had driven a wedge between Gravity and Particle Physics. This was true in the sense that in General Relativity fundamental equations are written in terms of the metric while, if you take Yang-Mill's Theory that describes QCD or electroweak interactions, the basic variable is a vector potential or, in a mathematical language, a connection, which enables you to transport charged particles in electromagnetism and quarks in QCD from one point to another, along any given curve.
Therefore, I thought, what we should do is to consider the vector potentials or connections as the basic variables. Then, thanks to the training I had received from Penrose and Geroch I realized that one should use spinors because if you've a left-handed spinor, it only sees the self-dual part of the gravitational connection, whereas if you've a right-handed spinor, it sees the anti-self-dual part. Therefore, I looked at real General Relativity in this spinorial way and considered self-dual gravitational connections as the fundamental mathematical variables. Then, it turned out that Einstein's equations simplify enormously. They become low-order polynomials in terms of these variables. That was both surprising and deeply satisfying.
In the beginning, it was quite confusing. How could it be, right? Can Einstein’s equations really be made so simple? They are literally at worst quadratic in the new configuration and momentum variables. In addition to this tremendous and unforeseen simplification, since general relativity is now described by putting connections at the forefront as in Yang-Mill's theory, certain techniques --particularly Wilson loops-- that were commonly used in the Yang-Mills theory become available in Quantum Gravity. Incidentally, in the final picture, this is the origin of the ‘loop’ in Loop Quantum Gravity.
However, there is also a big difference with respect to Yang-Mill's theory. In QCD, for example, you have a space-time in the background on which the gluon fields are defined. Here, you don't have a space-time in the background --the space-time metric is to emerge, at the end, from the dynamical trajectories on the phase space. The phase space variables themselves are the same as in QCD --the vector potential or the connection, and its conjugate momentum, which is the Yang-Mill's electric field. In QCD, to write down the Hamiltonian one has to use these phase space variables and the space-time metric. More precisely, given the metric, you can write down several distinct gauge invariant candidates for the Hamiltonian and Nature chooses just one of them. By contrast, in general relativity there is no background metric, and you have to write down gauge invariant expressions using just the phase space variables –the connection and the electric field. There are very few such expressions. You can say "Write down expressions that have only the vector potential and the conjugate electric field with no space-time metric." Surprisingly, it turns out that the simplest expression you can write down is precisely the Hamiltonian that yields Einstein's equations! It is literally true that if you give me a bright student who knows Yang-Mill's theory --but is not indoctrinated by perturbation theory-- and ask her to write down the simplest gauge invariant Hamiltonian she can, in a day or so she will discover Einstein’s equations. To me that was a revelation. It was turning General Relativity on its head. The standard formulation of General Relativity starts with the space-time metric. Now, the space-time metric becomes a derived –or emergent-- concept rather than a fundamental one.
By the way, ten years or so after I had discovered the connection variables, I learned that both Einstein and Schrödinger had independently worked on a similar idea in the 1950s! They used the standard Levi-Civita connection --that determines, for example, geodesics-- as the fundamental field rather than the space-time metric. The correspondence between them is fascinating for several reasons, quite apart from hard science. It brings out their different personalities. Schrödinger’s use of news media to publicize his work and Einstein’s high standards of personal integrity led to a definite rift between them that was never bridged. You can read about this, for example, in Schrödinger’s biography by Walter Moore. Returning to the use of connections, the reason one does not often hear of this work of Einstein’s and Schrödinger’s is that the equations became quite complicated with their use of the Levi-Civita connection that parallel transports vectors. For the simplification I mentioned above it is quite critical that one uses self-dual connections that parallel transport left-handed spinors.
Abhay, let me ask a very obvious question that perhaps you've asked yourself as you think about these things. Given the cast of characters that you've been around in your career, Stephen Hawking, Roger Penrose, Bob Geroch, Chandra, what was your insight on this that wasn't made before you came along? What did you have to offer that these luminaries in the field didn't think of themselves?
That you can take real General Relativity and simplify it so dramatically by just using new variables which have a deep geometrical and physical meaning --which is to say that they are the vehicles by which you transport left-handed spinors along any given curve in presence of gravity. I think they did not think of doing this. Penrose and Geroch, of course, knew about everything about spinors. Penrose knew about self-dual fields, but they did not think about using the self-dual connection as the vehicles to simplify real General Relativity of Einstein's.
What did you think was achievable in creating a theory of Quantum Gravity, and what was not achievable in the early years?
Right. So, I think that—
I mean the aim to merge the—the aim to merge Quantum Mechanics and General Relativity, was the hope that this was really going to be that breakthrough?
Already in the early years, there was a widespread feeling among researchers in quantum gravity within the General Relativity community that this was a breakthrough. Since one does not use perturbation theory, one could hope to get control over--or get a hold on-- the quantum nature of space-time itself. That possibility created excitement. The basic idea from the early days was that Einstein taught us that space-time geometry is not a spectator. It is not a stage just sitting there on which things happen. Rather, space-time geometry is a physical entity. It can be acted upon, and it reacts, right? It's a physical entity, and physical entities --like for example, the screen you're looking at-- have atomic structure. Your screen looks like a smooth continuum but if I put it under an electron microscope, I will see that it has atoms, right? Therefore, being a physical entity, space-time geometry too should also have atomic structure at the Planck scale. The question then is: what are the atoms of the geometry? And the new variables that I found seemed to be the appropriate vehicles to probe these atoms of geometry.
From the early days, I had an analogy in mind because I was quite impressed by the BCS superconductivity theory. They came with this very nice idea that the description simplifies if we think of the phenomenon in terms of cooper pairs, rather than individual electrons. The pair behaves as a boson and something new happens. Thus, if one reformulates the theory in terms of new variables, namely Cooper pairs, the phenomenon of superconductivity is much more tractable. I thought that the situation is qualitatively similar with gravity. The self-dual connection variables would reveal the quantum nature of geometry that was opaque in terms of the metric variables.
So I understand. Just so that we can understand everything that's going on right now, when the aim is to bring together Quantum Mechanics and General Relativity, does that mean that Gravity gets incorporated into the Standard Model or the Standard Model blows up and we have a new model altogether?
The idea is that the Standard Model will be perfectly fine in the regimes in which the space-time continuum makes sense because at macroscopic scales it is extremely, extremely well approximated by a smooth continuum of Einstein's when space-time curvature is low compared to the Planck scale. The continuum breaks down only when the curvature approaches the Planck scale. Then, all bets are off, and we have to rethink from scratch. What are the building blocks of the fundamental Standard Model? They should be able to interact with the excitations of the atoms of geometry. It could be that electrons and quarks really are point-like, in which case, they will propagate along Gravitational Wilson Lines. If they are not, there will be a deeper layer to the Standard Model. It's only when you've enough of those ‘densely packed’ Wilson lines that a space-time continuum emerges, and then, it just reduces to the description we currently have in terms of the standard Lagrangian in the continuum space-time.
The example that I often give in my general talks is the fabric of one’s shirt. It seems obvious that the fabric is a two-dimensional continuum. But I just have to take a magnifying glass to see that it is in fact one dimensional because it is woven by one-dimensional threads. It's just that those one-dimensional threads are crisscrossed and tightly bound together. So, for all practical purposes, it gives us the illusion of a two-dimensional continuum. Because of the prominence of the gravitational Wilson lines in this description, the fundamental excitations of geometry are one-dimensional. They're polymer-like, and these quantum threads of geometry fit together tightly under normal conditions to give us an illusion of this continuum, that is make the continuum an excellent approximation.
But if you go near the Planck scale, then this continuum approximation will break down, and you will have to work with the fundamental fiber-like excitations of geometry. It's rather similar to, say, boiling water. Under normal condition, the water is a nice continuum; one can just use continuum dynamics to describe it. But if one heats it up, then the continuum description will gradually fail, and one would have to describe physics in terms of molecules that evaporate. Your fundamental molecular theory should be such that when I densely pack the molecules and cool them so that their kinetic energy is low enough, then the continuum fluid description becomes an excellent approximation. Space-time continuum is similar. We can use the continuum picture under normal circumstances but the fabric tares under extreme conditions and we then have to describe dynamics using the fundamental building blocks –the analogs of molecules.
Abhay, did you ever envision Loop Quantum Gravity to be experimentally verified?
There are two things that I should say. The first is I didn't fully answer a question that you asked me a while ago. There is a key difference between Loop Quantum Gravity and Particle Physics-inspired approaches that dates back to the early days. Providing a unified description of all of nature is not the primary goal of Loop Quantum Gravity. Rather, the primary goal is to understand the microstructure of gravity, and hence of space-time. And the idea is that once you understand the microstructure of the quantum nature of space-time or of gravitational field, the qualitative difference from the continuum picture will provide us with radically new insights. So, at a fundamental level, the emphasis is not on unification. Already at the classical level, qualitatively new predictions arise in General Relativity -- for example, the existence of black holes-- because of a drastic revision of the notion of space-time. It doesn't have anything to do with other interactions. Similarly, the Big Bang arises in general relativity because geometry is allowed to change in time; non-gravitational interactions do not play a role. In the same vein, gravitational waves are just ripples in the space-time geometry. Qualitatively new possibilities arise because you think of space-time geometry as a dynamical physical entity, not frozen once and for all. In Loop Quantum Gravity, this entity has building blocks, it is built from ‘atoms.’ Since it has microstructure, new qualitative phenomena should emerge, and that's what we focus on. That is the most exciting thing for people working in the field. That doesn't mean that unification is not interesting. It is; but that's not the primary focus.
But that's a byproduct. The unification is fundamentally a byproduct if the theory is verified to be true.
Yes, ultimately it will be a byproduct once the theory is fully developed. But unification is not essential for new predictions from quantum gravity. At the classical level, the prediction of existence of black holes did not require unification of general relativity with other forces. Similarly, there may be qualitatively new phenomenon that are brought to forefront by carefully examining the quantum nature of geometry, without bringing in unification. This possibility is being realized in LQG.
Abhay, as we trace this history, of course, String Theory has its own history of ups and downs through the decades. So I understand, particularly when you begin thinking about these things in the mid-1980s, are you looking at String Theory as a competitor, as a competing way to understand Quantum Gravity, or is it more like it's a different method to get to the same endpoint?
Until about 2008, I had systematically followed developments in String Theory and made notes every year summarizing the main advances. So, I have a lot of respect for String Theory, unlike some of my colleagues in Loop Quantum Gravity.
My viewpoint was: Here is a really, very complicated problem, and we're approaching it in two different directions. In Loop Quantum Gravity, we think of the gravitational aspects, the space-time geometry aspects as being more fundamental, quantum nature of geometry as being more fundamental. Therefore, we are likely to succeed in addressing issues which have to do with space-time singularities; the nature and emergence of time; the emergence of the continuum on which everything happens in the low energy regime; and so on. These have been our primary goals. In String Theory, at least in the beginning, the goal was to create a unified theory using newer ideas that originated in particle physics, such as supersymmetry, higher dimensions, and extended objects. So, my viewpoint was that, well, here is a very complicated problem, and it's very nice that it is being explored in opposite directions. When you emphasize one aspect, then certain issues or certain problems become magnified, and you can focus on them, and hopefully address them. But then, you are blind to the other side. So, the idea was that, well, when enough progress is made then, hopefully, one would understand the relation between the two approaches. That was my point of view. It is not competitive because the two approaches were probing different aspects of Quantum Gravity, not the same aspect of Quantum Gravity. If it were the same aspect, then it would be competitive.
And Abhay, as I'm sure you recognize, there is a spectrum of approaches to String Theory where some people have lost patience about its ability to understand how nature actually operates. And others who say, actually, it does, and you should stay tuned because very exciting things have happened. Have you detected that same general spectrum and approach to the field that you're working in?
Not really. First of all, Loop Quantum Gravity is a smaller field in the sense that we only have several hundred people working world-wide. Our typical bi-annual conferences, draw about 200 people since not everybody can come. There are, of course, different approaches to the same problem within our community. For example, different groups attempt to understand the Big Bang and the early universe in slightly different ways. But they're not dramatically different from each other. And the differences that exist are healthy.
Secondly, since AdS/CFT --this beautiful conjecture of Maldecena’s-- was introduced, the focus has changed in String Theory. Quantum Gravity is no longer a central issue. There is a nice recent article on the website of the Institute of Advanced Study titled The strange second life of String Theory. It says that while String Theory so far has failed to live up to its promise as a way to unite Gravity and Quantum Mechanics, it has now become a very valuable toolbox and permeated very different branches of physics. The argument is made that, as toolbox, it is here to stay, and that I agree with. It has provided us new insights from Conformal Field Theory. It has provided us new insights into QCD. In its applications, generally one is not directly tacking the actual physical problem at hand but idealized versions thereof. That is why it is a toolbox.
Regarding Gravity, I would say the same thing. String Theory doesn't have concrete things to say about what happens at the physically most interesting space-time singularities. There are people who used to be String Theorists and are now working on such problems like black hole evaporation and so on, but often String Theory per se doesn't play a direct role in those investigations. On the other hand, Loop Quantum Gravity has remained much more focused on problems of Gravity per se --the problems that have been with us for a long time – and, in the last 15 years, on the observational consequences of Loop Quantum Gravity. Ideas are evolving; they are not etched in stone yet. But the fact that very detailed analysis can make direct contact with observations in Cosmology is very appealing to me. This answers the question you asked a while back regarding experimental verification of Loop Quantum Gravity.
On the other hand, Loop Quantum gravity has not provided a rich toolbox. Although the new tools that were introduced have been used by some mathematicians, it's not as widespread a usage as in String Theory.
In what ways is Loop Quantum Cosmology a subfield of Loop Quantum Gravity, and in what ways is its own discrete discipline, essentially?
It's a sub-field in the following sense. Loop Quantum Cosmology takes the basic premise of Loop Quantum Gravity, including constructions of Hilbert spaces and operators that encode the quantum nature of geometry, but restricts oneself to the cosmological setting. That is, one only looks at that sector of General Relativity which is spatially homogeneous and applies techniques from Loop Quantum Gravity to that sector. In this sense, it's a subfield of Loop Quantum Gravity. On the other hand, because we are looking at the symmetry-reduced sector of General Relativity, rather than full General Relativity there is richer structure and therefore Loop Quantum Cosmology has taken a life of its own. In particular, there are many more detailed and concrete results in Loop Quantum Cosmology. Ideally, one would like to start with full Loop Quantum Gravity and derive Loop Quantum Cosmology from it. These attempts have begun only in the last two or three. And there is good progress, but the subject is still pretty much in flux in the sense that as of now there's no definitive derivation.
It's not very different from what happens in classical General Relativity. In cosmology, we have explicit solutions to Einstein's equations, such as the Friedmann-Lemaître-Robertson-Walker solutions even though we are very far from obtaining a general solution of Einstein's equation. So, relativists have been able make much more detailed progress in the Cosmology.
Soon after, when you were calculating the entropy for a black hole, to what extent was this something that you were able to do just because of your general skills as a theoretical physicist? And to what extent was this really a demonstration of the value of what Loop Quantum Gravity was able to accomplish?
First of all, it's not just me—when you say ‘you’, I take it to be community, right?
You and your colleagues, of course.
Right. John Baez, Kirill Krasnov, Alex Corichi and I wrote the papers that provided the foundation for systematic investigations, but there have been lot of developments since then. As far as entropy is concerned, Quantum Geometry --that comes out of the Loop Quantum Gravity-- plays a central role. But we also used other notions, such mapping class groups, Chern Simons theory on a punctured sphere, and so on from pure mathematics and Quantum Field Theory which are very general. Later, various brilliant, younger people introduced techniques from Number Theory which are also very general and can be applied in other contexts.
But the heart of the idea is the quantum nature of Riemannian geometry. Geometric observables such as areas of physical surfaces and volumes of physical regions are all quantized, just like the energy levels of hydrogen atom are quantized. They have discrete eigenvalues. And these are hard mathematical results in the sense that field theoretic issues involving infinite number of degrees of freedom are faced squarely. One does not perform formal infinite dimensional integrals as one often does with path integrals in perturbative field theories. There are regular Borel measures on the appropriate infinite dimensional spaces to define the notion of square integrability of quantum wave functions and a well-developed differential calculus on these infinite dimensional spaces that is needed to define operators representing geometric observables. One then calculates the eigenvalues of these operators and finds they are discrete. And that mathematical precision is very important to get a final answer to the entropy problem.
Abhay, we talked about this before, and your interest in conveying these concepts to public audiences. And so I'm sure the fundamental question that you get when you talk about these concepts is, "Okay, Professor Ashtekar, very good. How does all of this help us understand how the universe works and where everything came from?" What are the most effective ways that you've gone about trying to answer those very fundamental questions?
The answer to the specific questions you asked are very concrete. General Relativity tells us that the universe began with a Big Bang. And at the Big Bang, the space-time curvature and matter density becomes infinite and physics just stops. You begin with Einstein's equations; you evolve fields backwards in time, and they just break down. That's it. But every time such a breakdown occurred in the history of physics, it turned out that Nature does not become crazy; Nature doesn't stop. Rather, our description breaks down. Why? Because we have taken the theory and applied it in a domain where it is not applicable. That's typically what happened in the history of physics. So here, why would General Relativity not be applicable? Well, because it assumes that classical physics is perfectly fine at all densities and no matter how high the curvature is. But we know that Quantum Physics is important. And then, the popular audience would ask, "Yeah, yeah, but that's all for microscopic systems --atoms and molecules and quarks and so on. We're talking about the universe, and why should quantum physics be important for describing this huge system?" But there are huge astrophysical objects that would not even exist if we ignored quantum physics. Look at a neutron star. Neutron star exists only because of Quantum Mechanics. Why? Because it is the Pauli Exclusion Principle, which tells us that we cannot put two fermions at the same place. Mathematically, it translates into an effective, repulsive force if we try to put two neutrons in the same place --or, as one says, there is a ‘degeneracy pressure’-- that balances the gravitational attractive pull. Without this repulsive force of quantum origin, a neutron star would collapse into a singularity.
Let me explain in greater detail. Suppose I have a star. It's shining like our sun, burning its nuclear fuel. The reason why it doesn't collapse under its own weight, rather, under its own mass is that the gravitational pull is balanced by the radiation pressure. And radiation is emitted because of nuclear reactions. But eventually it would run out of nuclear fuel. Then there is no radiation pressure, and therefore, the gravitation should win, and the star would have to collapse into a singularity. Classically, this reasoning is valid. But Quantum Mechanics intervenes in neutron stars or white dwarfs and there is a brand-new repulsive force of quantum origin that can counterbalance the gravitational attraction, resulting in a stable configuration. These white dwarfs and neutron stars do exist in the sky. So, even for some large, Astrophysical objects Quantum Mechanics is really important. Some of these large objects owe their very existence to quantum mechanics.
Let us now return to Cosmology and Quantum Gravity. Typical matter density in a neutron star is about 1015 or 1016 grams per cubic centimeter, to use the CGS system normally employed by astronomers. But for quantum gravity, there's another scale --the Planck density, which is about 1094 grams per cubic centimeter. It's eighty orders of magnitude larger than the neutron star density. At these matter densities, space-time curvature would also be absolutely huge. It seems a bit silly to think that we can nonetheless ignore quantum effects and continue to use classical physics.
What Loop Quantum Cosmology shows is that, indeed, quantum effects do become important and dramatically change the prediction of classical general relativity in the Planck regime, well before one can encounter the Big Bang. It's not because of fermionic nature of matter, but it is really because of the quantum nature of geometry itself. Let me explain. Already in general relativity there is no gravitational force. What we call gravitational attraction in Newtonian theory is a manifestation of space-time curvature. The same is true about the ‘repulsive force’ in Loop Quantum Cosmology. Quantum effects change the geometrical, left-hand side of Einstein’s equations. But you can rewrite the quantum corrected Einstein's equation and move the correction to the right side that represents matter. Then the equation has an effective negative energy density of quantum mechanical origin --comes with the Planck’s constant hbar-- and this new contribution creates a ‘repulsive’ in the common Newtonian language we use.
Equations of Loop Quantum Cosmology predict that the new, negative term goes like density-squared divided by a critical density –the maximum possible density that is allowed by Loop Quantum Gravity, which is about half the Planck density. And that comes out of the calculations of Loop Quantum Cosmology; it’s not postulated. And the statement is that when the physical matter density approaches this critical density, then the quantum corrections are no longer negligible. Then the ‘repulsive force’ just takes over. By the way, the critical energy density would go to infinity if you were to ignore quantum geometry. Then the correction term disappears, and one is back to Einstein’s equations with their Big-bang singularity.
Let us return to the backward time-evolution of the universe. In Loop Quantum Cosmology, at first the universe contracts and matter density and space-time curvature increase just as in classical General Relativity. But when the matter density or the curvature reach the Planck scale, the corrections to Einstein's equation become extremely important, and they overwhelm the classical attraction and instead of having a Big Bang, there's Big Bounce. Once you're on the ‘other side’ then, in this backward evolution, the universe expands again, the density and curvature drop, and we can again use classical general relativity to an excellent degree of approximation. So, we have a large pre-Big-Bounce branch joined to a large post-Big-Bounce branch by a quantum bridge in the Planck regime. What we thought was our universe is completely changed. This has happened several times in the past. For a long time, people thought solar system was the whole universe. Then, they realized that the solar system belongs to Milky Way and they thought that Milky Way was the whole universe. Then, they realized that there are galaxy clusters. Then we had the general relativistic notion that the universe had a singular beginning in the Big-Bang. Now, the very concept of space-time in Einsteinian physics is changed by Quantum Gravity. Quantum space-time is much larger than what Einstein taught us. There is a pre-Big-Bounce history to the Universe.
Thus, Loop Quantum Cosmology is really providing a concrete answer to your question about our universe and its origin. Over the past decade, researchers in Loop Quantum Cosmology have been looking for observable effects related to the Big Bounce and the new Planck scale physics. Can we see signatures of Loop Quantum Cosmology in the Cosmic Microwave Background (CMB)?
And the community has several interesting predictions. While the standard inflationary models work very well, there are also some discrepancies with respect to observations, known as anomalies. Significance of any one anomaly is small – they are 2-3 sigma effects – but taken together, two or more of these anomalies imply that we live in a very exceptional realization of the theoretical probability distribution of possible Lambda-CDM universes. The Planck satellite team --that has provided the most accurate measurements of the CMB to date—has suggested that it would be very interesting to have a fundamental theory rooted in new physics that simultaneously alleviates two or more of these anomalies. My team published a paper in the Physical Review Letters last year showing that two of the anomalies in the Cosmic Microwave Background disappear in Loop Quantum Cosmology. The detailed paper has just appeared. My younger colleague Ivan Agullo -- who was a postdoc with me a decade ago -- has papers showing that Loop Quantum Cosmology also alleviates the so-called hemispherical anomaly. In addition, there are predictions for future observational missions, particularly those that will measure the optical depth and the B-mode polarization more accurately. I am excited by the fact that Loop Quantum Cosmology is making contact with observations. Of course, there are assumptions behind these detailed calculations and some of them may turn out to be incorrect. But this work shows that the Loop Quantum Gravity program has descended from the lofty conceptual and mathematical perch –the traditional habitat of Quantum Gravity theories—and becoming testable.
Of course, these effects refer to small discrepancies between observations and theory, rather than to some gross features of the CMB. But we have to keep in mind that a similar role was played by the perihelion of mercury and gravitational redshift in the history of General Relativity. Small corrections can be hints that a big conceptual shift is needed.
Abhay, what ways or not, as it were, does your field and the theories of inflation work toward mutual benefit in understanding of the very early universe?
As of now, they work together. Although Loop Quantum Gravity per se does not need inflation and has been applied [in] inflationary scenarios, I would say that 80% to 90% of the work is done in the context of inflationary cosmologies. And so, it does go hand in hand with inflation. As I mentioned before, in Loop Quantum Gravity, Einstein’s equations receive quantum corrections. I personally think that these could naturally lead to a nearly exponential expansion in the early universe as in Starobinsky inflation. This issue is being investigated.
In our work that I mentioned before, one assumes inflation, and the question is whether we can extend standard inflation further back in time to the Planck regime of the Big Bounce. Standard inflation begins, so to say, in the middle, a little after the Big Bang of classical General Relativity. One doesn’t specify initial condition at the Big Bang itself because there is a singularity, and everything breaks down there. One simply assumes that there was an early phase of nearly exponential expansion, caused by a slow roll of an inflaton field down a potential. Since the expansion is nearly exponential, we can specify an initial state -- not at the Big Bang but at the onset of this phase of expansion-- which is compatible with symmetries of an exponentially expanding space-time, the de Sitter universe. So, in effect, one considers Quantum Field Theory in near de Sitter space-time, assumes that the scalar and tensor modes of cosmological perturbations are in the Bunch-Davies vacuum that is selected by the de Sitter symmetries, and evolves it in time. The quantum fluctuations in the vacuum are stretched by the expansion and leave imprints on the CMB, which are in agreement with what the Planck collaboration observed. Now, it doesn't prove that this mechanism is correct, but the success of mechanism cannot be ignored either. There are some other mechanisms that predict what we observe in the CMB but, at the moment, inflation is the leading scenario.
To go back to your question, what Loop Quantum Cosmology does is to extend this inflationary scenario even further back in time to the Planck regime near the bounce. This is possible because we don't have a singularity and we have a quantum geometry to adequately handle the Planck regime. Does that extension of standard inflation lead to observable effects? It could well have been that the extension predicts new features in the CMB that are not observed. Then the theory would have been ruled out. But the point is that Loop Quantum Cosmology predictions are perfectly in agreement with the observations for small angular scales where there the observational error bars are small. In the spherical harmonic decomposition this corresponds to ell bigger than 30 or so. There, the agreement between Loop Quantum Cosmology, standard inflation and observations is excellent. You can see this explicitly in the plots. And yet, on the larger angular scales, the Quantum Geometry effects create subtle differences, and these differences lead to predictions that are in better agreement with observations because the anomalies are alleviated.
Abhay, I'd like to ask a question that it touches on the philosophy of science and your approach to these things. So going back to, in the 1970s, when many people didn't even believe that black holes were anything other than mathematical concepts or constructs, right, what has been your reaction to things that have been observed that are relevant to your field, an actual photograph of a black hole, the actual detection of a Gravitational Wave, thanks to LIGO? What is your approach to these things as a theorist? Is it meaningful to you, or does it really not make a difference in terms of the equations and things that are most important to you?
Oh, it is very, very meaningful to me. I've been saying for 30 years that I have no doubt that there will be direct detection of gravitational waves. I have been on NSF panels—and Chaired an important one—on gravitational waves. Of course, we did not precisely know the required detector sensitivity because even now there were major uncertainties about compact binary populations. It's not a controlled laboratory experiment. But I had no doubt that there are black holes, and we will eventually see the gravitational waves emitted by compact binaries. As for the image of the black hole, it is an ingenious feat requiring coordination between observatories all over the world to produce in effect a telescope of the size of the earth! But it is not likely to provide us new insights into tests of general relativity beyond those provided by gravitational wave observatories. We will likely learn much more about accretion discs and astrophysical phenomena around black holes.
Returning to gravitational waves, I do not have the necessary expertise to do the data analysis kind of work because my skills are more aligned with Mathematical Physics. Therefore, I have focused on possible manifestations of the subtle and beautiful features of exact, non-linear general relativity in the gravitational wave observations. Recently, I have returned to the work on gravitational waves I had done in the 1980s. I had found several delicate, and interesting features of gravitational waves. All of us who work in General Relativity constantly encounter this beauty that emerges at different levels. It turns out that we can use those subtle features to discriminate between various model waveform that are currently used to extract (astro)physics from observations. It is very nice to see practical applications of those subtle, beautiful features of full General Relativity.
Abhay, to bring our conversation and the narrative right up to the present, over the last 20 years, Loop Quantum Gravity has grown significantly. There are research groups all over the world who are working on these things. And the field probably is bigger than you're able to keep a handle on yourself.
That's absolutely right. Until 15-20 years ago, I could understand and keep track of almost everything that was happening. But now, there are many things I understand only at a general level. I follow them at a distance.
And so from your vantage point, the view from 35,000 feet, where has the field gone in ways that you never saw coming? And in what ways have younger scholars advanced the questions that you introduced in ways that get us closer and closer to quantizing gravity?
In Loop Quantum Gravity we start right at the Planck scale and have a good mathematical control of quantum geometry that determines the microstructure of space-time. The open issue is to make detailed contact with low energy physics. In recent years, younger researchers with expertise in Field Theories have made significant advances. And they are applying novel Renormalization Group techniques to find what is traditionally called effective equations for low energy physics. That’s an important and rich area. It is still at the beginning stages, but I think it's going to be increasingly important. In another direction --that I mentioned before-- a handful of researchers are now trying to arrive at Loop Quantum Cosmology starting from Loop Quantum Gravity. They're introducing imaginative ideas, and I think that is also an important direction. There are also a few spin-offs from Loop Quantum Gravity, for example, better understanding of Field Theories in presence of boundaries and the boundary degrees of freedom. It's a rich mathematical area that younger researchers are contributing to. Ideas were inspired by Loop Quantum Gravity, but now, they've been applied more generally.
Another direction that has really taken off is the interface of computational physics and Loop Quantum Gravity. It began already some 15 years ago in the context of Loop Quantum Cosmology. Thanks to inputs from the numerical relativity community, new sophisticated computational techniques were introduced, leading to steady advances. More recently, this effort has been extended to the path integral investigations of full Loop Quantum Gravity through spinfoams. I am very impressed by the rapid progress in this area. They provide us with new insights that in turn serve as powerful guiding principles for new mathematical work. There is a confluence of ideas from several different directions, including quantum computing and quantum information theory.
And the last set of advances concerns various observational issues. Some of these new younger people that I mentioned understand phenomenological issues better than I do, even though I have spent several years on understanding observational papers in detail. For example, in the analysis of the CMB data there is contamination from the galactic plane, and one has to use masking techniques to remove them. It is quite technical but some of the younger people understand such issues quite well. So, these forays into cosmological observations and understanding how the data is actually taken is an important and growing area within Loop Quantum Gravity.
By the way, one thing that I personally do not see happening soon is seeing direct observational signatures of Quantum Gravity in Gravitational Waves. This is a controversial subject and I'm just stating my position on it.
Why do you have this position? Where is this coming from?
It is coming from the effective equations of Loop Quantum Gravity. I should qualify because this word effective is sometimes misused or misinterpreted. When we speak of effective equations in Loop Quantum Gravity, we are not integrating over modes beyond some energy scale as one does traditionally in Field Theory. Rather, we are coarse graining the system using symmetries, not in terms of an energy scale. For example, in the cosmological context, there are many, many degrees of freedom, and we're ignoring the inhomogeneous degrees of freedom. We're not concerned with observables that refer to local quantities. We're only interested in average values of observables. Thus, we do course-graining in the sense that we restrict our analysis to symmetry-reduced systems. That is the sense the word ‘effective’ is used in Loop Quantum Gravity. Quantum geometry effects at the Planck scale are always included. It's not ‘effective’ in the sense that we are only talking about low-energy physics, but we are talking about averaging over inhomogeneities.
For black holes, there are several approaches to these effective equations within Loop Quantum Gravity. But we find that near the horizon for a macroscopic black hole --not a Planck scale black hole, but an astrophysical one-- the corrections are completely negligible. In other words, we find that classical General Relativity continues to be an excellent approximation outside the black hole horizon. Indeed, it holds very well until the curvature becomes extremely large, i.e., comparable to the Planck scale. For horizons of black holes that are seen in LIGO and astrophysical black holes, the curvature is many orders of magnitude smaller than the Planck scale. There are of course corrections –just as there are quantum corrections to the orbit of the moob-- but they are tiny. This is the view coming from effective equations for black holes. We have to have views at the forefront of science. Otherwise, we cannot make progress, right?
That's right. Well, Abhay, now that we've worked up to the present in terms of the narrative, I'd like to ask for the last part of our talk, some broadly retrospective questions about your career and your achievements, and then some looking forward. So, one thing we haven't yet talked about is your career as a teacher to undergraduates and a mentor to graduate students. So first, I'd like to ask what have been your most favorite courses teaching undergraduates? What gives you the most pleasure?
I must confess that I've not taught too many undergraduate courses, but among the ones that I have taught, I derived greatest pleasure from Quantum Mechanics, Statistical Mechanics, and of course, General Relativity. I have had many graduate students, around 30 or so, and between 70 and 80 postdocs. So, I have mentored a fair number of younger researchers. I have found great joy in working with them -- pure joy! Especially when the graduate students ‘take off’. You work with them, and it's clear that they're following you, and they're good at calculations. But then suddenly, they're on their own, and then, they start telling you things that you did not think of. And that, to me, brings great pleasure. And of course, the same holds for postdocs. When they tell me something that I didn't suggest to them -- indeed, didn't even think of before -- I light up; that's a great pleasure. Since I have trained so many postdocs, not surprisingly, many of them are senior, distinguished professors and leading research groups, doing outstanding work. This transition from a mentee to a colleague is wonderful to witness. It is a great pleasure to see how many different branches they've gone into.
At one stage, my former students were leading all three major data analysis groups in the LIGO collaboration: The first group focuses on Compact Binary Coalescence, the second on Primordial Gravitational Radiation, and the third on Sudden Bursts and Unexpected Sources. So, it's great to see them doing all those things and going way beyond what they learned from me. Gabriela Gonzalez, who was the LIGO Spokesperson when the first LIGO discovery was announced came to Syracuse as a graduate student to work with me. Her first papers are on Loop Quantum Gravity. And then, at one stage, she realized that she really wanted to do Experimental Physics. And so, she switched, rose in the ranks, and became the LIGO spokesperson. Seeing students and postdocs grow in completely different dimensions also brings me great joy.
In what ways, if at all, have the rise in computational power and data analysis been relevant for your work over the years?
It's been relevant to me personally because this tremendous rise in computational power and data analysis enables us to test subtle aspects of Mathematical Relativity through Gravitational Waves. These are signatures of nonlinear General Relativity, which would be absent other theories, or in the weak field approximation of General Relativity. And, as I mentioned before, one can use them to discriminate between various waveform models. This is possible only because large computational power is now available.
On the Quantum Gravity side, there are some former postdocs of mine who had started doing these astonishing computations that I touched on before. They are related to spinfoams --the path integral approach of Loop Quantum Gravity. There are several mathematical conjectures of significant conceptual importance. If one tries to use analytical methods, one can only establish some bounds, and say, "Okay, that's the best I can do". Furthermore, these proofs can take weeks or even months. With new computational tools, this is changing rapidly. It is becoming possible to test these conjectures quickly –sometimes within hours! Of course, it takes a long time to set up the appropriate infrastructure. But once it is set, one can use it to test a wide variety of ideas. There are similar examples in Cosmology. Thanks to the improved computational tools, several conjectures were tested using simulations.
Abhay, given how lucky you've been to study under such luminaries, as a mentor to graduate students and postdocs, what are some of the big things that you learned from Bob Geroch and Roger Penrose and Chandra that you try to pass on to the next generation?
The crucial thing that I learned from Chandra is something that is tangible, and I have tried to pass it on by explaining "what constitutes the moral fiber of a scientist". In the controversy I mentioned before, Chandra was taken aback, and I would say also saddened, by Eddington’s unfair criticism. He did not counterattack but instead pursued his work with calm confidence for years, sharpening the arguments for the ‘Chandrasekhar limit’. This inner strength in face of adversity is not easy to come by. But for my students and postdocs to be conscious of this ideal stand early on can help a great deal. To me, it provided strong guidance in my work on Loop Quantum Gravity when our advances were met with unfair skepticism by the high energy community.
The other message I would like to pass on is that when you're doing work starting with some bold idea --not just calculating something from what is already known, such as finding the magnitude of an effect that is known to exist-- and if you really believe that it is a good idea, then you should go and push, and be optimistic while you are trying to develop it. Maybe there are all kinds of obstacles. Oh, there are 10 different reasons why it does not work. One of the senior people I have admired is Chris Isham. He had the Chair of Theoretical Physics at Imperial. During my sabbatical I spent two months in London and Chris told me candidly that when it comes to problems in Quantum Gravity, he saw many obstacles --precisely because he knew so much-- and was often discouraged. The attitude that was instilled in me by my mentors was different: if you believe in something, just push it. Ultimately, you may end up spending several years of your life down the road and get nothing out of it; but that's life. So long as you enjoy doing it, and you really believe in it, push it.
There is however a ‘but’; indeed, a big ‘but’: As soon as a significant result comes out, be your [own] worst critic and make the result pass all the tests that you can come up with. That is the essence of long-range success that I've witnessed in others. This is not an easy task. Emotionally, it can be very draining because one has worked long in the spirit of hope and/or faith, and then suddenly you have to change the role and carry out a critical evaluation and try your best to punch holes in your own arguments and results. If the result survives this critical examination, then you can build on it further. If you don't take the second step, your foundation would not be solid enough to build a house on; without your realization you may be building your house on a swamp and sooner or later the house would sink. Furthermore, if you've taken the second step of being critical, you understand your own results deeply and you've a better chance of correctly shaping your future work based on it. This is what I've tried to pass on. It is a collective wisdom that I have received from the successful scientists I know well.
Abhay, last question, looking to the future, what work remains for you personally? What do you want to accomplish and to continue contributing to the field? And looking even more broadly, where long-term do you see all of these things headed? What more will we learn about the universe as the theories advance?
I do not believe in the viewpoint that some eminent people have held: A ‘Theory of Everything’ is just around the corner. This optimism was expressed already in the context of supergravity during the 1979 celebrations of the centennial of Einstein’s birth, and was subsequently repeated often in the context of String Theory. Even if you succeed in constructing a fully satisfactory theory of Quantum Gravity, it won’t be a theory of everything. We will continue to make further progress using that framework. This has happened after every great leap we have made in science. Take for example general relativity. It is a giant leap of the human intellect. It has vastly extended our understanding of Nature. New phenomena can be envisaged, new observations can be made that could not even be imagined with Newtonian gravity. But these new possibilities themselves have created new puzzles. General Relativity did lead us to revolutionary notions such as black holes and the Big-Bang. But these very advances have led us to ask: What happens at the end of black hole evaporation? What really happens at and before the Big Bang? Similarly, a successful Quantum Gravity theory will lead to further questions and puzzles. That, I think, is how progress is made.
I do think that scientific advances require ambitious stands. But, at our present stage of understanding of Nature, it is important to be ambitious in proportion. Take QCD for example. It has been more fruitful to try to understand QCD well by itself, to deepen our understanding of the strong interaction between quarks and gluons, to probe how nuclear physics arises from QCD, etc., than to put all one’s energy in trying to construct a Grand Unified Theory, in one go, to encompass both strong and electroweak interactions. In my view, the situation is very similar with Quantum Gravity. We need optimism but not untempered exuberance. We would be better served by focusing on concrete open issues. There are some great questions such as whether information is lost because of the quantum evaporation of black holes. By the way, I don't think it's a problem as some people like to describe it, or even a puzzle because there is no clearly established tension. It’s a key open issue and we will learn a lot if we understand the final stages of the evaporation process.
In the same vein, just because there are important issues that we don't fully understand today doesn't mean further progress cannot occur unless we resolve them first. For example, in a fundamental sense, we don't understand Quantum Mechanics. We don't understand the Measurement Theory very well, particularly in the context of Quantum Field Theory. Of course, we can do calculations, we can do experiments and we can compare theoretical calculations with experimental results. But we don’t fully understand what really happens to the system --the objective nature of reality if you will-- during the experiment. I think these are deep problems and am happy that people have continued to work on them. But some leading researchers have expressed the view that we cannot hope to make genuine progress in Quantum Gravity unless we solve the measurement problem. I do not agree. Even at a more limited level, I think standpoints such as we will not understand anything worthwhile about how classical behavior emerged in the early universe unless we first solve the Measurement Problem are ill-placed. One can make significant progress in our overall understanding of the universe, even when outstanding conceptual problems remain.
Abhay, it's been a great pleasure spending this time with you. I want to thank you so much for doing this, for sharing all of your insights and perspectives over the course of your career. It's really historically significant, and I'm just so glad to have spent this time with you. Thank you so much.
It's my pleasure and thank you for your interest.