A Graduate Student
The Candidacy Examination was the litmus test used by the University to select students to its Ph.D. programme from among those admitted to its graduate school in Physics. The Chicago test was famous for its rigour and depth. It required twelve hours of problem solving spread in three sessions of four hours each followed by a viva voce of 30 minutes. It was conducted two times in the year, the first time at the end of the autumn quarter and the second time at the end of the spring quarter. Normally students took it in the spring quarter or in the autumn quarter of the following academic year.
I decided that I would write the Candidacy Examination in the autumn quarter of the following year, that is, in December 1965. I wanted to use the academic year in strengthening my physics foundations and decided to take only those courses which I had already studied in the University of Delhi as part of the M. Sc. course. I perhaps took in my first quarter an undergraduate course on complex variable analysis in the Mathematics Department, a course on Mathematical Physics and a course on Classical Electrodynamics. As I was not confident of my laboratory skills I also signed up for an undergraduate physics laboratory course.
I was appointed a teaching assistant for a freshman course in physics taught by Professor Mark Ingraham, who was the Chairman of the Department of Physics. There were six teaching assistants for this course. My fellow teaching assistants who became my lifelong friends were George Juris Kalnins, Milton Cole, Ross Amman, and Raymond Nackoney. I was not an effective teaching assistant because I lacked communication skills. My fellow teaching assistants shielded my weakness and helped me in settling down as a graduate student.
I had moved into the apartment of Keshav Dev Sharma and Dr. Shyam Manohar Pandey. As they were much older than me I addressed them with respect as Sharma Ji and Pandey Ji. I now had the privacy of a bathroom and was happy to have escaped the ordeal of taking communal showers in the International House. Cooking of meals was done by Sharma Ji and Pandey Ji did the dishes. I would go and eat with them when the meals were ready. It did not occur to me that I should help my elder roommates in running the apartment. On Sunday mornings they took me with them to the Vivekanand Centre in the north-side Chicago. I was surprised to see that it was laid out like the inside of a church rather than a Hindu temple. An elderly monk gave a sermon from a podium to an audience consisting mostly of Americans who were seated on chairs facing the statue of Shri Ramakrishna Paramhamsa. When the service was over, offerings were made in sealed envelopes by the participants of the service. The participants dispersed to nearby restaurants for breakfast and discussed the sermon or conversed generally about Yoga and Hinduism.
Just as I began to feel that life was running smoothly on its tracks, I was jolted out of my complacency by Pandey Ji, who asked me to do some cooking. I recalled how easily Nand Lal had cooked baiganbharta. I wrapped a whole eggplant in aluminium foil and placed it inside the oven for roasting. In the mean time I had chopped onions, cut ginger root and green chillies. I opened the oven when I thought eggplant would have roasted from inside and took out the pulp. I stir fried the pulp with onion and ginger and added chopped green chillies at the end. I think my first try with cooking brought me praise I did not deserve from the two roommates. Pandey Ji said to me, “Maheshwari Ji, Sharma Ji does not cook sukhisabji well so you take charge of cooking sukhi” It was a warning signal that my happy days were coming to an end soon. I did not enter the kitchen for one week after my maiden cooking experience. I was reminded to cook again. I did not know how to cook any other sukhisabji. I decided to cook baiganbharta once agin. But this time there was an explosion inside the oven. The moisture inside the eggplant had turned into steam which got trapped inside the aluminium foil and produced pressure to cause the wrapped eggplant to explode inside the oven. I was not held responsible for the mess that had been created as it fell in the category of natural hazards of cooking not covered by any insurance clause. It took Pandey Ji half an hour to clean the oven. I repeated the eggplant blast once again a few days later. Now all hell broke loose and I was held fully responsible for my act of vandalism. I checked with Nand Lal the cause behind the eggplant explosions. He asked me whether I had punctured holes in the eggplant through the aluminium foil for steam to escape, which I had not noticed when Nand Lal cooked baiganbharta in Ithaca. I was asked to vacate the apartment as now they needed the dining room for entertaining their guests and they could not do it with the dining table placed inside the kitchen.
Returning to the International House was out of question. I went to the University Bookstore to look for announcements of vacant private accommodation. I found one announcement of a room available in a house in the campus itself. I contacted the landlady. I was in luck. The announcement had been put by the wife of a professor of music in the University. She had an India connection. Her father was then the ambassador of Sweden in India. She showed me the room, which was in the back of the house and could be reached using the fire escape. I was given the use of a small kitchen and a separate telephone. On payment of an additional 20 dollars a month I could get the services of a cleaning woman for changing sheets and cleaning the portion of the house I used. I reconciled to eating what I could select in the Billings Hospital cafeteria. I liked eating pies with milk, particularly pecan, apple and cherry. I also liked tapioca pudding. I was not happy with my daily struggle in working out my meals. I decided to become non vegetarian. My attempts to shift my food habit turned into a misadventure. I picked up a hamburger from the University Bookstore but could not eat more than a bite. The taste was unfamiliar and the thought of eating meat was repulsive.
A couple of senior graduate students conducted weekly workshops on solving problems from candidacy examinations of previous years. Proceedings of those workshops were put together and published as a book titled ‘Chicago Problems in Physics’. I attended a couple of those workshops but was disturbed to watch the ease with which some other students could solve the problems and I could not even formulate them. I developed an inferiority complex. It was damaging to my self-image. I wanted to escape from the University of Chicago for some time. I saw on the department notice board announcement of summer fellowships at the National Radio Astronomy Observatory (NRAO), Green Bank, West Virginia. I was not even remotely interested in Radio Astronomy but was keen to get away from Chicago. I applied for summer placement in response to the announcement. My good luck was that Dr. T. K. Menon, a radio astronomer at the Green Bank Observatory, noticed my application and decided to make me an offer to spend the summer with him.
I had to pass an advanced physics laboratory course. It was called the Course 334. This course was a compulsory requirement for graduate studies at the physics department of the university. It was offered once in a year in the spring quarter. The lab was kept open throughout the night. It took me more than double the suggested time for completing each experiment. Invariably I would miss dinner and return to my room hungry. I liked French fries. I picked up a packet of frozen cut potatoes and a bottle of cooking oil from the supermarket. One night it was around 3 am when I returned from the lab and decided to cook French fries. I heated oil in a pan and poured the frozen potatoes in the heated oil. It caused a blast with noise. It woke up everyone in my landlady’s family. They rushed to see what catastrophe their crazy Indian tenant had caused. I explained to them what I had done. They were amused by my ignorance that ice covered potatoes should not be put in heated oil. They were worried that I might have burnt myself by the splashes of the heated oil. They asked me to go to sleep and said that they would get the kitchen cleaned in the morning.
Professor S. Chandrasekhar, the famous physicist, offered to teach a course on quantum mechanics. I thought I knew quantum mechanics well and signed up for this course as it offered me an opportunity to get to know him. What he taught was simple and I knew it well but his method of testing was unusual. My performance in it was the turning point in my graduate studies at the University of Chicago. In 1995 soon after his death I wrote a tribute to him. I am reproducing that tribute as it brings out my extraordinary relationship with Professor S. Chandrasekhar and the period of my graduate studies at the University of Chicago.
My association with Professor Chandrasekhar dates back to 1964 when I reached the University of Chicago to do my Ph.D. studies in physics. I saw an Indian looking Professor dressed in a black suit and a Cambridge University tie sitting in the first row of a physics colloquium and could connect that the distinguished person was Professor Chandrasekhar, whom everybody affectionately called Chandra. He appeared to me then both very reserved and unapproachable. I changed this opinion as I began to know him more closely.
My next encounter with Chandra was at a Phi-Club meeting, which was specially arranged by the Department of Physics of the University to provide face-to-face interactions to the fresh class of graduate students with the senior faculty of the University. Professor Chandrasekhar spoke on General Theory of Relativity and its relevance to Cosmology & Astrophysics. I do not think I followed the lecture but can distinctly recall the remark made by Chandra; "Veracity of Einstein's theory of Gravitation is as undisputed as the findings of Justice Warren on the assassination of President John F. Kennedy". I left the meeting with more awe and a feeling of a vast distance between his intellectual abilities and what I possessed as a twenty-one year old graduate student.
I was thrilled to see the announcement that Professor Chandrasekhar would teach a course on Non-relativistic quantum mechanics. I had studied it as part of M. Sc. course in physics at the University of Delhi. I signed up for it perhaps thinking that I should be able to impress the Professor with my background and the head start I thought I had. In the first lecture Professor entered the class and demanded that no smoking be observed, as he was allergic to tobacco smoke. This was obeyed by the class but Chandra's reasons were suspect as he could be seen sitting between Professor Mark Ingraham and Professor Gregor Wentzel who continuously puffed away cigar smoke at pollution levels that could only be matched by coal-fed boilers in Chicago City.
Chandra spoke Cambridge-English without a trace of American accent and wrote on blackboard as though he was doing calligraphy. He did not like being disturbed during his lecture and looked reprovingly at students drinking coffee or eating sandwiches. The course was uneventful as it progressed but a jolt was experienced by the entire class when he announced at the end of the eleventh week that the examination would be of six hours duration with an optimum response time of about four hours. He further elaborated that there would be only one problem to be solved in closed-book/closed-notes setting and that rough-calculation sheets were to be appended to the answer-script. He also advised students to bring their pack lunch to the examination hall. The problems to be solved turned out to be on finding analytically changes in energy levels of hydrogen atom in strong electric field by setting up the Hamiltonian and writing the Schrodinger equation. Hints were given for various stages to be reached after about each successive hour of work. I vaguely recall that I could not proceed further beyond the fourth hour and closed my test after eating sandwiches, which I had specially prepared and rounded up my snack by an apple.
I wrote from the National Radio Astronomy Observatory, Green Bank, where I had gone to undergo summer training, with misgivings, to the Graduate Students Advisor of the Department of Physics to let me know how I had fared in Professor Chandrasekhar's course and whether the University would continue to give me financial assistance in the next academic year. I received a reassuring reply that Professor Chandrasekhar was happy by my performance and that the University would be pleased to support my further graduate studies. I have narrated this incident at length because it brings out how a teacher probed the mind of each of his students so painstakingly and without complaining of an inordinate demand on his time in spite of pressure of research and other professional commitments.
Although, I chose to work in the field of theoretical high-energy physics, not of direct research interest of Professor Chandrasekhar, Chandra decided to be one of the four advisors for supervising my doctoral studies. I began to experience Chandra's warmth from smile on his face in acknowledging my greetings. Gradually I started to know the real Chandra and Mrs. Chandrasekhar. Occasionally I would join both of them at dinner table in the restaurant of the International House and listen to episodes from the life of the esteemed Professor as narrated by his wife. She knew how uncomfortable students were in Chandra's presence and that we felt elated and inspired on being chosen to be shared stories from the life of the great man.
One story on how Chandra handled his graduate students I contribute to this essay, because I was the second party in the incident. I wanted to fix up with my advisory group the date and time for holding an assessment, a requirement of the Ph.D. course. Meeting Chandra in his Office in the Laboratory for Space Research and Astrophysics was difficult as an appointment was required. I knew Chandra's daily habits and decided to catch him during his walk to the laboratory. I accosted Chandra and asked point blank whether he would be in station on such and such date and whether he could be available for conducting my assessment. He suggested that I defer the assessment for a week. I told him, 'Chandra, do I not come under your priority and can you not spare half-an-hour for a graduate student?' Chandra's immediate response was a yes to the scheduling of my assessment on the date I had proposed but he said, 'Maheshwari, can you explain the concept of negative temperature?' Chandra continued to remind me whenever I met him since that I had pleaded to him to postpone the assessment for another month so I could prepare myself better.
In between I used to meet Chandra to discuss physics and sometimes he would walk to me at my desk with some newspaper report on India in his hand and share his anguish. He once asked me to explain to him the concept of pseudo energy-momentum tensor for the gravitational field. I felt honoured in having been approached by the Professor but specially privileged when Professor Chandrasekhar gave me a person-to-person seminar on how he had used this concept in his research work. This aspect of his life is also important because he took pride in pointing out that he benefited in research more from his students than from his colleagues in the University. In 1969 he told me that during the course of his career in the University except for one research paper, which he had jointly written with Enrico Fermi, all his research work was either independent or was carried out with his graduate students.
He would emphasise to me the importance of diligence and observance of discipline in daily working habits. He emphasised that personal targets to be continually further advanced so that life may remain an unending challenge without ever getting the feeling of arrived at. He once mentioned that in having decided to live abroad he could only live the life of a scientist. From his own experience he pointed out that living the life of a scientist in a foreign country is extremely difficult and very rarely and very few persons can hope to contribute to science at levels that bring lasting recognition and scientific immortality.
At the age of nineteen, Chandrasekhar had made the scientific discovery of the existence of a fundamental stellar mass from his study of the physics of white dwarf stars, the famous Chandrasekhar limit. Although Chandrasekhar had carried out his monumental work during his long sea voyage to England from India in 1930 and published it in 1931 in the Astrophysical Journal of the University of Chicago, but was awarded the Nobel Prize in physics for this work only in 1983. Chandra did not let recognition slow down his pace of work and kept on moving his targets throughout his life; to wit physics of white dwarf, stellar structure and radiative transfer, magneto-hydrodynamics, mathematical theory of black holes, study of Newton's Principia.
He was a perfect embodiment of what he practised and his advice to his students was based on his experience. He might have influenced me in deciding to return to India after getting my Ph.D. degree. In what follows next I would describe the role he played in my later professional life.
Professor Chandrasekhar was happy to know when I informed him that I had joined the University at Simla. Once, he wrote to me that while taking a walk at Aspen in the Rocky Mountains in the U.S.A. he imagined that in Simla I would also be similarly situated in an ideal setting conducive for pursuing theoretical physics. Soon after, in early 1973 I met Chandra in New Delhi. He asked me how I was progressing and if there was something he could do to help me. I told Chandra, "Nice climate and beautiful natural environment are fine but I need journals to do my scientific work, which the new University I had joined was unable to provide me.” Chandra instantaneously decided to gift to the Himachal Pradesh University his personal collection of journals. Within three months of that fateful meeting the Himachal Pradesh University received collection dating back to 1935 of the Physical Review, the Physical Review Letters and the Reviews of Modern Physics. This gift by Professor Chandrasekhar was without any expectation in return except that the journals should be made available for research consultation to all students and faculty. This act of generosity is unparalleled and brings out his genuine concern for his students and interest in their academic growth.
What has been described here is a humble tribute of an Eklavya to his Dronacharya. His other pupils will have similar stories to recount on how this great teacher influenced their life.
Although what I write next has some overlap with my tribute to Professor Chandrasekhar I will continue with it. My friend George Kalnins's parents came to Chicago to visit him. At the end of the spring quarter he was returning home to Willimantic, Connecticut. Though it involved a big detour for them, George offered to drive me to Green Bank, West Virginia with his parents in his car. His parents were from Latvia. They invited me to visit them at their home and said, “George will come to the New York City to meet you and after visiting us both of you can return to Chicago together.”
When I reached the National Radio Astronomy Observatory I found that it was located in a remote place with the nearest town at least forty miles away. It was isolated electromagnetically as its radio telescopes were used for detecting faint radio signals from distant regions of the universe. With the giant 300 feet parabolic radio telescope astronomers had detected QUASARS (quasi stellar radio sources). Unlike me the other students who had come for the summer programme were students of astronomy and were taking advantage of lectures given by the experts in radio astronomy. I spent most of my time in the library. I came across in the library the recently published Feynman Lectures in Physics. These were a set of three red books. I found Feynman’s explanation of physics transparent and fascinating. When I started reading them concepts of physics began to take shape in my mind. It will not be an exaggeration if I say that I remained glued to these books during my stay at the NRAO. Dr. T. K. Menon gave me a freehand to spend my time in the library. I forgot about the candidacy examinations and spent my time enjoying Physics as explained by Richard Feynman.
At the end of my summer placement I went to New York City. George and I saw the World’s Fair also called the New York Expo. I remember even today the giant globe displayed in it. After spending a couple of days in Willimantic with George’s parents and his other family members we drove back to Chicago. Raymond Nackoney whom we called Ray had passed his candidacy examination in the spring quarter of 1965. He joined Chandra for research. As Ray had stayed back in Chicago for the summer we asked him to find an apartment which we could all share. Ray could find an apartment for three but there were four claimants including me. The other three were George, Milton, and Ray. Ray offered to withdraw his claim and let George, Milton and me keep the apartment. George persuaded me to spend well in buying my bed. He pointed out that we spend at least one-third of our life sleeping and therefore should have a good bed. All three roommates were to write the candidacy examination at the end of the quarter. We had an understanding that none of us would discuss our preparations for the candidacy examinations. One day with trepidation I opened a set of problems from the earlier candidacy examinations. It was a pleasant surprise to discover that I could answer at least 80% of the randomly selected problems. I decided that it was not worth investing time in trying to push up my problem solving abilities. I signed up for three advanced physics courses in that quarter as I was now no longer worried about my performance in the coming candidacy examination. In the second week of December 1965 I wrote my candidacy examination. I perhaps had a near perfect score. A problem which I had left unfinished involved the Dirac delta function. In the viva voce I was shown the integral form of the Dirac delta function. I vehemently argued, “It is mathematically ill defined and is inadmissible as a function.” The Examination Committee members had a big laugh. Although mathematically ill defined the Dirac delta function is crucial for quantum mechanics. The result of the examination was declared. I was at the top of the 16 candidates out of 40 who had cleared the candidacy examination with me. Milton, Peter Lam, Edmond Schonberg and I were placed in the group A of the successful candidates. Once again I had gone up from the bottom to the top. I knew I had turned the corner and getting my Ph.D. degree was a matter of time.
Milton, George, Robert Sandling and I had decided to go on vacation to see the Grand Canyon in George’s car irrespective of our performances in the candidacy examination. A precondition laid by the group was that I would eat whatever the group ate as it was not possible to arrange special dietary needs in a camping vacation. I successfully changed my food habits during this trip and became a non vegetarian!