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Wikipedia

Paul Dirac

May 19, 2023

"Dirac" redirects here. For other uses, see Dirac (disambiguation).

Paul Adrien Maurice Dirac OM FRS[9] (/dɪˈræk/; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is considered to be one of the founders of quantum mechanics and quantum electrodynamics.[10] He was the Lucasian Professor of Mathematics at the University of Cambridge, a professor of physics at Florida State University and the University of Miami, and a 1933 Nobel Prize in Physics recipient.

Paul Dirac

OM FRS
Dirac, photographed in 1933
Born
Paul Adrien Maurice Dirac

(1902-08-08)8 August 1902
Bristol, England
Died20 October 1984(1984-10-20) (aged 82)
Tallahassee, Florida, U.S.
NationalityBritish
Alma mater
Known for
 
Spouse
Margit Wigner
​
(m. 1937)​
Children2
Awards
Scientific career
FieldsTheoretical physics
Institutions
ThesisQuantum mechanics (1926)
Doctoral advisorRalph Fowler
Doctoral students
InfluencesJohn Stuart Mill[7][8]
Portrait of Paul Dirac by Clara Ewald (1939)

Dirac made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics. Among other discoveries, he formulated the Dirac equation which describes the behaviour of fermions and predicted the existence of antimatter. Dirac shared the 1933 Nobel Prize in Physics with Erwin Schrödinger "for the discovery of new productive forms of atomic theory".[11] He also made significant contributions to the reconciliation of general relativity with quantum mechanics.

Dirac was regarded by his friends and colleagues as unusual in character. In a 1926 letter to Paul Ehrenfest, Albert Einstein wrote of a Dirac paper, "I am toiling over Dirac. This balancing on the dizzying path between genius and madness is awful." In another letter concerning the Compton effect he wrote, "I don't understand the details of Dirac at all."[12]

Personal life

Early years

Paul Adrien Maurice Dirac was born at his parents' home in Bristol, England, on 8 August 1902,[13] and grew up in the Bishopston area of the city.[14] His father, Charles Adrien Ladislas Dirac, was an immigrant from Saint-Maurice, Switzerland who worked in Bristol as a French teacher. His mother, Florence Hannah Dirac, née Holten, was born to a Cornish Methodist family in Liskeard, Cornwall.[15][16] She was named after Florence Nightingale by her father, a ship's captain, who had met Nightingale while he was a soldier during the Crimean war.[17] His mother moved to Bristol as a young woman, where she worked as a librarian at the Bristol Central Library; despite this she still considered her identity to be Cornish rather than English.[18] Paul had a younger sister, Béatrice Isabelle Marguerite, known as Betty, and an older brother, Reginald Charles Félix, known as Felix,[19][20] who died by suicide in March 1925.[21] Dirac later recalled: "My parents were terribly distressed. I didn't know they cared so much ... I never knew that parents were supposed to care for their children, but from then on I knew."[22]

Charles and the children were officially Swiss nationals until they became naturalised on 22 October 1919.[23] Dirac's father was strict and authoritarian, although he disapproved of corporal punishment.[24] Dirac had a strained relationship with his father, so much so that after his father's death, Dirac wrote, "I feel much freer now, and I am my own man." Charles forced his children to speak to him only in French so that they might learn the language. When Dirac found that he could not express what he wanted to say in French, he chose to remain silent.[25][26]

Education

Dirac was educated first at Bishop Road Primary School[27] and then at the all-boys Merchant Venturers' Technical College (later Cotham School), where his father was a French teacher.[28] The school was an institution attached to the University of Bristol, which shared grounds and staff.[29] It emphasised technical subjects like bricklaying, shoemaking and metalwork, and modern languages.[30] This was unusual at a time when secondary education in Britain was still dedicated largely to the classics, and something for which Dirac would later express his gratitude.[29]

Dirac studied electrical engineering on a City of Bristol University Scholarship at the University of Bristol's engineering faculty, which was co-located with the Merchant Venturers' Technical College.[31] Shortly before he completed his degree in 1921, he sat for the entrance examination for St John's College, Cambridge. He passed and was awarded a £70 scholarship, but this fell short of the amount of money required to live and study at Cambridge. Despite his having graduated with a first class honours Bachelor of Science degree in engineering, the economic climate of the post-war depression was such that he was unable to find work as an engineer. Instead, he took up an offer to study for a Bachelor of Arts degree in mathematics at the University of Bristol free of charge. He was permitted to skip the first year of the course owing to his engineering degree.[32]

In 1923, Dirac graduated, once again with first class honours, and received a £140 scholarship from the Department of Scientific and Industrial Research.[33] Along with his £70 scholarship from St John's College, this was enough to live at Cambridge. There, Dirac pursued his interests in the theory of general relativity, an interest he had gained earlier as a student in Bristol, and in the nascent field of quantum physics, under the supervision of Ralph Fowler.[34] From 1925 to 1928 he held an 1851 Research Fellowship from the Royal Commission for the Exhibition of 1851.[35] He completed his PhD in June 1926 with the first thesis on quantum mechanics to be submitted anywhere.[36] He then continued his research in Copenhagen and Göttingen.[35] In the spring of 1929, he was a visiting professor at the University of Wisconsin–Madison.[37][38]

Family

 
Paul and Manci Dirac in Copenhagen, July 1963

In 1937, Dirac married[39] Margit Wigner, a sister of physicist Eugene Wigner[40] and a divorcee.[41] Dirac raised Margit's two children, Judith and Gabriel, as if they were his own.[42] Paul and Margit Dirac also had two daughters together, Mary Elizabeth and Florence Monica.[43]

Margit, known as Manci, had visited her brother in 1934 in Princeton, New Jersey, from their native Hungary and, while at dinner at the Annex Restaurant, met the "lonely-looking man at the next table". This account from a Korean physicist, Y. S. Kim, who met and was influenced by Dirac, also says: "It is quite fortunate for the physics community that Manci took good care of our respected Paul A. M. Dirac. Dirac published eleven papers during the period 1939–46. Dirac was able to maintain his normal research productivity only because Manci was in charge of everything else".[44]

Personality

Dirac was known among his colleagues for his precise and taciturn nature. His colleagues in Cambridge jokingly defined a unit called a "dirac", which was one word per hour.[45] When Niels Bohr complained that he did not know how to finish a sentence in a scientific article he was writing, Dirac replied, "I was taught at school never to start a sentence without knowing the end of it."[46] He criticised the physicist J. Robert Oppenheimer's interest in poetry: "The aim of science is to make difficult things understandable in a simpler way; the aim of poetry is to state simple things in an incomprehensible way. The two are incompatible."[47]

Dirac himself wrote in his diary during his postgraduate years that he concentrated solely on his research, and stopped only on Sunday when he took long strolls alone.[48]

An anecdote recounted in a review of the 2009 biography tells of Werner Heisenberg and Dirac sailing on an ocean liner to a conference in Japan in August 1929. "Both still in their twenties, and unmarried, they made an odd couple. Heisenberg was a ladies' man who constantly flirted and danced, while Dirac—'an Edwardian geek', as biographer Graham Farmelo puts it—suffered agonies if forced into any kind of socializing or small talk. 'Why do you dance?' Dirac asked his companion. 'When there are nice girls, it is a pleasure,' Heisenberg replied. Dirac pondered this notion, then blurted out: 'But, Heisenberg, how do you know beforehand that the girls are nice?'"[49]

Margit Dirac told both George Gamow and Anton Capri in the 1960s that her husband had said to a house visitor, "Allow me to present Wigner's sister, who is now my wife."[50][51]

Another story told of Dirac is that when he first met the young Richard Feynman at a conference, he said after a long silence, "I have an equation. Do you have one too?"[52]

After he presented a lecture at a conference, one colleague raised his hand and said: "I don't understand the equation on the top-right-hand corner of the blackboard". After a long silence, the moderator asked Dirac if he wanted to answer the question, to which Dirac replied: "That was not a question, it was a comment."[53][54]

Dirac was also noted for his personal modesty. He called the equation for the time evolution of a quantum-mechanical operator, which he was the first to write down, the "Heisenberg equation of motion". Most physicists speak of Fermi–Dirac statistics for half-integer-spin particles and Bose–Einstein statistics for integer-spin particles. While lecturing later in life, Dirac always insisted on calling the former "Fermi statistics". He referred to the latter as "Bose statistics" for reasons, he explained, of "symmetry".[55]

Views on religion

Heisenberg recollected a conversation among young participants at the 1927 Solvay Conference about Einstein and Planck's views on religion between Wolfgang Pauli, Heisenberg and Dirac. Dirac's contribution was a criticism of the political purpose of religion, which Bohr regarded as quite lucid when hearing it from Heisenberg later.[56] Among other things, Dirac said:

I cannot understand why we idle discussing religion. If we are honest—and scientists have to be—we must admit that religion is a jumble of false assertions, with no basis in reality. The very idea of God is a product of the human imagination. It is quite understandable why primitive people, who were so much more exposed to the overpowering forces of nature than we are today, should have personified these forces in fear and trembling. But nowadays, when we understand so many natural processes, we have no need for such solutions. I can't for the life of me see how the postulate of an Almighty God helps us in any way. What I do see is that this assumption leads to such unproductive questions as to why God allows so much misery and injustice, the exploitation of the poor by the rich, and all the other horrors He might have prevented. If religion is still being taught, it is by no means because its ideas still convince us, but simply because some of us want to keep the lower classes quiet. Quiet people are much easier to govern than clamorous and dissatisfied ones. They are also much easier to exploit. Religion is a kind of opium that allows a nation to lull itself into wishful dreams and so forget the injustices that are being perpetrated against the people. Hence the close alliance between those two great political forces, the State and the Church. Both need the illusion that a kindly God rewards—in heaven if not on earth—all those who have not risen up against injustice, who have done their duty quietly and uncomplainingly. That is precisely why the honest assertion that God is a mere product of the human imagination is branded as the worst of all mortal sins.[57]

Heisenberg's view was tolerant. Pauli, raised as a Catholic, had kept silent after some initial remarks, but when finally he was asked for his opinion, said: "Well, our friend Dirac has got a religion and its guiding principle is 'There is no God, and Paul Dirac is His prophet.'" Everybody, including Dirac, burst into laughter.[58][59]

Later in life, Dirac's views towards the idea of God were less acerbic. As an author of an article appearing in the May 1963 edition of Scientific American, Dirac wrote:

It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better.[60]

In 1971, at a conference meeting, Dirac expressed his views on the existence of God.[61] Dirac explained that the existence of God could be justified only if an improbable event were to have taken place in the past:

It could be that it is extremely difficult to start life. It might be that it is so difficult to start a life that it has happened only once among all the planets... Let us consider, just as a conjecture, that the chance of life starting when we have got suitable physical conditions is 10−100. I don't have any logical reason for proposing this figure, I just want you to consider it as a possibility. Under those conditions ... it is almost certain that life would not have started. And I feel that under those conditions it will be necessary to assume the existence of a god to start off life. I would like, therefore, to set up this connection between the existence of a god and the physical laws: if physical laws are such that to start off life involves an excessively small chance so that it will not be reasonable to suppose that life would have started just by blind chance, then there must be a god, and such a god would probably be showing his influence in the quantum jumps which are taking place later on. On the other hand, if life can start very easily and does not need any divine influence, then I will say that there is no god.[62]

Dirac did not commit himself to any definite view, but he described the possibilities for scientifically answering the question of God.[62]

Career

Dirac established the most general theory of quantum mechanics and discovered the relativistic equation for the electron, which now bears his name. The remarkable notion of an antiparticle to each fermion particle – e.g. the positron as antiparticle to the electron – stems from his equation. He was the first to develop quantum field theory, which underlies all theoretical work on sub-atomic or "elementary" particles today, work that is fundamental to our understanding of the forces of nature. He proposed and investigated the concept of a magnetic monopole, an object not yet known empirically, as a means of bringing even greater symmetry to James Clerk Maxwell's equations of electromagnetism.

Quantum theory

Dirac's first step into a new quantum theory was taken late in September 1925. Ralph Fowler, his research supervisor, had received a proof copy of an exploratory paper by Werner Heisenberg in the framework of the old quantum theory of Bohr and Sommerfeld. Heisenberg leaned heavily on Bohr's correspondence principle but changed the equations so that they involved directly observable quantities, leading to the matrix formulation of quantum mechanics. Fowler sent Heisenberg's paper on to Dirac, who was on vacation in Bristol, asking him to look into this paper carefully.[63]

Dirac's attention was drawn to a mysterious mathematical relationship, at first sight unintelligible, that Heisenberg had established. Several weeks later, back in Cambridge, Dirac suddenly recognised that this mathematical form had the same structure as the Poisson brackets that occur in the classical dynamics of particle motion.[63] At the time, his memory of Poisson brackets was rather vague, but he found E. T. Whittaker's Analytical Dynamics of Particles and Rigid Bodies illuminating.[64] From his new understanding, he developed a quantum theory based on non-commuting dynamical variables. This led him to the most profound and significant general formulation of quantum mechanics to date.[65] Dirac's formulation allowed him to obtain the quantisation rules in a novel and more illuminating manner. For this work,[66] published in 1926, Dirac received a PhD from Cambridge. This formed the basis for Fermi-Dirac statistics that applies to systems consisting of many identical spin 1/2 particles (i.e. that obey the Pauli exclusion principle), e.g. electrons in solids and liquids, and importantly to the field of conduction in semi-conductors.

Dirac was famously not bothered by issues of interpretation in quantum theory. In fact, in a paper published in a book in his honour, he wrote: "The interpretation of quantum mechanics has been dealt with by many authors, and I do not want to discuss it here. I want to deal with more fundamental things."[67]

The Dirac equation

Further information: Dirac equation

In 1928, building on 2×2 spin matrices which he purported to have discovered independently of Wolfgang Pauli's work on non-relativistic spin systems (Dirac told Abraham Pais, "I believe I got these [matrices] independently of Pauli and possibly Pauli got these independently of me."),[68] he proposed the Dirac equation as a relativistic equation of motion for the wave function of the electron.[69] This work led Dirac to predict the existence of the positron, the electron's antiparticle, which he interpreted in terms of what came to be called the Dirac sea.[70] The positron was observed by Carl Anderson in 1932. Dirac's equation also contributed to explaining the origin of quantum spin as a relativistic phenomenon.

The necessity of fermions (matter) being created and destroyed in Enrico Fermi's 1934 theory of beta decay led to a reinterpretation of Dirac's equation as a "classical" field equation for any point particle of spin ħ/2, itself subject to quantisation conditions involving anti-commutators. Thus reinterpreted, in 1934 by Werner Heisenberg, as a (quantum) field equation accurately describing all elementary matter particles – today quarks and leptons – this Dirac field equation is as central to theoretical physics as the Maxwell, Yang–Mills and Einstein field equations. Dirac is regarded as the founder of quantum electrodynamics, being the first to use that term. He also introduced the idea of vacuum polarisation in the early 1930s. This work was key to the development of quantum mechanics by the next generation of theorists, in particular Schwinger, Feynman, Sin-Itiro Tomonaga and Dyson in their formulation of quantum electrodynamics.

Dirac's The Principles of Quantum Mechanics, published in 1930, is a landmark in the history of science. It quickly became one of the standard textbooks on the subject and is still used today. In that book, Dirac incorporated the previous work of Werner Heisenberg on matrix mechanics and of Erwin Schrödinger on wave mechanics into a single mathematical formalism that associates measurable quantities to operators acting on the Hilbert space of vectors that describe the state of a physical system. The book also introduced the Dirac delta function. Following his 1939 article,[71] he also included the bra–ket notation in the third edition of his book,[72] thereby contributing to its universal use nowadays.

Magnetic monopoles

In 1931, Dirac proposed that the existence of a single magnetic monopole in the universe would suffice to explain the quantisation of electrical charge.[73] In 1975,[74] 1982[75] and 2009,[76][77][78] intriguing results suggested the possible detection of magnetic monopoles, but there is, to date, no direct evidence for their existence (see also Searches for magnetic monopoles).

Gravity

He quantized the gravitational field and developed a general theory of the quantum field with dynamical constraints, which forms the basis of the gauge theories and superstring theories of today.[79] The influence and importance of Dirac's work have increased with the decades, and physicists use daily the concepts and equations that he developed.

University of Cambridge

Dirac was the Lucasian Professor of Mathematics at the University of Cambridge from 1932 to 1969. In 1937, he proposed a speculative cosmological model based on the so-called large numbers hypothesis. During World War II, he conducted important theoretical and experimental research on uranium enrichment by gas centrifuge.[80]

Dirac's quantum electrodynamics (QED) made predictions that were – more often than not – infinite and therefore unacceptable. A workaround known as renormalisation was developed, but Dirac never accepted this. "I must say that I am very dissatisfied with the situation", he said in 1975, "because this so-called 'good theory' does involve neglecting infinities which appear in its equations, neglecting them in an arbitrary way. This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it is small – not neglecting it just because it is infinitely great and you do not want it!"[81] His refusal to accept renormalisation resulted in his work on the subject moving increasingly out of the mainstream.

However, from his once rejected notes he managed to work on putting quantum electrodynamics on "logical foundations" based on Hamiltonian formalism that he formulated. He found a rather novel way of deriving the anomalous magnetic moment "Schwinger term" and also the Lamb shift, afresh in 1963, using the Heisenberg picture and without using the joining method used by Weisskopf and French, and by the two pioneers of modern QED, Schwinger and Feynman. That was two years before the Tomonaga–Schwinger–Feynman QED was given formal recognition by an award of the Nobel Prize for physics.

Weisskopf and French (FW) were the first to obtain the correct result for the Lamb shift and the anomalous magnetic moment of the electron. At first FW results did not agree with the incorrect but independent results of Feynman and Schwinger.[82] The 1963–1964 lectures Dirac gave on quantum field theory at Yeshiva University were published in 1966 as the Belfer Graduate School of Science, Monograph Series Number, 3.

Florida State University and University of Miami

After having relocated to Florida to be near his elder daughter, Mary, Dirac spent his last fourteen years of both life and physics research at the University of Miami in Coral Gables, Florida, and Florida State University in Tallahassee, Florida.

In the 1950s in his search for a better QED, Paul Dirac developed the Hamiltonian theory of constraints[83] based on lectures that he delivered at the 1949 International Mathematical Congress in Canada. Dirac[84] had also solved the problem of putting the Schwinger–Tomonaga equation into the Schrödinger representation[85] and given explicit expressions for the scalar meson field (spin zero pion or pseudoscalar meson), the vector meson field (spin one rho meson), and the electromagnetic field (spin one massless boson, photon).

The Hamiltonian of constrained systems is one of Dirac's many masterpieces. It is a powerful generalisation of Hamiltonian theory that remains valid for curved spacetime. The equations for the Hamiltonian involve only six degrees of freedom described by  ,  for each point of the surface on which the state is considered. The   (m = 0, 1, 2, 3) appear in the theory only through the variables  ,   which occur as arbitrary coefficients in the equations of motion. There are four constraints or weak equations for each point of the surface   = constant. Three of them   form the four vector density in the surface. The fourth   is a 3-dimensional scalar density in the surface HL ≈ 0; Hr ≈ 0 (r = 1, 2, 3)

In the late 1950s, he applied the Hamiltonian methods he had developed to cast Einstein's general relativity in Hamiltonian form[86][87] and to bring to a technical completion the quantization problem of gravitation and bring it also closer to the rest of physics according to Salam and DeWitt. In 1959 he also gave an invited talk on "Energy of the Gravitational Field" at the New York Meeting of the American Physical Society.[88] In 1964 he published his Lectures on Quantum Mechanics (London: Academic) which deals with constrained dynamics of nonlinear dynamical systems including quantization of curved spacetime. He also published a paper entitled "Quantization of the Gravitational Field" in the 1967 ICTP/IAEA Trieste Symposium on Contemporary Physics.

From September 1970 to January 1971, Dirac was a visiting professor at Florida State University in Tallahassee. During that time he was offered a permanent position there, which he accepted, becoming a full professor in 1972. Contemporary accounts of his time there describe it as happy except that he apparently found the summer heat oppressive and liked to escape from it to Cambridge.[89]

He would walk about a mile to work each day and was fond of swimming in one of the two nearby lakes (Silver Lake and Lost Lake), and was also more sociable than he had been at the University of Cambridge, where he mostly worked at home apart from giving classes and seminars. At Florida State, he would usually eat lunch with his colleagues before taking a nap.[90]

Dirac published over 60 papers in those last twelve years of his life, including a short book on general relativity.[91] His last paper (1984), entitled "The inadequacies of quantum field theory," contains his final judgment on quantum field theory: "These rules of renormalisation give surprisingly, excessively good agreement with experiments. Most physicists say that these working rules are, therefore, correct. I feel that is not an adequate reason. Just because the results happen to be in agreement with observation does not prove that one's theory is correct." The paper ends with the words: "I have spent many years searching for a Hamiltonian to bring into the theory and have not yet found it. I shall continue to work on it as long as I can and other people, I hope, will follow along such lines."[92]

Students

Amongst his many students[4][93] were Homi J. Bhabha,[2] Fred Hoyle, John Polkinghorne[6] and Freeman Dyson.[94] Polkinghorne recalls that Dirac "was once asked what was his fundamental belief. He strode to a blackboard and wrote that the laws of nature should be expressed in beautiful equations."[95]

Honours

Dirac shared the 1933 Nobel Prize for physics with Erwin Schrödinger "for the discovery of new productive forms of atomic theory".[11] Dirac was also awarded the Royal Medal in 1939 and both the Copley Medal and the Max Planck Medal in 1952. He was elected a Fellow of the Royal Society in 1930, [9] a member of the American Philosophical Society in 1938,[96] an Honorary Fellow of the American Physical Society in 1948, a member of the United States National Academy of Sciences in 1949,[97] a member of the American Academy of Arts and Sciences in 1950,[98] and an Honorary Fellow of the Institute of Physics, London in 1971. He received the inaugural J. Robert Oppenheimer Memorial Prize in 1969.[99][100] Dirac became a member of the Order of Merit in 1973, having previously turned down a knighthood as he did not want to be addressed by his first name.[49][101]

Death

 
The tombstone of Dirac and his wife in Roselawn Cemetery, Tallahassee, Florida. Their daughter Mary Elizabeth Dirac, who died 20 January 2007, is buried next to them.
 
The commemorative marker in Westminster Abbey.
 
Dirac (front row 3rd from left), next to Éamon de Valera (front row 4th from left), Erwin Schrödinger (front row 2nd from right) at Dublin Institute for Advanced Studies in 1942.
 
The 1927 Solvay Conference in Brussels, a gathering of the world's top physicists. Dirac is in the center of the middle row, seated behind Albert Einstein.

In 1984, Dirac died in Tallahassee, Florida, and was buried at Tallahassee's Roselawn Cemetery.[102] Dirac's childhood home in Bishopston, Bristol is commemorated with a blue plaque,[103] and the nearby Dirac Road is named in recognition of his links with the city of Bristol. A commemorative stone was erected in a garden in Saint-Maurice, Switzerland, the town of origin of his father's family, on 1 August 1991. On 13 November 1995 a commemorative marker, made from Burlington green slate and inscribed with the Dirac equation, was unveiled in Westminster Abbey.[102][104] The Dean of Westminster, Edward Carpenter, had initially refused permission for the memorial, thinking Dirac to be anti-Christian, but was eventually (over a five-year period) persuaded to relent.[105]

Legacy

In 1975, Dirac gave a series of five lectures at the University of New South Wales which were subsequently published as a book, Directions in Physics (1978). He donated the royalties from this book to the university for the establishment of the Dirac Lecture Series. The Silver Dirac Medal for the Advancement of Theoretical Physics is awarded by the University of New South Wales to commemorate the lecture.[106]

Immediately after his death, two organizations of professional physicists established annual awards in Dirac's memory. The Institute of Physics, the United Kingdom's professional body for physicists, awards the Paul Dirac Medal for "outstanding contributions to theoretical (including mathematical and computational) physics".[107] The first three recipients were Stephen Hawking (1987), John Stewart Bell (1988), and Roger Penrose (1989). The International Centre for Theoretical Physics awards the Dirac Medal of the ICTP each year on Dirac's birthday (8 August).[108]

The Dirac-Hellman Award at Florida State University was endowed by Bruce P. Hellman in 1997 to reward outstanding work in theoretical physics by FSU researchers.[109] The Paul A.M. Dirac Science Library at Florida State University, which Manci opened in December 1989,[110] is named in his honour, and his papers are held there.[111] Outside is a statue of him by Gabriella Bollobás.[112] The street on which the National High Magnetic Field Laboratory in Innovation Park of Tallahassee, Florida, is located is named Paul Dirac Drive. As well as in his hometown of Bristol, there is also a road named after him, Dirac Place, in Didcot, Oxfordshire.[113]

The BBC named a video codec, Dirac, in his honour. An asteroid discovered in 1983 was named after Dirac.[114] The Distributed Research utilising Advanced Computing (DiRAC) and Dirac software are named in his honour.

Publications

  • The Principles of Quantum Mechanics (1930): This book summarises the ideas of quantum mechanics using the modern formalism that was largely developed by Dirac himself. Towards the end of the book, he also discusses the relativistic theory of the electron (the Dirac equation), which was also pioneered by him. This work does not refer to any other writings then available on quantum mechanics.
  • Lectures on Quantum Mechanics (1966): Much of this book deals with quantum mechanics in curved space-time.
  • Lectures on Quantum Field Theory (1966): This book lays down the foundations of quantum field theory using the Hamiltonian formalism.
  • Spinors in Hilbert Space (1974): This book based on lectures given in 1969 at the University of Miami, Coral Gables, Florida, USA, deals with the basic aspects of spinors starting with a real Hilbert space formalism. Dirac concludes with the prophetic words "We have boson variables appearing automatically in a theory that starts with only fermion variables, provided the number of fermion variables is infinite. There must be such boson variables connected with electrons..."
  • General Theory of Relativity (1975): This 69-page work summarises Einstein's general theory of relativity.

References

Citations

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General sources

Further reading

  • Brown, Helen (24 January 2009). . The Daily Telegraph (Review). p. 20. Archived from the original on 2 February 2009. Retrieved 11 April 2011..
  • Gilder, Louisa (13 September 2009). "Quantum Leap – Review of 'The Strangest Man: The Hidden Life of Paul Dirac by Graham Farmelo'". The New York Times. Retrieved 11 April 2011. Review.
  • Mukunda, N. (1987) "The life and work of P.A.M. Dirac", pages 260 to 282 in Recent Developments in Theoretical Physics, World Scientific MR935624

External links

 
Wikimedia Commons has media related to:
Paul Dirac (category)
 
Wikiquote has quotations related to Paul Dirac.
  • Oral history interview transcript with P. A. M. Dirac on 1 April 1962, American Institute of Physics, Niels Bohr Library & Archives - Session I
  • Oral history interview transcript with P. A. M. Dirac on 6 May 1963, American Institute of Physics, Niels Bohr Library & Archives - Session II
  • Oral history interview transcript with P. A. M. Dirac on 7 Mary 1963, American Institute of Physics, Niels Bohr Library & Archives - Session III
  • Oral history interview transcript with P. A. M. Dirac on 10 May 1963, American Institute of Physics, Niels Bohr Library & Archives - Session IV
  • Oral history interview transcript with P. A. M. Dirac on 14 May 1963, American Institute of Physics, Niels Bohr Library & Archives - V
  • Free online access to Dirac's classic 1920s papers from Royal Society's Proceedings A
  • The Paul Dirac Collection at Florida State University
  • The Papers of Professor Paul Dirac at Churchill Archives Centre

May 19, 2023
paul, dirac, dirac, redirects, here, other, uses, dirac, disambiguation, paul, adrien, maurice, dirac, august, 1902, october, 1984, english, theoretical, physicist, considered, founders, quantum, mechanics, quantum, electrodynamics, lucasian, professor, mathem. Dirac redirects here For other uses see Dirac disambiguation Paul Adrien Maurice Dirac OM FRS 9 d ɪ ˈ r ae k 8 August 1902 20 October 1984 was an English theoretical physicist who is considered to be one of the founders of quantum mechanics and quantum electrodynamics 10 He was the Lucasian Professor of Mathematics at the University of Cambridge a professor of physics at Florida State University and the University of Miami and a 1933 Nobel Prize in Physics recipient Paul DiracOM FRSDirac photographed in 1933BornPaul Adrien Maurice Dirac 1902 08 08 8 August 1902Bristol EnglandDied20 October 1984 1984 10 20 aged 82 Tallahassee Florida U S NationalityBritishAlma materUniversity of Bristol University of CambridgeKnown for Dirac adjoint Dirac algebra Dirac bracket Dirac comb Dirac Coulomb Breit Equation Dirac constant Dirac delta function Dirac equation Dirac fermion Dirac field Dirac gauge Dirac hole theory Dirac large numbers hypothesis Dirac matrices Dirac measure Dirac membrane Dirac monopole Dirac notation Dirac operator Dirac picture Dirac sea Dirac spectrum Dirac spinor Dirac string Dirac s string trick Dirac von Neumann axioms Abraham Lorentz Dirac force Antiparticles Canonical quantisation Canonical quantum gravity Exchange interaction First class constraint Fermi Dirac integral Complete Fermi Dirac integral Fermi Dirac statistics Kapitsa Dirac effect Energy momentum relation Helikon vortex separation process Light front quantization Mathematical formulation of quantum mechanics Negative probability Path integral formulation Primary constraint Quantum electrodynamics Singleton field Spin magnetic moment Time variation of fundamental constants Transformation theory Vacuum polarization Virtual particle List of things named after Paul DiracSpouseMargit Wigner m 1937 wbr Children2AwardsNobel Prize in Physics 1933 Royal Medal 1939 Copley Medal 1952 Max Planck Medal 1952 Fellow of the Royal Society 1930 1 Scientific careerFieldsTheoretical physicsInstitutionsUniversity of Cambridge University of Miami Florida State UniversityThesisQuantum mechanics 1926 Doctoral advisorRalph FowlerDoctoral studentsHomi J Bhabha 2 Harish Chandra 3 Dennis Sciama Fred Hoyle 4 Behram Kursunoglu 5 John Polkinghorne 6 InfluencesJohn Stuart Mill 7 8 Portrait of Paul Dirac by Clara Ewald 1939 Dirac made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics Among other discoveries he formulated the Dirac equation which describes the behaviour of fermions and predicted the existence of antimatter Dirac shared the 1933 Nobel Prize in Physics with Erwin Schrodinger for the discovery of new productive forms of atomic theory 11 He also made significant contributions to the reconciliation of general relativity with quantum mechanics Dirac was regarded by his friends and colleagues as unusual in character In a 1926 letter to Paul Ehrenfest Albert Einstein wrote of a Dirac paper I am toiling over Dirac This balancing on the dizzying path between genius and madness is awful In another letter concerning the Compton effect he wrote I don t understand the details of Dirac at all 12 Contents 1 Personal life 1 1 Early years 1 2 Education 1 3 Family 1 4 Personality 1 5 Views on religion 2 Career 2 1 Quantum theory 2 2 The Dirac equation 2 3 Magnetic monopoles 2 4 Gravity 2 5 University of Cambridge 2 6 Florida State University and University of Miami 2 7 Students 2 8 Honours 2 9 Death 3 Legacy 4 Publications 5 References 5 1 Citations 5 2 General sources 6 Further reading 7 External linksPersonal lifeEarly years Paul Adrien Maurice Dirac was born at his parents home in Bristol England on 8 August 1902 13 and grew up in the Bishopston area of the city 14 His father Charles Adrien Ladislas Dirac was an immigrant from Saint Maurice Switzerland who worked in Bristol as a French teacher His mother Florence Hannah Dirac nee Holten was born to a Cornish Methodist family in Liskeard Cornwall 15 16 She was named after Florence Nightingale by her father a ship s captain who had met Nightingale while he was a soldier during the Crimean war 17 His mother moved to Bristol as a young woman where she worked as a librarian at the Bristol Central Library despite this she still considered her identity to be Cornish rather than English 18 Paul had a younger sister Beatrice Isabelle Marguerite known as Betty and an older brother Reginald Charles Felix known as Felix 19 20 who died by suicide in March 1925 21 Dirac later recalled My parents were terribly distressed I didn t know they cared so much I never knew that parents were supposed to care for their children but from then on I knew 22 Charles and the children were officially Swiss nationals until they became naturalised on 22 October 1919 23 Dirac s father was strict and authoritarian although he disapproved of corporal punishment 24 Dirac had a strained relationship with his father so much so that after his father s death Dirac wrote I feel much freer now and I am my own man Charles forced his children to speak to him only in French so that they might learn the language When Dirac found that he could not express what he wanted to say in French he chose to remain silent 25 26 Education Dirac was educated first at Bishop Road Primary School 27 and then at the all boys Merchant Venturers Technical College later Cotham School where his father was a French teacher 28 The school was an institution attached to the University of Bristol which shared grounds and staff 29 It emphasised technical subjects like bricklaying shoemaking and metalwork and modern languages 30 This was unusual at a time when secondary education in Britain was still dedicated largely to the classics and something for which Dirac would later express his gratitude 29 Dirac studied electrical engineering on a City of Bristol University Scholarship at the University of Bristol s engineering faculty which was co located with the Merchant Venturers Technical College 31 Shortly before he completed his degree in 1921 he sat for the entrance examination for St John s College Cambridge He passed and was awarded a 70 scholarship but this fell short of the amount of money required to live and study at Cambridge Despite his having graduated with a first class honours Bachelor of Science degree in engineering the economic climate of the post war depression was such that he was unable to find work as an engineer Instead he took up an offer to study for a Bachelor of Arts degree in mathematics at the University of Bristol free of charge He was permitted to skip the first year of the course owing to his engineering degree 32 In 1923 Dirac graduated once again with first class honours and received a 140 scholarship from the Department of Scientific and Industrial Research 33 Along with his 70 scholarship from St John s College this was enough to live at Cambridge There Dirac pursued his interests in the theory of general relativity an interest he had gained earlier as a student in Bristol and in the nascent field of quantum physics under the supervision of Ralph Fowler 34 From 1925 to 1928 he held an 1851 Research Fellowship from the Royal Commission for the Exhibition of 1851 35 He completed his PhD in June 1926 with the first thesis on quantum mechanics to be submitted anywhere 36 He then continued his research in Copenhagen and Gottingen 35 In the spring of 1929 he was a visiting professor at the University of Wisconsin Madison 37 38 Family Paul and Manci Dirac in Copenhagen July 1963 In 1937 Dirac married 39 Margit Wigner a sister of physicist Eugene Wigner 40 and a divorcee 41 Dirac raised Margit s two children Judith and Gabriel as if they were his own 42 Paul and Margit Dirac also had two daughters together Mary Elizabeth and Florence Monica 43 Margit known as Manci had visited her brother in 1934 in Princeton New Jersey from their native Hungary and while at dinner at the Annex Restaurant met the lonely looking man at the next table This account from a Korean physicist Y S Kim who met and was influenced by Dirac also says It is quite fortunate for the physics community that Manci took good care of our respected Paul A M Dirac Dirac published eleven papers during the period 1939 46 Dirac was able to maintain his normal research productivity only because Manci was in charge of everything else 44 Personality Dirac was known among his colleagues for his precise and taciturn nature His colleagues in Cambridge jokingly defined a unit called a dirac which was one word per hour 45 When Niels Bohr complained that he did not know how to finish a sentence in a scientific article he was writing Dirac replied I was taught at school never to start a sentence without knowing the end of it 46 He criticised the physicist J Robert Oppenheimer s interest in poetry The aim of science is to make difficult things understandable in a simpler way the aim of poetry is to state simple things in an incomprehensible way The two are incompatible 47 Dirac himself wrote in his diary during his postgraduate years that he concentrated solely on his research and stopped only on Sunday when he took long strolls alone 48 An anecdote recounted in a review of the 2009 biography tells of Werner Heisenberg and Dirac sailing on an ocean liner to a conference in Japan in August 1929 Both still in their twenties and unmarried they made an odd couple Heisenberg was a ladies man who constantly flirted and danced while Dirac an Edwardian geek as biographer Graham Farmelo puts it suffered agonies if forced into any kind of socializing or small talk Why do you dance Dirac asked his companion When there are nice girls it is a pleasure Heisenberg replied Dirac pondered this notion then blurted out But Heisenberg how do you know beforehand that the girls are nice 49 Margit Dirac told both George Gamow and Anton Capri in the 1960s that her husband had said to a house visitor Allow me to present Wigner s sister who is now my wife 50 51 Another story told of Dirac is that when he first met the young Richard Feynman at a conference he said after a long silence I have an equation Do you have one too 52 After he presented a lecture at a conference one colleague raised his hand and said I don t understand the equation on the top right hand corner of the blackboard After a long silence the moderator asked Dirac if he wanted to answer the question to which Dirac replied That was not a question it was a comment 53 54 Dirac was also noted for his personal modesty He called the equation for the time evolution of a quantum mechanical operator which he was the first to write down the Heisenberg equation of motion Most physicists speak of Fermi Dirac statistics for half integer spin particles and Bose Einstein statistics for integer spin particles While lecturing later in life Dirac always insisted on calling the former Fermi statistics He referred to the latter as Bose statistics for reasons he explained of symmetry 55 Views on religion Heisenberg recollected a conversation among young participants at the 1927 Solvay Conference about Einstein and Planck s views on religion between Wolfgang Pauli Heisenberg and Dirac Dirac s contribution was a criticism of the political purpose of religion which Bohr regarded as quite lucid when hearing it from Heisenberg later 56 Among other things Dirac said I cannot understand why we idle discussing religion If we are honest and scientists have to be we must admit that religion is a jumble of false assertions with no basis in reality The very idea of God is a product of the human imagination It is quite understandable why primitive people who were so much more exposed to the overpowering forces of nature than we are today should have personified these forces in fear and trembling But nowadays when we understand so many natural processes we have no need for such solutions I can t for the life of me see how the postulate of an Almighty God helps us in any way What I do see is that this assumption leads to such unproductive questions as to why God allows so much misery and injustice the exploitation of the poor by the rich and all the other horrors He might have prevented If religion is still being taught it is by no means because its ideas still convince us but simply because some of us want to keep the lower classes quiet Quiet people are much easier to govern than clamorous and dissatisfied ones They are also much easier to exploit Religion is a kind of opium that allows a nation to lull itself into wishful dreams and so forget the injustices that are being perpetrated against the people Hence the close alliance between those two great political forces the State and the Church Both need the illusion that a kindly God rewards in heaven if not on earth all those who have not risen up against injustice who have done their duty quietly and uncomplainingly That is precisely why the honest assertion that God is a mere product of the human imagination is branded as the worst of all mortal sins 57 Heisenberg s view was tolerant Pauli raised as a Catholic had kept silent after some initial remarks but when finally he was asked for his opinion said Well our friend Dirac has got a religion and its guiding principle is There is no God and Paul Dirac is His prophet Everybody including Dirac burst into laughter 58 59 Later in life Dirac s views towards the idea of God were less acerbic As an author of an article appearing in the May 1963 edition of Scientific American Dirac wrote It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power needing quite a high standard of mathematics for one to understand it You may wonder Why is nature constructed along these lines One can only answer that our present knowledge seems to show that nature is so constructed We simply have to accept it One could perhaps describe the situation by saying that God is a mathematician of a very high order and He used very advanced mathematics in constructing the universe Our feeble attempts at mathematics enable us to understand a bit of the universe and as we proceed to develop higher and higher mathematics we can hope to understand the universe better 60 In 1971 at a conference meeting Dirac expressed his views on the existence of God 61 Dirac explained that the existence of God could be justified only if an improbable event were to have taken place in the past It could be that it is extremely difficult to start life It might be that it is so difficult to start a life that it has happened only once among all the planets Let us consider just as a conjecture that the chance of life starting when we have got suitable physical conditions is 10 100 I don t have any logical reason for proposing this figure I just want you to consider it as a possibility Under those conditions it is almost certain that life would not have started And I feel that under those conditions it will be necessary to assume the existence of a god to start off life I would like therefore to set up this connection between the existence of a god and the physical laws if physical laws are such that to start off life involves an excessively small chance so that it will not be reasonable to suppose that life would have started just by blind chance then there must be a god and such a god would probably be showing his influence in the quantum jumps which are taking place later on On the other hand if life can start very easily and does not need any divine influence then I will say that there is no god 62 Dirac did not commit himself to any definite view but he described the possibilities for scientifically answering the question of God 62 CareerDirac established the most general theory of quantum mechanics and discovered the relativistic equation for the electron which now bears his name The remarkable notion of an antiparticle to each fermion particle e g the positron as antiparticle to the electron stems from his equation He was the first to develop quantum field theory which underlies all theoretical work on sub atomic or elementary particles today work that is fundamental to our understanding of the forces of nature He proposed and investigated the concept of a magnetic monopole an object not yet known empirically as a means of bringing even greater symmetry to James Clerk Maxwell s equations of electromagnetism Quantum theory Dirac s first step into a new quantum theory was taken late in September 1925 Ralph Fowler his research supervisor had received a proof copy of an exploratory paper by Werner Heisenberg in the framework of the old quantum theory of Bohr and Sommerfeld Heisenberg leaned heavily on Bohr s correspondence principle but changed the equations so that they involved directly observable quantities leading to the matrix formulation of quantum mechanics Fowler sent Heisenberg s paper on to Dirac who was on vacation in Bristol asking him to look into this paper carefully 63 Dirac s attention was drawn to a mysterious mathematical relationship at first sight unintelligible that Heisenberg had established Several weeks later back in Cambridge Dirac suddenly recognised that this mathematical form had the same structure as the Poisson brackets that occur in the classical dynamics of particle motion 63 At the time his memory of Poisson brackets was rather vague but he found E T Whittaker s Analytical Dynamics of Particles and Rigid Bodies illuminating 64 From his new understanding he developed a quantum theory based on non commuting dynamical variables This led him to the most profound and significant general formulation of quantum mechanics to date 65 Dirac s formulation allowed him to obtain the quantisation rules in a novel and more illuminating manner For this work 66 published in 1926 Dirac received a PhD from Cambridge This formed the basis for Fermi Dirac statistics that applies to systems consisting of many identical spin 1 2 particles i e that obey the Pauli exclusion principle e g electrons in solids and liquids and importantly to the field of conduction in semi conductors Dirac was famously not bothered by issues of interpretation in quantum theory In fact in a paper published in a book in his honour he wrote The interpretation of quantum mechanics has been dealt with by many authors and I do not want to discuss it here I want to deal with more fundamental things 67 The Dirac equation Further information Dirac equation In 1928 building on 2 2 spin matrices which he purported to have discovered independently of Wolfgang Pauli s work on non relativistic spin systems Dirac told Abraham Pais I believe I got these matrices independently of Pauli and possibly Pauli got these independently of me 68 he proposed the Dirac equation as a relativistic equation of motion for the wave function of the electron 69 This work led Dirac to predict the existence of the positron the electron s antiparticle which he interpreted in terms of what came to be called the Dirac sea 70 The positron was observed by Carl Anderson in 1932 Dirac s equation also contributed to explaining the origin of quantum spin as a relativistic phenomenon The necessity of fermions matter being created and destroyed in Enrico Fermi s 1934 theory of beta decay led to a reinterpretation of Dirac s equation as a classical field equation for any point particle of spin ħ 2 itself subject to quantisation conditions involving anti commutators Thus reinterpreted in 1934 by Werner Heisenberg as a quantum field equation accurately describing all elementary matter particles today quarks and leptons this Dirac field equation is as central to theoretical physics as the Maxwell Yang Mills and Einstein field equations Dirac is regarded as the founder of quantum electrodynamics being the first to use that term He also introduced the idea of vacuum polarisation in the early 1930s This work was key to the development of quantum mechanics by the next generation of theorists in particular Schwinger Feynman Sin Itiro Tomonaga and Dyson in their formulation of quantum electrodynamics Dirac s The Principles of Quantum Mechanics published in 1930 is a landmark in the history of science It quickly became one of the standard textbooks on the subject and is still used today In that book Dirac incorporated the previous work of Werner Heisenberg on matrix mechanics and of Erwin Schrodinger on wave mechanics into a single mathematical formalism that associates measurable quantities to operators acting on the Hilbert space of vectors that describe the state of a physical system The book also introduced the Dirac delta function Following his 1939 article 71 he also included the bra ket notation in the third edition of his book 72 thereby contributing to its universal use nowadays Magnetic monopoles In 1931 Dirac proposed that the existence of a single magnetic monopole in the universe would suffice to explain the quantisation of electrical charge 73 In 1975 74 1982 75 and 2009 76 77 78 intriguing results suggested the possible detection of magnetic monopoles but there is to date no direct evidence for their existence see also Searches for magnetic monopoles Gravity He quantized the gravitational field and developed a general theory of the quantum field with dynamical constraints which forms the basis of the gauge theories and superstring theories of today 79 The influence and importance of Dirac s work have increased with the decades and physicists use daily the concepts and equations that he developed University of Cambridge Dirac was the Lucasian Professor of Mathematics at the University of Cambridge from 1932 to 1969 In 1937 he proposed a speculative cosmological model based on the so called large numbers hypothesis During World War II he conducted important theoretical and experimental research on uranium enrichment by gas centrifuge 80 Dirac s quantum electrodynamics QED made predictions that were more often than not infinite and therefore unacceptable A workaround known as renormalisation was developed but Dirac never accepted this I must say that I am very dissatisfied with the situation he said in 1975 because this so called good theory does involve neglecting infinities which appear in its equations neglecting them in an arbitrary way This is just not sensible mathematics Sensible mathematics involves neglecting a quantity when it is small not neglecting it just because it is infinitely great and you do not want it 81 His refusal to accept renormalisation resulted in his work on the subject moving increasingly out of the mainstream However from his once rejected notes he managed to work on putting quantum electrodynamics on logical foundations based on Hamiltonian formalism that he formulated He found a rather novel way of deriving the anomalous magnetic moment Schwinger term and also the Lamb shift afresh in 1963 using the Heisenberg picture and without using the joining method used by Weisskopf and French and by the two pioneers of modern QED Schwinger and Feynman That was two years before the Tomonaga Schwinger Feynman QED was given formal recognition by an award of the Nobel Prize for physics Weisskopf and French FW were the first to obtain the correct result for the Lamb shift and the anomalous magnetic moment of the electron At first FW results did not agree with the incorrect but independent results of Feynman and Schwinger 82 The 1963 1964 lectures Dirac gave on quantum field theory at Yeshiva University were published in 1966 as the Belfer Graduate School of Science Monograph Series Number 3 Florida State University and University of Miami After having relocated to Florida to be near his elder daughter Mary Dirac spent his last fourteen years of both life and physics research at the University of Miami in Coral Gables Florida and Florida State University in Tallahassee Florida In the 1950s in his search for a better QED Paul Dirac developed the Hamiltonian theory of constraints 83 based on lectures that he delivered at the 1949 International Mathematical Congress in Canada Dirac 84 had also solved the problem of putting the Schwinger Tomonaga equation into the Schrodinger representation 85 and given explicit expressions for the scalar meson field spin zero pion or pseudoscalar meson the vector meson field spin one rho meson and the electromagnetic field spin one massless boson photon The Hamiltonian of constrained systems is one of Dirac s many masterpieces It is a powerful generalisation of Hamiltonian theory that remains valid for curved spacetime The equations for the Hamiltonian involve only six degrees of freedom described by g r s displaystyle g rs p r s displaystyle p rs for each point of the surface on which the state is considered The g m 0 displaystyle g m0 m 0 1 2 3 appear in the theory only through the variables g r 0 displaystyle g r0 g 00 1 2 displaystyle g 00 1 2 which occur as arbitrary coefficients in the equations of motion There are four constraints or weak equations for each point of the surface x 0 displaystyle x 0 constant Three of them H r displaystyle H r form the four vector density in the surface The fourth H L displaystyle H L is a 3 dimensional scalar density in the surface HL 0 Hr 0 r 1 2 3 In the late 1950s he applied the Hamiltonian methods he had developed to cast Einstein s general relativity in Hamiltonian form 86 87 and to bring to a technical completion the quantization problem of gravitation and bring it also closer to the rest of physics according to Salam and DeWitt In 1959 he also gave an invited talk on Energy of the Gravitational Field at the New York Meeting of the American Physical Society 88 In 1964 he published his Lectures on Quantum Mechanics London Academic which deals with constrained dynamics of nonlinear dynamical systems including quantization of curved spacetime He also published a paper entitled Quantization of the Gravitational Field in the 1967 ICTP IAEA Trieste Symposium on Contemporary Physics From September 1970 to January 1971 Dirac was a visiting professor at Florida State University in Tallahassee During that time he was offered a permanent position there which he accepted becoming a full professor in 1972 Contemporary accounts of his time there describe it as happy except that he apparently found the summer heat oppressive and liked to escape from it to Cambridge 89 He would walk about a mile to work each day and was fond of swimming in one of the two nearby lakes Silver Lake and Lost Lake and was also more sociable than he had been at the University of Cambridge where he mostly worked at home apart from giving classes and seminars At Florida State he would usually eat lunch with his colleagues before taking a nap 90 Dirac published over 60 papers in those last twelve years of his life including a short book on general relativity 91 His last paper 1984 entitled The inadequacies of quantum field theory contains his final judgment on quantum field theory These rules of renormalisation give surprisingly excessively good agreement with experiments Most physicists say that these working rules are therefore correct I feel that is not an adequate reason Just because the results happen to be in agreement with observation does not prove that one s theory is correct The paper ends with the words I have spent many years searching for a Hamiltonian to bring into the theory and have not yet found it I shall continue to work on it as long as I can and other people I hope will follow along such lines 92 Students Amongst his many students 4 93 were Homi J Bhabha 2 Fred Hoyle John Polkinghorne 6 and Freeman Dyson 94 Polkinghorne recalls that Dirac was once asked what was his fundamental belief He strode to a blackboard and wrote that the laws of nature should be expressed in beautiful equations 95 Honours Dirac shared the 1933 Nobel Prize for physics with Erwin Schrodinger for the discovery of new productive forms of atomic theory 11 Dirac was also awarded the Royal Medal in 1939 and both the Copley Medal and the Max Planck Medal in 1952 He was elected a Fellow of the Royal Society in 1930 9 a member of the American Philosophical Society in 1938 96 an Honorary Fellow of the American Physical Society in 1948 a member of the United States National Academy of Sciences in 1949 97 a member of the American Academy of Arts and Sciences in 1950 98 and an Honorary Fellow of the Institute of Physics London in 1971 He received the inaugural J Robert Oppenheimer Memorial Prize in 1969 99 100 Dirac became a member of the Order of Merit in 1973 having previously turned down a knighthood as he did not want to be addressed by his first name 49 101 Death The tombstone of Dirac and his wife in Roselawn Cemetery Tallahassee Florida Their daughter Mary Elizabeth Dirac who died 20 January 2007 is buried next to them The commemorative marker in Westminster Abbey Dirac front row 3rd from left next to Eamon de Valera front row 4th from left Erwin Schrodinger front row 2nd from right at Dublin Institute for Advanced Studies in 1942 The 1927 Solvay Conference in Brussels a gathering of the world s top physicists Dirac is in the center of the middle row seated behind Albert Einstein In 1984 Dirac died in Tallahassee Florida and was buried at Tallahassee s Roselawn Cemetery 102 Dirac s childhood home in Bishopston Bristol is commemorated with a blue plaque 103 and the nearby Dirac Road is named in recognition of his links with the city of Bristol A commemorative stone was erected in a garden in Saint Maurice Switzerland the town of origin of his father s family on 1 August 1991 On 13 November 1995 a commemorative marker made from Burlington green slate and inscribed with the Dirac equation was unveiled in Westminster Abbey 102 104 The Dean of Westminster Edward Carpenter had initially refused permission for the memorial thinking Dirac to be anti Christian but was eventually over a five year period persuaded to relent 105 LegacyIn 1975 Dirac gave a series of five lectures at the University of New South Wales which were subsequently published as a book Directions in Physics 1978 He donated the royalties from this book to the university for the establishment of the Dirac Lecture Series The Silver Dirac Medal for the Advancement of Theoretical Physics is awarded by the University of New South Wales to commemorate the lecture 106 Immediately after his death two organizations of professional physicists established annual awards in Dirac s memory The Institute of Physics the United Kingdom s professional body for physicists awards the Paul Dirac Medal for outstanding contributions to theoretical including mathematical and computational physics 107 The first three recipients were Stephen Hawking 1987 John Stewart Bell 1988 and Roger Penrose 1989 The International Centre for Theoretical Physics awards the Dirac Medal of the ICTP each year on Dirac s birthday 8 August 108 The Dirac Hellman Award at Florida State University was endowed by Bruce P Hellman in 1997 to reward outstanding work in theoretical physics by FSU researchers 109 The Paul A M Dirac Science Library at Florida State University which Manci opened in December 1989 110 is named in his honour and his papers are held there 111 Outside is a statue of him by Gabriella Bollobas 112 The street on which the National High Magnetic Field Laboratory in Innovation Park of Tallahassee Florida is located is named Paul Dirac Drive As well as in his hometown of Bristol there is also a road named after him Dirac Place in Didcot Oxfordshire 113 The BBC named a video codec Dirac in his honour An asteroid discovered in 1983 was named after Dirac 114 The Distributed Research utilising Advanced Computing DiRAC and Dirac software are named in his honour PublicationsThe Principles of Quantum Mechanics 1930 This book summarises the ideas of quantum mechanics using the modern formalism that was largely developed by Dirac himself Towards the end of the book he also discusses the relativistic theory of the electron the Dirac equation which was also pioneered by him This work does not refer to any other writings then available on quantum mechanics Lectures on Quantum Mechanics 1966 Much of this book deals with quantum mechanics in curved space time Lectures on Quantum Field Theory 1966 This book lays down the foundations of quantum field theory using the Hamiltonian formalism Spinors in Hilbert Space 1974 This book based on lectures given in 1969 at the University of Miami Coral Gables Florida USA deals with the basic aspects of spinors starting with a real Hilbert space formalism Dirac concludes with the prophetic words We have boson variables appearing automatically in a theory that starts with only fermion variables provided the number of fermion variables is infinite There must be such boson variables connected with electrons General Theory of Relativity 1975 This 69 page work summarises Einstein s general theory of relativity ReferencesCitations Nobel Bio Nobel Foundation Retrieved 27 January 2014 a b Bhabha Homi Jehangir 1935 On cosmic radiation and the creation and annihilation of positrons and electrons PhD thesis University of Cambridge EThOS uk bl ethos 727546 Harish Chandra School of Mathematics and Statistics University of St Andrews a b Paul Dirac at the Mathematics Genealogy Project DeWitt C M amp Rickles D eds The Role of Gravitation in Physics Report from the 1957 Chapel Hill Conference Berlin Edition Open Access 2011 p 30 permanent dead link a b Polkinghorne John Charlton 1955 Contributions to quantum field theory PhD thesis University of Cambridge EThOS uk bl ethos 727138 Farmelo 2009 Cassidy David C 2010 Graham Farmelo The Strangest Man The Hidden Life of Paul Dirac Mystic of the Atom Isis 101 3 661 doi 10 1086 657209 Farmelo also discusses across several chapters the influences of John Stuart Mill a b Dalitz R H Peierls R 1986 Paul Adrien Maurice Dirac 8 August 1902 20 October 1984 Biographical Memoirs of Fellows of the Royal Society 32 137 185 doi 10 1098 rsbm 1986 0006 JSTOR 770111 Mukunda N Images of Twentieth Century Physics Bangalore Jawaharlal Nehru Centre for Advanced Scientific Research 2000 p 9 a b The Nobel Prize in Physics 1933 The Nobel Foundation Retrieved 4 April 2013 Kragh 1990 p 82 Dirac verstehe ich im Einzelnen uberhaupt nicht Compton Effekt Farmelo 2009 p 10 Farmelo 2009 pp 18 19 Paul Dirac a genius in the history of physics Cern Courier 15 August 2002 Retrieved 4 February 2022 Farmelo 2009 pp 8 441 Farmelo 2009 pp 8 Farmelo 2009 pp 441 Kragh 1990 p 1 Farmelo 2009 pp 10 11 Farmelo 2009 pp 77 78 Farmelo 2009 p 79 Farmelo 2009 p 34 Farmelo 2009 p 22 Mehra 1972 p 17 Kragh 1990 p 2 Farmelo 2009 pp 13 17 Farmelo 2009 pp 20 21 a b Mehra 1972 p 18 Farmelo 2009 p 23 Farmelo 2009 p 28 Farmelo 2009 pp 46 47 Farmelo 2009 p 53 Farmelo 2009 pp 52 53 a b 1851 Royal Commission Archives Farmelo 2009 p 101 Kursunoglu Behram N Wigner Eugene Paul eds 1990 Paul Adrien Maurice Dirac Reminiscences about a Great Physicist Cambridge University Press p 132 ISBN 0521386888 Retrieved 30 September 2020 Paul Adrien Maurice Dirac University of Wisconsin Madison Retrieved 30 September 2020 Farmelo 2009 p 284 Farmelo 2009 p 253 Farmelo 2009 p 256 Farmelo 2009 p 288 Farmelo 2009 pp 305 323 Kim Young Suh 1995 Wigner s Sisters Archived from the original on 3 March 2008 Farmelo 2009 p 89 Paul Adrien Maurice Dirac University of St Andrews Retrieved 4 April 2013 Mehra 1972 pp 17 59 Kragh 1990 p 17 a b McKie Rob 1 February 2009 Anti matter and madness The Guardian Retrieved 4 April 2013 Gamow 1966 p 121 Capri 2007 p 148 Zee 2010 p 105 Raymo Chet 17 October 2009 A quantum leap into oddness The Globe and Mail Review of Farmelo s The Strangest Man Farmelo 2009 pp 161 162 who attributes the story to Niels Bohr Mehra Jagdish Rechenberg Helmut 2001 The Historical Development of Quantum Theory Springer Science amp Business Media p 746 ISBN 9780387951805 Pais A Niels Bohr s Times In Physics Philosophy and Polity Oxford Clarendon Press 1991 p 320 Heisenberg 1971 pp 85 86 Heisenberg 1971 p 87 Farmelo 2009 p 138 who says this was an old joke pointing out a Punch footnote in the 1850s that There is no God and Harriet Martineau is her prophet Dirac Paul May 1963 The Evolution of the Physicist s Picture of Nature Scientific American Retrieved 4 April 2013 Kragh 1990 pp 256 257 a b Kragh 1990 a b Farmelo 2009 pp 83 88 Coutinho S C 1 May 2014 Whittaker s analytical dynamics a biography Archive for History of Exact Sciences 68 3 355 407 doi 10 1007 s00407 013 0133 1 ISSN 1432 0657 S2CID 122266762 Paul Dirac a genius in the history of physics Cern Courier 15 August 2002 Retrieved 13 May 2013 Dirac Paul A M 1926 On the Theory of Quantum Mechanics Proceedings of the Royal Society A 112 762 661 77 Bibcode 1926RSPSA 112 661D doi 10 1098 rspa 1926 0133 JSTOR 94692 Dirac The inadequacies of quantum field theory in B N Kursunoglu amp E P Wigner eds Paul Adrien Maurice Dirac Cambridge Cambridge University Press 1987 p 194 Behram N Kursunoglu Eugene Paul Wigner eds Reminiscences about a Great Physicist Cambridge University Press p 98 Dirac P A M 1 February 1928 The Quantum Theory of the Electron Proceedings of the Royal Society of London A 117 778 610 24 Bibcode 1928RSPSA 117 610D doi 10 1098 rspa 1928 0023 Paul Dirac on Nobelprize org with his Nobel Lecture December 12 1933 Theory of Electrons and Positrons P A M Dirac 1939 A New Notation for Quantum Mechanics Proceedings of the Cambridge Philosophical Society 35 3 416 Bibcode 1939PCPS 35 416D doi 10 1017 S0305004100021162 S2CID 121466183 Gieres 2000 Mathematical surprises and Dirac s formalism in quantum mechanics Reports on Progress in Physics 63 12 1893 arXiv quant ph 9907069 Bibcode 2000RPPh 63 1893G doi 10 1088 0034 4885 63 12 201 S2CID 10854218 Dirac P A M 1931 Quantised Singularities in the Electromagnetic Field Proceedings of the Royal Society A 133 821 60 72 Bibcode 1931RSPSA 133 60D doi 10 1098 rspa 1931 0130 P B Price E K Shirk W Z Osborne L S Pinsky 25 August 1975 Evidence for Detection of a Moving Magnetic Monopole Physical Review Letters 35 8 487 90 Bibcode 1975PhRvL 35 487P doi 10 1103 PhysRevLett 35 487 Blas Cabrera 17 May 1982 First Results from a Superconductive Detector for Moving Magnetic Monopoles Physical Review Letters 48 20 1378 81 Bibcode 1982PhRvL 48 1378C doi 10 1103 PhysRevLett 48 1378 S2CID 17169500 Magnetic Monopoles Detected in a Real Magnet for the First Time Science Daily 4 September 2009 Retrieved 13 May 2013 D J P Morris D A Tennant S A Grigera B Klemke C Castelnovo R Moessner C Czternasty M Meissner K C Rule J U Hoffmann K Kiefer S Gerischer D Slobinsky amp R S Perry 3 September 2009 Dirac Strings and Magnetic Monopoles in Spin Ice Dy2Ti2O7 Science 326 5951 411 4 arXiv 1011 1174 Bibcode 2009Sci 326 411M doi 10 1126 science 1178868 PMID 19729617 S2CID 206522398 S T Bramwell S R Giblin S Calder R Aldus D Prabhakaran T Fennell 15 October 2009 Measurement of the charge and current of magnetic monopoles in spin ice Nature 461 7266 956 9 arXiv 0907 0956 Bibcode 2009Natur 461 956B doi 10 1038 nature08500 PMID 19829376 S2CID 4399620 Misha S Quantum Field Theory II Singapore World Scientific 2019 p 287 Kemp R S Gas Centrifuge Theory and Development A Review of US Programs Science and Global Security June 2009 Kragh 1990 p 184 Schweber 1994 Canadian Journal of Mathematics 1950 vol 2 129 1951 vol 3 1 1951 The Hamiltonian Form of Field Dynamics Canad Jour Math vol 3 1 Phillips R J N 1987 Tributes to Dirac p31 London Adam Hilger Proc Roy Soc 1958 A vol 246 333 Dirac P A M 1 May 1959 Fixation of Coordinates in the Hamiltonian Theory of Gravitation Physical Review 114 3 924 Bibcode 1959PhRv 114 924D doi 10 1103 PhysRev 114 924 Retrieved 16 October 2020 Dirac P A M Energy of the Gravitational Field Physical Review Letters Vol 2 Nr 8 20 March 1959 pp 368 371 Paul Dirac Famous Scientists Pais Abraham 2009 Paul Dirac The Man and His Work Cambridge University Press p 27 ISBN 978 0 511 56431 4 OCLC 958553083 via Google Books Baer H A amp Belyaev A eds Proceedings of the Dirac Centennial Symposium Singapore World Scientific 2003 p 3 Pais Abraham 2009 Paul Dirac The Man and His Work Cambridge University Press p 28 ISBN 978 0 511 56431 4 OCLC 958553083 via Google Books O Connor John J Robertson Edmund F Paul Dirac MacTutor History of Mathematics archive University of St Andrews Sandberg L Freeman J Dyson 1923 2020 Scientist and Writer Who Dreamt Among the Stars Dies at 96 IAS 28 February 2020 John Polkinghorne Belief in God in an Age of Science p 2 APS Member History search amphilsoc org Retrieved 16 May 2023 Paul A Dirac www nasonline org Retrieved 16 May 2023 Paul Adrien Maurice Dirac American Academy of Arts amp Sciences 9 February 2023 Retrieved 16 May 2023 Walter Claire 1982 Winners the blue ribbon encyclopedia of awards Facts on File Inc p 438 ISBN 9780871963864 Dirac Receives Miami Center Oppenheimer Memorial Prize Physics Today 22 4 127 April 1969 doi 10 1063 1 3035512 Farmelo 2009 pp 403 404 a b Dirac takes his place next to Isaac Newton Florida State University Archived from the original on 27 April 1997 Retrieved 4 April 2013 Fells M Bristol Plaques Cheltenham The History Press 2016 p 40 Paul Dirac Gisela Dirac Retrieved 4 April 2013 Farmelo 2009 pp 414 415 Dirac Medal awards University of New South Wales Archived from the original on 12 April 2013 Retrieved 4 April 2013 The Dirac Medal Institute of Physics Retrieved 24 November 2007 The Dirac Medal International Centre for Theoretical Physics Retrieved 4 April 2013 Undergraduate Awards Florida State University Archived from the original on 12 April 2013 Retrieved 4 April 2013 Remodelled Dirac Science Library Opened at FSU Graham Farmelo 22 February 2015 Retrieved 12 October 2015 Paul A M Dirac Papers Florida State University Retrieved 18 March 2021 Farmelo 2009 p 417 Dirac Place Didcot OX11 8TL Google Maps 5997 Dirac 1983 TH Jet Propulsion Laboratory Retrieved 9 January 2015 General sources Capri Anton Z 2007 Quips Quotes and Quanta An Anecdotal History of Physics Hackensack New Jersey World Scientific ISBN 978 981 270 919 6 OCLC 214286147 Crease Robert P Mann Charles C 1986 The Second Creation Makers of the Revolution in Twentieth Century Physics New York City Macmillan Publishing ISBN 978 0 02 521440 8 OCLC 13008048 Farmelo Graham 2009 The Strangest Man The Hidden Life of Paul Dirac Quantum Genius London Faber and Faber ISBN 978 0 571 22278 0 Published in the United States as The Strangest Man The Hidden Life of Paul Dirac Mystic of the Atom ISBN 978 0 465 01827 7 Gamow George 1966 Thirty Years That Shook Physics The Story of Quantum Theory Garden City New York Doubleday ISBN 978 0 486 24895 0 OCLC 11970045 Heisenberg Werner 1971 Physics and Beyond Encounters and Conversations New York City Harper amp Row ISBN 978 0 06 131622 7 OCLC 115992 Kragh Helge 1990 Dirac A Scientific Biography Cambridge Cambridge University Press ISBN 978 0 521 38089 8 OCLC 20013981 Mehra Jagdish 1972 The Golden Age of Theoretical Physics P A M Dirac s Scientific Works from 1924 1933 In Wigner Eugene Paul Salam Abdus eds Aspects of Quantum Theory Cambridge University Press pp 17 59 ISBN 978 0 521 08600 4 OCLC 532357 Schweber Silvan S 1994 QED and the men who made it Dyson Feynman Schwinger and Tomonaga Princeton New Jersey Princeton University Press ISBN 978 0 691 03685 4 OCLC 28966591 Zee Anthony 2010 Quantum Field Theory in a Nutshell Princeton New Jersey Princeton University Press ISBN 978 1 4008 3532 4 OCLC 318585662 Further readingBrown Helen 24 January 2009 The Strangest Man The Hidden Life of Paul Dirac by Graham Farmelo review print version The man behind the maths The Daily Telegraph Review p 20 Archived from the original on 2 February 2009 Retrieved 11 April 2011 Gilder Louisa 13 September 2009 Quantum Leap Review of The Strangest Man The Hidden Life of Paul Dirac by Graham Farmelo The New York Times Retrieved 11 April 2011 Review Mukunda N 1987 The life and work of P A M Dirac pages 260 to 282 in Recent Developments in Theoretical Physics World Scientific MR935624External links Wikimedia Commons has media related to Paul Dirac category Wikiquote has quotations related to Paul Dirac Oral history interview transcript with P A M Dirac on 1 April 1962 American Institute of Physics Niels Bohr Library amp Archives Session I Oral history interview transcript with P A M Dirac on 6 May 1963 American Institute of Physics Niels Bohr Library amp Archives Session II Oral history interview transcript with P A M Dirac on 7 Mary 1963 American Institute of Physics Niels Bohr Library amp Archives Session III Oral history interview transcript with P A M Dirac on 10 May 1963 American Institute of Physics Niels Bohr Library amp Archives Session IV Oral history interview transcript with P A M Dirac on 14 May 1963 American Institute of Physics Niels Bohr Library amp Archives V Free online access to Dirac s classic 1920s papers from Royal Society s Proceedings A Annotated bibliography for Paul Dirac from the Alsos Digital Library for Nuclear Issues The Paul Dirac Collection at Florida State University The Papers of Professor Paul Dirac at Churchill Archives Centre Portals Physics History of science Retrieved from https en wikipedia org w index php title Paul Dirac amp oldid 1155404190, wikipedia, wiki, book, books, library,

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