Dirac graduated from theUniversity of Bristol with afirst class honours Bachelor of Science degree in electrical engineering in 1921, and a first class honours Bachelor of Arts degree in mathematics in 1923.[11] Dirac then graduated fromSt John's College, Cambridge with a PhD in physics in 1926, writing the first ever thesis on quantum mechanics.[12]
Dirac made fundamental contributions to the early development of both quantum mechanics andquantum electrodynamics, coining the latter term.[8] Among other discoveries, he formulated theDirac equation in 1928. It connectedspecial relativity and quantum mechanics and predicted the existence ofantimatter.[13][14] The Dirac equation is one of the most important results in physics,[6] regarded by some physicists as the "real seed of modern physics".[15] He wrote a famous paper in 1931,[16] which further predicted the existence of antimatter.[17][18][14] Dirac also contributed greatly to the reconciliation ofgeneral relativity with quantum mechanics. He contributed toFermi–Dirac statistics, which describes the behaviour offermions, particles with half-integerspin. His 1930 monograph,ThePrinciples of Quantum Mechanics, is one of the most influential texts on the subject.[19]
In 1987,Abdus Salam declared that "Dirac was undoubtedly one of the greatest physicists of this or any century ... No man exceptEinstein has had such a decisive influence, in so short a time, on the course of physics in this century."[20] In 1995,Stephen Hawking stated that "Dirac has done more than anyone this century, with the exception of Einstein, to advance physics and change our picture of the universe".[21]Antonino Zichichi asserted that Dirac had a greater impact on modern physics than Einstein,[15] whileStanley Deser remarked that "We all stand on Dirac's shoulders."[22]
Early life
Paul Adrien Maurice Dirac was born on 8 August 1902 at his parents' home inBristol, England,[23] and grew up in theBishopston area of the city.[24] His father, Charles Adrien Ladislas Dirac, was an immigrant fromSaint-Maurice, Switzerland, ofFrench descent,[25] who worked in Bristol as a French teacher. His mother, Florence Hannah Dirac, née Holten, was born to aCornishMethodist family inLiskeard,Cornwall.[26][27] She was named afterFlorence Nightingale by her father, a ship's captain, who had met Nightingale while he was a soldier during theCrimean War.[28] His mother moved to Bristol as a young woman, where she worked as a librarian at theBristol Central Library; despite this she still considered her identity to be Cornish rather than English.[29] Paul had a younger sister, Béatrice Isabelle Marguerite, known as Betty, and an older brother, Reginald Charles Félix, known as Felix,[30][31] who died by suicide in March 1925.[32] 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."[33]
Charles and the children were officially Swiss nationals until they becamenaturalised on 22 October 1919.[34] Dirac's father was strict and authoritarian, although he disapproved of corporal punishment.[35] 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.[36][37]
Education
Dirac was educated first atBishop Road Primary School[38] and then at the all-boysMerchant Venturers' Technical College (laterCotham School), where his father was a French teacher.[39] The school was an institution attached to theUniversity of Bristol, which shared grounds and staff.[40] It emphasised technical subjects like bricklaying, shoemaking and metalwork, and modern languages.[41] 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.[40] One of his peers at Bishop Road School was Archibald Leach, later famous asCary Grant.[42]
Dirac studiedelectrical 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.[43] Shortly before he completed his degree in 1921, he sat for the entrance examination forSt 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 having graduated with afirst class honoursB.Sc. in electrical engineering, the economic climate of thepost-war depression was such that he was unable to find work as an engineer. Instead, he took up an offer to study for aB.A. 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.[44] Under the influence of Peter Fraser, whom Dirac called the best mathematics teacher, he had the most interest inprojective geometry, and began applying it to the geometrical version of relativityHermann Minkowski developed.[45]
In 1937, Dirac married[52] Margit Wigner, the sister of physicistEugene Wigner[53] and a divorcee.[54] Dirac raised Margit's two children, Judith andGabriel, as if they were his own.[55] Paul and Margit Dirac also had two daughters together, Mary Elizabeth and Florence Monica.[56]
Margit, known as Manci, had visited her brother in 1934 inPrinceton, 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".[57]
Dirac was regarded by his friends and colleagues as unusual in character. In a 1926 letter toPaul 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 theCompton effect he wrote, "I don't understand the details of Dirac at all."[58]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.[59] WhenNiels 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."[60] He criticised the physicistJ. 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."[61] Bohr called Dirac "a complete logical genius" and also the "strangest man" who had ever visited his Institute.[62]
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.[63]
An anecdote recounted in a review of the 2009 biography tells ofWerner 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 biographerGraham 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?'"[64]
Margit Dirac told bothGeorge 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."[65][66]
Paul Dirac and Richard Feynman at Jabłonna, Poland. July 1962.
Another story told of Dirac is that when he first met the youngRichard Feynman at a conference, he said after a long silence, "I have an equation. Do you have one too?"[67]
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."[68][69]
Dirac was also noted for his personal modesty. He called the equation for thetime evolution of a quantum-mechanical operator, which he was the first to write down, the "Heisenberg equation of motion". Most physicists speak ofFermi–Dirac statistics for half-integer-spin particles (fermions) andBose–Einstein statistics for integer-spin particles (bosons). 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".[70]
Philosophy of physics
When asked to summarize his philosophy of physics, Dirac wrote "Physical laws should have mathematical beauty."[71]
Dirac was famously not bothered byissues 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."[72]
Views on religion
Werner Heisenberg recollected a conversation among young participants at the 1927Solvay Conference about Einstein andMax Planck's views on religion betweenWolfgang 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.[73] 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.[74][75]
Later in life, in an article mentioning God that appeared in the May 1963 edition ofScientific American, Dirac wrote:
It seems to be one of the fundamental features of nature that fundamentalphysical laws are described in terms of amathematical 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.[76]
In 1971, at a conference meeting, Dirac described the possibilities for scientifically answering the question of God.[77] Dirac explained that
... 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,... 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.[78]
Dirac discovered therelativistic 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 is credited as being the one to createquantum 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, alongside creating quantum electrodynamics and coining the term.[7][9] He proposed and investigated the concept of amagnetic monopole, an object not yet known empirically, as a means of bringing even greater symmetry toJames Clerk Maxwell's equations ofelectromagnetism. Dirac also coined the terms "fermion" (particles with half-integer spin) and "boson" (particles with whole-integer spin).[79]
Throughout his career, Dirac was motivated by the principles ofmathematical beauty,[80] withPeter Goddard stating that "Dirac cited mathematical beauty as the ultimate criterion for selecting the way forward in theoretical physics".[81] Dirac was recognised for being mathematically gifted, as during his time in university, academics had affirmed that Dirac had an "ability of the highest order in mathematical physics",[82] withEbenezer Cunningham stating that Dirac was "quite the most original student I have met in the subject of mathematical physics".[83] Therefore, Dirac was known for his "astounding physical intuition combined with the ability to invent new mathematics to create new physics".[17] During his career, Dirac made numerous important contributions to mathematical subjects, including theDirac delta function,Dirac algebra and theDirac operator.
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 anexploratory paper byWerner Heisenberg in the framework of the old quantum theory of Bohr andSommerfeld. Heisenberg leaned heavily on Bohr's correspondence principle but changed the equations so that they involved directly observable quantities, leading to thematrix 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.[84]
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 thePoisson brackets that occur in theclassical dynamics of particle motion.[84] At the time, his memory of Poisson brackets was rather vague, but he foundE. T. Whittaker'sAnalytical Dynamics of Particles and Rigid Bodies illuminating.[85] From his new understanding, he developed a quantum theory based onnon-commuting dynamical variables. This led him to the most profound and significant general formulation of quantum mechanics to date.[86] His novel formulation usingDirac brackets allowed him to obtain thequantisation rules in anovel and more illuminating manner. For this work,[87] published in 1926, Dirac received a PhD from Cambridge.
Shortly afterWolfgang Pauli proposed hisPauli exclusion principle (that two electrons cannot occupy the same quantum energy level),Enrico Fermi and Dirac[87] both realized the principle would dramatically alter the statistical mechanics of electron systems. This work became the basis forFermi–Dirac statistics.[88]: 488 This applies to systems consisting of many identicalspin-1/2 particles, orfermions (i.e. that obey the Pauli exclusion principle), e.g. electrons in solids and liquids, and importantly to the field of conduction insemiconductors.
In 1928, building on 2×2 spin matrices which he purported to have discovered independently ofWolfgang Pauli's work on non-relativisticspin systems (Dirac toldAbraham Pais, "I believe I got these [matrices] independently of Pauli and possibly Pauli got these independently of me."),[89] he proposed theDirac equation as arelativisticequation of motion for thewave function of theelectron.[90] This work led Dirac to predict the existence of thepositron, the electron'santiparticle, which he interpreted in terms of what came to be called theDirac sea.[91] The positron was observed byCarl Anderson in 1932. Dirac's equation also contributed to explaining the origin ofquantum spin as a relativistic phenomenon.
Dirac'sThePrinciples of Quantum Mechanics, published in 1930, is a landmark in thehistory 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 Heisenberg onmatrix mechanics and ofErwin Schrödinger onwave mechanics into a single mathematical formalism that associates measurable quantities to operators acting on theHilbert space of vectors that describe the state of aphysical system. The book also introduced theDirac delta function. Following his 1939 article,[92] he also included thebra–ket notation in the third edition of his book,[93] thereby contributing to its universal use nowadays.
Quantum electrodynamics
Dirac'squantum electrodynamics (QED) included terms with infiniteself-energy. A workaround known asrenormalisation 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!"[94] His refusal to accept renormalisation resulted in his work on the subject moving increasingly out of the mainstream.Shin'ichirō Tomonaga,Schwinger andFeynman mastered this approach, producing a QED with unprecedented accuracy, resulting in formal recognition by being awarded the 1965 Nobel Prize in Physics.[95]
In 1931, Dirac proposed that the existence of a single magnetic monopole in the universe would suffice to explain the quantisation of electrical charge.[99] No such monopole has been detected, despite numerous attempts and preliminary claims.[100] (See also:Searches for magnetic monopoles.)
Dirac quantised the gravitational field.[26][107] His work laid the foundations forcanonical quantum gravity.[108] In his 1959 lecture at theLindau Meetings, Dirac discussed whygravitational waves have "physical significance".[109] Dirac predicted gravitational waves would have well defined energy density in 1964.[107] Dirac reintroduced the term "graviton" in a number of lectures in 1959, noting that the energy of the gravitational field should come in quanta.[110][111]
In a 1963 paper,[128] Dirac initiated the study of field theory onanti-de Sitter space (AdS).[129] The paper contains the mathematics of combining special relativity with the quantum mechanics of quarks inside hadrons, and lays the foundations oftwo-mode squeezed states that are essential tomodern quantum optics, though Dirac did not realize it at the time.[130] Dirac previously worked on AdS during the 1930s,[131] publishing a paper in 1935.[132]
In 1930,Victor Weisskopf andEugene Wigner published their famous and now standard calculation of spontaneous radiation emission in atomic and molecular physics.[133] Remarkably, in a letter toNiels Bohr in February 1927, Dirac had come to the same calculation,[134] but he did not publish it.[135]
In 1938,[136] Dirac renormalized the mass in the theory of Abraham-Lorentz electron, leading to theAbraham–Lorentz–Dirac force, which is the relativistic-classical electron model; however, this model has solutions that suggest force increase exponentially with time.[137]
Fermi's golden rule, the formula for computing quantum transitions in time dependent systems, declared a "golden rule" byEnrico Fermi, was derived by Dirac.[138] Dirac was the one to initiate the development oftime-dependent perturbation theory in his early work on semi-classical atoms interacting with an electromagnetic field. Dirac, withWerner Heisenberg,John Archibald Wheeler, Richard Feynman, andFreeman Dyson ultimately developed this concept into an invaluable tool for modern physics, used in the calculation of the properties of any physical system and a wide array of phenomena.[139]
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 surfaceHL ≈ 0;Hr ≈ 0 (r = 1, 2, 3).[145]
In the late 1950s, he applied the Hamiltonian methods he had developed to cast Einstein'sgeneral relativity in Hamiltonian form[146][147] and to bring to a technical completion the quantisation 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.[148] In 1964 he published hisLectures on Quantum Mechanics (London: Academic) which deals with constrained dynamics of nonlinear dynamical systems including quantisation of curved spacetime. He also published a paper entitled "Quantization of the Gravitational Field" in the 1967 ICTP/IAEA Trieste Symposium on Contemporary Physics.
The 1963–1964 lectures Dirac gave on quantum field theory atYeshiva University were published in 1966 as the Belfer Graduate School of Science, Monograph Series Number, 3.
Contemporary accounts of his time in Tallahassee describe it as happy, except that he apparently found the summer heat oppressive and liked to escape from it to Cambridge.[152] 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 theUniversity 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.[153]
Dirac published over 60 papers at FSU during those last twelve years of his life, including a short book on general relativity.[154] 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."[155]
In 1975, Dirac gave a series of five lectures at theUniversity 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 Dirac Lecture Series. TheSilver Dirac Medal for the Advancement of Theoretical Physics is awarded by the University of New South Wales to commemorate the lecture.[156]
Students
Amongst his many students[157][158] wereHomi J. Bhabha,[159]Fred Hoyle,John Polkinghorne[160] andFreeman Dyson.[161] 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."[162]: 2 In 1930,Subrahmanyan Chandrasekhar attended Dirac's course on quantum mechanics four times, describing it as "just like a piece of music you want to hear over and over again."[163]
Death and recognition
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 inWestminster Abbey
Dirac died on 20 October 1984 inTallahassee, Florida, at the age of 82, and is buried at Tallahassee's Roselawn Cemetery.[164] Dirac's childhood home inBishopston, Bristol, is commemorated with ablue plaque,[165] and the nearby Dirac Road is named in recognition of his links with the city ofBristol. A commemorative stone was erected in a garden inSaint-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 greenslate and inscribed with theDirac equation, was unveiled inWestminster Abbey.[164][166] TheDean 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.[167]
The Dirac–Hellman Award atFlorida State University was endowed by Bruce P. Hellman in 1997 to reward outstanding work in theoretical physics by FSU researchers.[178] The Paul A.M. Dirac Science Library at Florida State University, which Manci opened in December 1989,[179] is named in his honour, and his papers are held there.[180] Outside is a statue of him by Gabriella Bollobás.[181] The street on which theNational 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, inDidcot, Oxfordshire.[182] The Dirac-Higgs Science Centre in Bristol is also named in his honour.[183]
The BBC named avideo codec,Dirac, in his honour. Anasteroid discovered in 1983 was named after Dirac.[184] The Distributed Research utilising Advanced Computing (DiRAC) andDirac software are named in his honour.
On the occasion of the 100th anniversary of Dirac's birth,Richard Dalitz wrote "The influence and importance of Dirac's work have increased with the decades, and physicists use daily the concepts and equations that he developed."[26]
InLev Landau'slogarithmic scale of physicists from 0 to 5 based on productivity and genius, (0 being the highest and 5 the lowest) he ranked Dirac a 1, along with other fathers of quantum mechanics such as Schrödinger andWerner Heisenberg.[189]
John Polkinghorne wrote: "Not only was Dirac the greatest theoretical physicist known to me personally, his purity of spirt and modesty of demeanour (he never emphasized in the slightest degree his own immense contributions to the fundamentals of the subject) made him an inspiring figure and a kind of scientific saint."[190]: xii
Books
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 (theDirac 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 incurved space-time.
Lectures on Quantum Field Theory (1966): This book lays down the foundations ofquantum field theory using theHamiltonian formalism.
Spinors in Hilbert Space (1974): This book based on lectures given in 1969 at the University of Miami deals with the basic aspects ofspinors starting with a realHilbert space formalism.
General Theory of Relativity (1975): Based on Dirac's 1975 lectures at Florida State University, this 69-page work summarises Einstein's general theory of relativity.[191]
^Dirac, "The inadequacies of quantum field theory", in B. N. Kursunoglu & E. P. Wigner, eds.,Paul Adrien Maurice Dirac (Cambridge: Cambridge University Press, 1987), p. 194.
^Farmelo 2009, p. 138, who says this was an old joke, pointing out aPunch footnote in the 1850s that "There is no God, andHarriet Martineau is her prophet."
^Seto, K.; Zhang, S.; Koga, J.; Nagatomo, H.; Nakai, M.; Mima, K. (1 April 2014). "Stabilization of radiation reaction with vacuum polarization".Progress of Theoretical and Experimental Physics.2014 (4): 43A01–0.arXiv:1310.6646.doi:10.1093/ptep/ptu031.ISSN2050-3911.
^Kaufmann, André (2022), Kaufmann, André (ed.), "Useful Applications of the RHVT",The Ranque Hilsch Vortex Tube Demystified: Understanding the Working Principles of the Vortex Tube, Cham: Springer International Publishing, p. 69,doi:10.1007/978-3-030-89766-6_6,ISBN978-3-030-89766-6
^Farmelo 2009, pp. 248–249 quote=During a visit to Cambridge in May 1934, Wigner saw the apparatus and asked Dirac questions about it,
