# Paul Dirac

Paul Dirac

Born

August 8 1902
Bristol, England

Died October 20 1984 (aged 82)

Tallahassee, Florida, U.S.

Residence United Kingdom
United States
Nationality  United Kingdom
Field Physicist
Institutions Cambridge University
Florida State University
Alma mater University of Bristol
Cambridge University
Notable students  Homi Bhabha
Harish Chandra Mehrotra
Dennis Sciama
Behram Kurşunoğlu
John Polkinghorne
Per-Olov Löwdin
Known for theoretical physics
Notable prizes Nobel Prize in Physics (1933)
Religious stance Atheist[1]
 Quantum physics $\Delta x \, \Delta p \ge \frac{\hbar}{2}$ Quantum mechanics Introduction to... Mathematical formulation of... Fundamental concepts Decoherence · Interference Uncertainty · Exclusion Transformation theory Ehrenfest theorem · Measurement Experiments Double-slit experiment Davisson-Germer experiment Stern–Gerlach experiment EPR paradox · Popper's experiment Schrödinger's cat Equations Schrödinger equation Pauli equation Klein-Gordon equation Dirac equation Advanced theories Quantum field theory Wightman axioms Quantum electrodynamics Quantum chromodynamics Quantum gravity Feynman diagram Interpretations Copenhagen · Ensemble Hidden variables · Transactional Many-worlds · Consistent histories Quantum logic Consciousness causes collapse Scientists Planck · Schrödinger Heisenberg · Bohr · Pauli Dirac · Bohm · Born de Broglie · von Neumann Einstein · Feynman Everett · Others

Paul Adrien Maurice Dirac, OM, FRS (August 8, 1902 – October 20, 1984) was a British theoretical physicist and a founder of the field of quantum mechanics. He held the Lucasian Professor of Mathematics at the University of Cambridge and spent the last ten years of his life at Florida State University. Among other discoveries, he formulated the so-called "Dirac equation," which describes the behavior of fermions and which led to the prediction of the existence of antimatter. Dirac shared the Nobel Prize in physics for 1933 with Erwin Schrödinger, "for the discovery of new productive forms of atomic theory."

## Biography

### Birth and education

Paul Dirac was born in Bristol, England and grew up in the Bishopston area of the city. His father, Charles Dirac, was an immigrant from Saint-Maurice in the Canton of Valais, Switzerland and taught French for a living. His mother was originally from Cornwall and the daughter of a mariner. Paul had an elder brother, Félix, who committed suicide in March 1925, and a younger sister, Béatrice. His early family life appears to have been unhappy due to his father's unusually strict and authoritarian nature. He was educated first at Bishop Road Primary School and then at Merchant Venturers' Technical College (later Cotham Grammar School), where his father was a teacher. The latter was an institution attached to the University of Bristol that emphasized scientific subjects and modern languages. This was an unusual arrangement at a time when secondary education in Britain was still dedicated largely to the classics, and something for which Dirac would later express gratitude.

Dirac studied electrical engineering at the University of Bristol, completing his degree in 1921. He then decided that his true calling lay in the mathematical sciences and, after completing a BA in applied mathematics at Bristol in 1923, he received a grant to conduct research at St John's College, Cambridge, where he would remain for most of his career. At Cambridge, Dirac pursued his interests in the theory of general relativity (an interest he gained earlier as a student in Bristol) and in the nascent field of quantum physics, working under the supervision of Ralph Fowler.

### Middle years

Dirac noticed an analogy between the old Poisson brackets of classical mechanics and the recently-proposed quantization rules in Werner Heisenberg's matrix formulation of quantum mechanics. This observation allowed Dirac to obtain the quantization rules in a novel and more illuminating manner. For this work, published in 1926, he received a Doctor of Philosophy from Cambridge.

In 1928, building on Wolfgang Pauli's work on non-relativistic spin systems, he proposed the Dirac equation as a relativistic equation of motion for the wavefunction of the electron. 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. The positron was subsequently 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 electron matter being created and destroyed in Enrico Fermi's 1934 theory of beta decay, however, led to a reinterpretation of Dirac's equation as a "classical" field equation for any point matter of spin ħ/2, itself subject to quantization conditions involving anti-commutators. Thus reinterpreted, the Dirac 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 polarization in the early 1930s.

Dirac's 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 bra-ket notation and the delta function, which are now universally used.

Guided by a comment in Dirac's textbook and by Dirac's 1933 article "The Lagrangian in quantum mechanics" (published in the Soviet journal Physikalische Zeitschrift der Sowjet Union), Richard Feynman developed the path integral formulation of quantum mechanics in 1948. This work would prove exceedingly useful in relativistic quantum field theory, in part because it is based on the Lagrangian, whose relativistic invariance is explicit, while the invariance is only implicit in the Hamiltonian formulation.

In 1931 Dirac showed that the existence of a single magnetic monopole in the universe would suffice to explain the observed quantization of electrical charge. This proposal received much attention, but there is to date no convincing evidence for the existence of magnetic monopoles.

He married Eugene Wigner's sister, Margit, in 1937. This took some courage on his part, because he was unused to solving problems that would not yield to reason. But once he had noted that the relapses in his favorable inclinations towards Margit were getting less and less as time went on, the matter was settled quickly.[2] He adopted Margit's two children, Judith and Gabriel. Paul and Margit Dirac had two children together, daughters Mary Elizabeth and Florence Monica.

### Later years

Dirac was the Lucasian Professor of Mathematics at Cambridge from 1932 to 1969. During World War II, he conducted important theoretical and experimental research on uranium enrichment by gas centrifuge. In 1937, he proposed a speculative cosmological model based on the so called "large numbers hypothesis." Dirac would write, "I am very disturbed by the situation because the so-called good theory quantum theory does involve neglecting infinities in an arbitrary way. This is not sensible. Sensible Mathematics involves neglecting a quantity when it's small; not because it's infinitely great and we do not want it."[3] Dirac became unsatisfied with the renormalization approach to dealing with these infinities in quantum field theory and his work on the subject moved increasingly out of the mainstream. After having relocated to Florida in order to be near his elder daughter, Mary, Dirac spent his last ten years (both of life and as a physicist) at Florida State University (FSU) in Tallahassee, Florida.

Amongst his many students was John Polkinghorne who 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."[4]

### Death and afterwards

Dirac died in 1984 in Tallahassee, Florida, where he is buried.[5] The Dirac-Hellmann Award at FSU was endowed by Dr. Bruce P. Hellmann (Dirac's last doctoral student) in 1997 to reward outstanding work in theoretical physics by FSU researchers. The Dirac Prize is also awarded by the International Centre for Theoretical Physics in his memory. The Paul A.M. Dirac Science Library at FSU is named in his honor. In 1995, a plaque in his honor bearing his equation was unveiled at Westminster Abbey in London with a speech from Stephen Hawking. A commemorative garden has been established opposite the railway station in Saint-Maurice, Switzerland, the town of origin of his father's family.

## Honors and tributes

Dirac shared the 1933 Nobel Prize for physics with Erwin Schrödinger "for the discovery of new productive forms of atomic theory." [6] 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, and of the American Physical Society in 1948.

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 and Prize for "outstanding contributions to theoretical (including mathematical and computational) physics." The first three recipients were Stephen Hawking (1987), John Bell (1988), and Roger Penrose (1989). The Abdus Salam International Centre for Theoretical Physics (ICTP) awards the Dirac Medal of the ICTP each year on Dirac's birthday (August 8).

The street on which the National High Magnetic Field Laboratory in Tallahassee, Florida, is located was named Paul Dirac Drive. There is also a road named after him in his home town of Bristol, UK. The BBC named its video codec Dirac in his honor. And in the popular British television show Doctor Who, the character Adric was named after him (Adric is an anagram of Dirac).

## Personality

Dirac was known among his colleagues for his precise and taciturn nature. 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." [6]. When asked about his views on poetry, he responded, "In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it's the exact opposite." [7].

Dirac was also noted for his personal modesty. He called the equation for the time-evolution of a quantum-mechanical operator, which Dirac was in fact 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.[8] While lecturing later in life, Dirac always insisted on calling the former "Fermi statistics." He referred to the latter as "Einstein statistics" for reasons, he explained, of symmetry.

He was apparently not good at social small talk. A well-known story is that at a society dinner, after an awkward silence, he turned to the young Richard Feynman sitting next to him and said, "I have an equation." A pause followed, then, "Do you have an equation?" [9]

## Religious Views

Dirac did not believe in God. He once said: "God used beautiful mathematics in creating the world," but here he used 'God' as a metaphor for nature.[10]

Werner Heisenberg[11] recollects a friendly conversation among young participants at the 1927 Solvay Conference about Einstein and Planck's views on religion. Wolfgang Pauli, Heisenberg and Dirac took part in it. Dirac's contribution was a poignant and clear criticism of the political manipulation of religion, that was much appreciated for its lucidity by Bohr, when Heisenberg reported it to him later. Among other things, Dirac said: "I cannot understand why we idle discussing religion. If we are honest - and as scientists honesty is our precise duty - we cannot help but admit that any religion is a pack of false statements, deprived of any real foundation. The very idea of God is a product of human imagination. … I do not recognize any religious myth, at least because they contradict one another. …" Heisenberg's view was tolerant. Pauli had kept silent, after some initial remarks, but when finally he was asked for his opinion, jokingly he said: "Well, I'd say that also our friend Dirac has got a religion and the first commandment of this religion is 'God does not exist and Paul Dirac is his prophet.'" Everybody burst into laughter, including Dirac.

## Legacy

Dirac is widely regarded as one of the greatest physicists of all time. He was one of the founders of quantum mechanics and quantum electrodynamics. Many physicists consider Dirac the greatest physicist of the twentieth century. Physicist Antonino Zichichi, a professor of advanced physics at the University of Bologna, believes that Dirac had a much bigger impact on modern science in the twentieth century than Albert Einstein.[12]

His main contribution to the development of modern science was uniting the equations of special relativity with the equations of quantum mechanics into a unified whole. It is this equation which allows for anti-matter—which is well-established—as well as faster-than-light tachyonsolutions of negative energy and anti-gravity—speculative, but as the universe is apparently filled with dark energy with anti-gravitational properties pushing the galaxies apart, these solutions may yet play a role in a complete description of creation.

The work of Dirac in the early Sixties proved extremely useful to modern practitioners of Superstring theory and its closely related successor, M-Theory.[13]

## Selected publications by Dirac

• Dirac, P. A. M. 1958. The Principles of Quantum Mechanics. Oxford: Clarendon Press. OCLC 534829. (This book summarizes 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, also pioneered by him.)
• Dirac, P. A. M. 1964. Lectures on Quantum Mechanics. New York: Belfer Graduate School of Science, Yeshiva University. OCLC 537128. (Much of this book deals with quantum mechanics in curved space-time.)
• Dirac, P. A. M. 1975. General Theory of Relativity. New York: Wiley. ISBN 0471215759. (This 68-page work summarizes Einstein's general theory of relativity.)

## Notes

1. Werner Heisenberg recollects a friendly conversation among young participants at the 1927 Solvay Conference about Einstein and Planck's views on religion. Wolfgang Pauli, Heisenberg and Dirac took part in it. Among other things, Dirac said: "I cannot understand why we idle discussing religion. If we are honest - and as scientists honesty is our precise duty - we cannot help but admit that any religion is a pack of false statements, deprived of any real foundation. The very idea of God is a product of human imagination. … I do not recognize any religious myth, at least because they contradict one another. …" Pauli jokingly said: "Well, I had say that also our friend Dirac has got a religion and the first commandment of this religion is: God does not exist and Paul Dirac is his prophet." Wermer Heisenberg. Physics and Beyond: Encounters and Conversations. (New York: Harper & Row, 1971)
2. Dirac to Isobel Whitehead (mother of J. H. C. Whitehead), 6 December 1936. In St. John's College, Cambridge Library, miscellaneous personal papers.
3. Notes in overhead slide. October 20, 2003 - Public Lecture Series Roger Penrose, (Oxford University: "Fashion, Faith and Fantasy in the New Physics of the Universe, Lecture 2: FAITH")
4. John Polkinghorne. Belief in God in an Age of Science. (New Haven: Yale University Press, 1998), 2
5. See this web site from Florida State University for his burial site. Retrieved January 7, 2008.
6. J J O'Connor and E F Robertson [1] "Paul Adrien Maurice Dirac." MacTutor History of Mathematics. Retrieved October 7, 2007.
7. Ibid. [2] Retrieved October 7, 2007.
8. A rough illustration of the difference is that while the probability of two classical coins coming up the same is 50 percent, for two fermion coins it is 0 percent, and two boson coins it is 100 percent. The quantum spin-one-half gives fermions the odd property of having to be rotated 720° in order to get back to where you started. A familiar example of this sort of behavior is the Moebius Strip. The photon and gluon are bosons with quantum spin-1, they take only the usual 360° to return to the start.
9. Ira C. Gunning [3]Review.Retrieved January 7, 2008.
10. For some physicists, 'God' is not a personal deity in the usual religious sense, but rather a metaphor for the nature.
11. Werner Heisenberg. Physics and Beyond: Encounters and Conversations. (New York: Harper & Row, 1971. ISBN 0061316229)
12. Dirac, "Einstein and physics" [4]
13. Britains answer to Einstein [5]

## References

• Crease, Robert P. and Charles C. Mann. The Second Creation: makers of the revolution in twentieth century physics,revised. New York: Macmillan Publishing, Rutgers University Press.(Original 1986), 1996. Entertaining personality-based history of particle physics/quantum mechanics in the twentieth century.
• Schweber, Silvan S. QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga. Princeton University Press, 1994. Includes a chapter on Dirac as the founder of quantum electrodynamics.
• Gisela Dirac "Paul Adrien Maurice Dirac" Family geneology, and additional biographical sources.