Paul Adrien Maurice Dirac The Unifier of Quantum Mechanics and Relativity Theory

“The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth.” Paul Dirac “…it is more important to have beauty in one’s equations than to have them fit experiment…It seems that if one is working from the point of view of getting beauty in one’s equations, and if one has really a sound insight, one is on a sure line of progress.” Paul Dirac

“An era in physics came to an end when Paul Adrien Maurice Dirac passed away on 20th October, 1984, at the age of 82. Our last surviving link with the birth of quantum mechanics was also broken with his death. Anyone acquainted with the development of modern physics would be well aware of the range, depth and profound beauty of Dirac’s work and ideas which appeared in steady and staggering profusion over half a century.” N. Mukunda in Images of Twentieth Century Physics (2000)

Paul Adrien Maurice Dirac is regarded as one of the greatest theoretical physicists of the 20th century. In fact he will always rank one of the greatest scientists of all time. Dirac’s work was mainly concerned with a branch of science known as quantum mechanics. It takes considerable time and effort to develop familiarity with quantum mechanics. However, it is not something beyond comprehension. It is quantum mechanics which has provided us the best model we have of the physical reality. We find the use of quantum mechanics in many technological applications including quantum optics and nanoelectronics. It may not be very far away when computers will be developed based on quantum logic. The present article does not attempt to explain Dirac’s contribution in quantum mechanics but merely states his accomplishments and briefly touches upon his other aspects of life. Dirac was a founder of quantum mechanics. In 1926, slightly later than Max Born (1882-1970) and Pascual Jordan (1902-80) in Germany, Dirac developed a general theoretical structure (formalism) for quantum mechanics. By applying the ideas of Einstein’s special theory of relativity to quantum mechanics, Dirac unified the theories of quantum mechanics and relativity. This gave birth to the relativistic form of quantum mechanics. His relativistic quantum mechanics described the properties of the electron and corrected the failure of Schrodinger’s theory to explain electron spin, discovered by George Eugene Uhlenbeck (1900-88) and Samuel Abraham Goudsmit (1902-78) in 1925. In his attempt to unify quantum mechanics and relativity theory he came up with an elegant equation, which is called Dirac equation. While working out the solution of his equation in 1930, Dirac predicted the existence of antiparticle of electron—a particle with the same properties as electron but with positive charge. Carl David Anderson (1905-91) confirmed Dirac’s prediction in 1932 by discovering a positively charged electron, which he called positron. Dirac’s argument applies all particles, and not just electrons. It meant wherever matter existed its mirror or antimatter must also exist. Werner Heisenberg termed Dirac’s prediction of antimatter as “the most decisive discovery in connection with the properties or nature of elementary particles.” Dirac’s vision of quantum mechanics was marked by its generality and simplicity. Thus Albert Einstein (1879-1955) said: “Dirac, to whom in my opinion we owe the most logically perfect presentation of quantum mechanics.” Niels Bohr (1885-1962) said: “Of all physicists, Dirac had the purest soul”. Though Dirac’s work mainly concerned with the mathematical and theoretical aspects of quantum mechanics, but he also made outstanding work on the magnetic monopole, fundamental length, the delta function, etc. According to Dirac the principle of mathematical beauty is the key concept in the relationship between mathematics and physics. He said: “The research worker, in his efforts to express the fundamental laws of Nature in mathematical form, should strive for mathematical beauty. I should still take simplicity into consideration in a subordinate way to beauty.” Dirac had a scintillating academic career. He wrote his first research paper at 22. At the age of 28 Dirac was elected a Fellow of Royal Society of London. He became a Lucasian Professor (a chair once held by Isaac Newton) at the Cambridge University at 31. He received the Nobel Prize at 33. He produced about 200 research papers. Of these about 90 were devoted to the development of quantum theory. All his papers were truly original and contained path-breaking ideas. N. Mukunda wrote: “The number of scientific papers that Dirac wrote is not particularly great. A bibliography compiled at the time of his 70th birthday contained a little over one hundred publications; in all it may run to some 200 papers or so. But the number and variety of entirely original and trail-blazing ideas in these papers are truly stupendous.” Dirac was something more than a genius. The mathematician Mark Kac divided geniuses into two classes—the ordinary geniuses and the “magicians”. While one can imagine that the achievements of the first category of geniuses--that is the ordinary geniuses, might be emulated by others with enormous hard work and a bit of luck but the achievements of the second category of geniuses or the so called the “magicians” are so astounding that one fails to see how any human mind imagined them. Dirac was truly a “magician”. Dirac was born on August 08, 1902 in Bristol England. His father Charles Adrien Ladislas Dirac taught French at the secondary school attached to the Merchant Ventures College in Bristol. Charles Dirac was a Swiss citizen and he was educated at the University of Geneva. He came to England around 1888. Dirac’s mother was Florence Hannah Holten, the daughter of a Master Mariner of a Bristol Ship. Before her marriage, Florence was working in a library. Dirac was one of three children. He had an older brother and a younger sister. Dirac’s childhood was not a happy one. Dirac’s father Charles was very strict with his children. He insisted that only French be spoken at the dinner table. As there was no exception to the rule, Dirac was the only person to dine with his father. The other members of the family dined in the kitchen. Since Dirac had to speak with his father only in French, he spoke very little. He took lot of time to frame proper sentences. Perhaps this was the reason for Dirac’s pronounced tendency to speak very little and the utmost care he took in choosing words while speaking. Dirac once said: “I had no social life at all as a child…My father made a rule that I should talk to him in French. He thought it would be good for me to learn French that way. Since I found I could not express myself in French, it was better for me to stay silent than talk English. So I became very silent from an early age.” Because of his father’s dominating personality hardly anybody came to meet the Diracs. Dirac’s elder brother Reginald Charles Felix Dirac wanted to become a physician but his father forced him to study mechanical engineering at Bristol. He obtained a third class degree and he started working as a draftsman with an engineering firm. Reginald committed suicide at 24. After this incident Dirac was totally elienated with his father. Perhaps Dirac thought his father was in some way responsible for his brother’s suicide. The first school, which Dirac attended, was Bishop Primary School. Dirac’s exceptional mathematical ability showed itself at an early age. In his school he was given rather advanced books on mathematics for independent study. His father also encouraged his son to develop his mathematical ability. At the age of 12 Dirac entered the Merchant Ventures Secondary School. Commenting on his school Dirac wrote: “The Merchant Ventures was an excellent school for science and modern languages. There was no Latin or Greek, something of which I was rather glad, because I did not appreciate the value of old cultures. I consider myself very lucky in having been able to attend the school…I was rushed through the lower forms, and was introduced at an especially early age to the basis of mathematics, physics and chemistry in the higher forms. In mathematics I was studying from books, which mostly were ahead of the rest of the class. The rapid advancement was a great help to me in my latter career.” After completing his secondary school education in 1918, Dirac decided to study electrical engineering at the University of Bristol. This is in spite of the fact that his favourite subject was mathematics. However, in those days the only possible career for a mathematician was school teaching. As Dirac wanted to avoid the profession of a school teacher, he ended up in studying electrical engineering. He obtained his degree in electrical engineering in 1921. However, he could not find a permanent job as an engineer. In the meantime his interest in mathematics had become more intense. He unsuccessfully attempted to study mathematics at Cambridge. The reason for his not been able to study mathematics at Cambridge was financial. Though he obtained a scholarship to study mathematics at St John’s College at Cambridge but it was not enough for meeting his financial needs. He failed to get additional support from the local education authority. He was not given the additional support because his father had not been a British citizen long enough for his son to be eligible for such support. However, Dirac got an opportunity to study mathematics at the Bristol University without paying fees. As a student of electrical engineering he did hardly any experimental work. In any case Dirac was not good at practical work. He did not appreciate the fact that topics such as atomic physics and Maxwell’s electromagnetic theory were excluded from electrical engineering course. However, his engineering studies had a bearing on his future work in mathematical physics. Particularly the use of approximations that he learnt while studying engineering exerted a strong influence on his later work. The use of approximation strengthened his confidence in the intuitive approach to problem solving and which in turn led him to believe that to construct a theory expressing fundamental law of nature one need not have the exact knowledge of actualities. It can be done being guided by intuition. He was of the opinion that a physicist must be satisfied to work only with approximate knowledge of reality—the actual phenomena were too complex to be understood in a precise way. On the influence of engineering studies on his work in mathematical physics Dirac himself said : “If I had not this engineering training I should not have had any success with the kind of work that I did later on, because it was really necessary to get away from the point of view that one should deal only with results which could be deduced from known exact laws, in which one had implicit faith.” He obtained a first class honours degree in mathematics in 1923 and he was awarded a grant to undertake research at Cambridge. Because of his fascination with the general theory of relativity, Dirac was interested in working with Ebenezer Cunningham. But Cunningham had as many students as he was prepared to take and so Dirac started working under the supervision of Ralph Howard Fowler(1899-1944), who had collaborated with Niels Bohr in his pioneering work in atomic physics. R. H. Dalitz and R. Peierls while writing on Dirac in Biographical Memoirs of Fellows of the Royal Society of London, wrote: “Fowler was then the leading theoretician in Cambridge, well versed in the quantum theory of atoms; his own research was mostly on statistical mechanics. He recognized in Dirac a student of unusual ability. Under his influence Dirac worked on some problems in statistical mechanics. Within six months of arriving in Cambridge he wrote two papers on these problems. No doubt Fowler aroused his interest in the quantum theory, and in May 1924 Dirac completed his first paper dealing with quantum problem. Four more papers were completed by November 1925.” It was after going through the proofs of Werner Heisenberg’s paper on uncertainty principles that Dirac got a clue to formulate for the first time a mathematically consistent general theory of quantum mechanics in correspondence with Hamiltonian mechanics. The paper was sent to Fowler and who in turn passed it to Dirac. After reading the paper for the second time Dirac realized “that it (Heisenberg’s paper) provided the key to the problem of quantum mechanics. Dirac’s work on quantum mechanics became the basis for his Doctoral thesis on Quantum Mechanics. It is important to note that before submission his doctoral thesis, Dirac had published eleven papers. Dirac was awarded a PhD degree in 1926. He then went to Copenhagen to work with Niels Bohr. From Copenhagen he moved to Gottingen in February 1927 where he interacted with J. Robert Oppenheimer (1904-67), Max Born, James Franck (1882-1964) and Igor Yevgenevich Tamm (1895-1971). He also spent a few weeks in Leiden before he returned to Cambridge. In 1927 Dirac was elected a Fellow of St John’s College, Cambridge. In 1930 Dirac was elected a Fellow of Royal Society of London. He was only 28 years old. What is more Dirac was given the honour on the very first occasion his name was put forward. This was an indication of the extremely high opinion that Dirac’s fellow scientists had of him. In 1930 Dirac published The Principles of Quantum Mechanics. In this book Dirac developed the so-called transformation theory of quantum mechanics that furnished a machinery for calculating the statistical distribution of certain variables when others are specified. Commenting on the book one reviewer wrote: “ Dirac was not influenced by the feeding frenzy in experimental phenomenology of the time. This has given Dirac’s book …a lasting quality that few works match.” This book confirmed Dirac’s stature as the 20th century Newton in the minds of many physicists. Thus N. Mukunda wrote: “ This book is often compared for its spirit and style to the Principia of Isaac Newton.” It has guided several generations of physicists. His other published works include Lectures on Quantum Mechanics (1966), The Development of Quantum Theory (1971), Spinors in Hilbert Space (1974), and General Theory of Relativity (1975 ). In 1932, Dirac was appointed Lucasian professor of mathematics at the Cambridge University. He held this post for 37 years. The post was once held by Isaac Newton. Stephen Hawking succeeded Dirac. In 1937 Dirac married Eugene Paul Wigner’s sister Margit, whom she met at Priceton. This was second marriage for Margit. She had two children Judith and Gabriel Andrew from her first marriage. Both the children adopted the name of Dirac. Dirac was an extremely modest man. He never talked about the importance of his own work. He was ever ready to acknowledge his debt to others. Once commenting on his work Dirac said: “Well, from the initial idea of Heisenberg, one could make fairly rapid development, and I was able to join in it. I was just a research student at that time. I was lucky enough to be born at the right time to make it possible for that to be so.” On another occasion he said: “It was very easy in those days for any second-rate physicist to do first-rate work. There has not been such a glorious time since then. It is very difficult now for a first rate physicist to do second-rate work”. Dirac had an unusual personality. He was extremely shy. He avoided company. Dirac spent most of his time alone in libraries. His only pastime was solitary walk. He was reluctant to take part in conversation. Dirac is well-known for clarity and simplicity in his writing. Bohr commenting on Dirac’s style of writing said: “Whenever Dirac send me a manuscript, the writing is so neat and free of corrections that merely looking at it is an aesthetic pleasure. If I suggest even minor changes, Paul becomes terribly unhappy and generally changes nothing at all.” Like many other great personalities innumerable stories have become attached to Dirac. Most of these stories had to do with Dirac’s unusual logic and precision that he adopted while interacting with world. Often such stories do not represent the true facts. But in case of Dirac all the stories are claimed to be true. George Gamow in his Thirty Years that Shook Physics wrote: “Now it often happens that ‘absent minded professor’ stories grow up around famous scientists. In most cases these stories are not true, merely inventions of wags, but in case of Dirac all the stories are really true, at least in the opinion of this writer… Being a great theoretical physicist, Dirac liked to theorise about all the problems of daily life, rather than to find solutions by direct experiment. Once at a party at Copenhagen, he proposed a theory according to which there must be a certain distance at which a woman’s face looks its best. He argued that at d=infinite one cannot see anything anyway, while at d=0 the oval of the face is deformed because of the small aperture of the human eye, and many other imperfections (such as small wrinkles) become exaggerated. ‘Tell me, Paul,’ I asked, ‘how close you have seen a woman’s face?’ ‘Oh’, replied Dirac, holding his palms about two feet apart, ‘about that close’”. After Dirac delivered a lecture at the University of Toronto, somebody in audience asked during the question period; “Professor Dirac, I do not understand how you derived the formula on the top left side of the blackboard.” Dirac did not reply. He simply said: “This is not a question, it is a statement. Next question, please.” As mentioned earlier that Dirac’s writing was marked for its clarity and simplicity. Niels Bohr, while writing a paper with many hesitations and redrafting once remarked in Dirac’s presence : “ I do not know how to finish this sentence.” To this Dirac replied: “I was taught at school that you should never start a sentence without knowing the end of it.” Once Leonidovich Pjotr Kapitza (1894-1984) had given an English translation of Dostoevski’s Crime and Punishment. When Dirac went to return the book, Kaptza asked: “Well, how do you like it?” Dirac’s only comment was: “It is nice, but in one of the chapters the author made a mistake. He describes the Sun rising twice on the same day.” An interesting interaction with Dirac was narrated by his colleague Jagdish Mehra: “The weather outside was very bad, and since in England it is always respectable to start a conversation with the weather, I said to Dirac, ‘t is very windy, Professor.’ He said nothing at all, and a few seconds later he got up and left. I was mortified, as I thought that I had somehow offended him. He went to the door, opened it, looked out, came back, sat down, and said, ‘Yes.’” Dirac traveled extensively and studied at various foreign universities including Copenhagen, Gottingen, Leyden, Wisconsin, Michigan and Princeton. Dirac visited the erstwhile Soviet Union a number of times. During 1973 and 1975 Dirac lectured on the problems of cosmology in the Physical Engineering Institute in Leningrad. Dirac also visited India. After retiring from the Lucasian Chair of Mathematics at Cambridge in 1969, Dirac went with his family to Florida in United States of America. He held visiting lecturership at four US universities before he was appointed Professor of Physics at Florida State University in 1971. Dirac received the Nobel Prize in Physics 1933 at the age of 33. He shared the Prize with Erwin Schrodinger (1887-1963). At the first instance Dirac was contemplating to turn down the Prize on the grounds that he did not relish publicity. But on being pointed out that he would receive far more publicity in case he decided to refuse the Prize, he accepted it. Though Dirac could invite his parents but he only invited his mother and not his father, a reflection of his strained relation with his father. Some of the other honours that Dirac received are: Fellow of the Royal Society of London (1930), the Order of Merit (1933), Royal Society Royal Medal (1939), Royal Society Copley Medal (1952), Royal Socity Bakerian lecturer (1941). While Dirac refused to accept honorary degrees but he accepted membership of academic societies. Among these academic bodies included USSR Academy of Sciences (1931), Indian Academy of Sciences (1939), Chinese Physical Society (1943), Royal Irish Academy (1944), Royal Society of Edinburgh (1946), Instut de France (1946), National Institute of Science of India (1947), American Physical Society (1948), Pontifical Academy of Sciences, Vatican City (1958), Royal Danish Academy (1962) and Academy of Sciences Paris (1963). Dirac died on October 20, 1984 in Tallahassee, Florida, USA. In November 1995 a plaque was unveiled in Westminster Abbey commemorating Paul Dirac. The memorial address was present by Stephen Hawking. We would like to end this article by quoting Dirac on what he had to say about quantum mechanics: “… the present form of quantum mechanics should not be considered as the final form. There are great difficulties…with the present quantum mechanics. It is the best that one can do up till now. But one should not suppose that it will survive indefinitely into the future. And I think that it quite likely that at some future time we may get an improved quantum mechanics in which there will be a return to determinism and which will, therefore, justify the Einstein point of view.” References Dirac: A Scientific Biography by Cambridge: Cambridge University Press, 1990. Reminiscences About a Great Physicist: Paul Adrien Maurice Dirac. Edited by Behram N. Kursunoglu and Eugene P. Wigner. Cambridge: Cambridge University Press, 1987. Images of Twentieth Century Physics by N. Mukunda. Hyderabad: Universities Press India Limited, 2000. (Published in collaboration with Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore). The Oxford Companion to the History of Modern Science J. L. Heilborn (edited by). Oxford: Oxford University Press, 2003. The Cambridge Dictionary of Scientists (Second edition) by David, Ian, John and Margaret Millar. Cambridge: Cambridge University Press, 2002. A Dictionary of Scientists. Oford: Oxford University Press, 1999. The History of Science from 1895 to 1945 by Ray Spangenburg and Diane K. Moser. Hyderabad: Universities Press (India) Limited, 1999. Chambers Biographical Dictionary. New York: Chambers Harrap Publishers Ltd., 1997. Paths of Innovators by R. Parthasarathy. Chennai: East West Books (Madars) Private Ltd., 2000.