Paul Adrien Maurice Dirac (pronounced dih-RAK; August 8, 1902 – October 20, 1984) was a British theoretical physicist who helped create quantum mechanics. He played a key role in developing quantum electrodynamics and quantum field theory, and he was the first to use the term "quantum electrodynamics." From 1932 to 1969, Dirac held the Lucasian Professor of Mathematics position at the University of Cambridge. He later taught physics at Florida State University from 1970 to 1984. In 1933, Dirac shared the Nobel Prize in Physics with Erwin Schrödinger for their discoveries in atomic theory.

Dirac earned a First Class Honours Bachelor of Science degree in electrical engineering from the University of Bristol in 1921 and a First Class Honours Bachelor of Arts degree in mathematics in 1923. He completed his Ph.D. in physics at St John's College, Cambridge, in 1926, writing the first thesis on quantum mechanics.

In 1928, Dirac created the Dirac equation, a major scientific achievement that combined special relativity with quantum mechanics and predicted the existence of antimatter. He published a paper in 1931 that further supported the idea of antimatter. Dirac also helped combine general relativity with quantum mechanics. He contributed to Fermi–Dirac statistics, which explains how particles called fermions behave. His 1930 book, The Principles of Quantum Mechanics, is widely regarded as a key text in the field. In a Physics World poll, Dirac and Schrödinger were tied for eighth place among the greatest physicists of all time.

In 1987, Abdus Salam said, "Dirac was undoubtedly one of the greatest physicists of this or any century… No man except Einstein has had such a decisive influence, in so short a time, on the course of physics in this century." In 1995, Stephen Hawking stated, "Dirac has done more than anyone this century, with the exception of Einstein, to advance physics and change our picture of the universe." Stanley Deser added, "We all stand on Dirac's shoulders."

Early life

Paul Dirac was born on August 8, 1902, at his family's home in Bristol, England. He grew up in the Bishopston area of the city. His father, Charles Adrien Ladislas Dirac, was born in Saint-Maurice, Switzerland, and came from a French family. He worked in Bristol as a teacher of the French language. His mother, Florence Hannah Holten, was born in Liskeard, Cornwall, to a family of Cornish Methodists. Her father, a ship captain, named her after Florence Nightingale, a famous nurse he had met during the Crimean War. Florence moved to Bristol as a young woman and worked as a librarian at the Bristol Central Library. She always considered herself Cornish, not English. Paul had a younger sister named Béatrice Isabelle Marguerite, known as Betty, and an older brother named Reginald Charles Félix, known as Felix, who died by suicide in March 1925. Dirac later said, "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."

Charles and the children were officially Swiss citizens until they became naturalized on October 22, 1919. Dirac's father was strict and did not like physical punishment. Dirac had a difficult relationship with his father, and after his father's death, Dirac wrote, "I feel much freer now, and I am my own man." Charles required his children to speak only French to him so they could learn the language. When Dirac found it difficult to express his thoughts in French, he chose to remain silent.

Education

Paul Dirac first attended Bishop Road Primary School. Later, he studied at the all-boys Merchant Venturers' Technical College, which later became Cotham School. His father worked as a French teacher there. The school was connected to the University of Bristol, sharing the same grounds and staff. It focused on technical subjects such as bricklaying, shoemaking, and metalwork, as well as modern languages. This was uncommon in Britain at the time, as most secondary schools emphasized classical subjects. Dirac later thanked the school for this unique approach. One of his classmates at Bishop Road School was Archibald Leach, who later became famous as Cary Grant.

Dirac studied electrical engineering at the University of Bristol’s engineering faculty, supported by a City of Bristol University Scholarship. The university was located near the Merchant Venturers' Technical College. Before finishing his degree in 1921, he took an entrance exam for St John’s College, Cambridge. He passed and received a £70 scholarship, but this amount was not enough to cover living and study costs in Cambridge. After graduating with a first-class honors B.Sc. in electrical engineering, Dirac struggled to find work due to the economic challenges of the post-war depression. Instead, he accepted a free offer to study mathematics at the University of Bristol. Because of his engineering degree, he was allowed to skip the first year of the mathematics program. Under the guidance of Peter Fraser, whom Dirac considered the best mathematics teacher, he became especially interested in projective geometry and applied it to Hermann Minkowski’s geometric version of special relativity.

In 1923, Dirac graduated again with first-class honors and received a £140 scholarship from the Department of Scientific and Industrial Research. Combined with his £70 scholarship from St John’s College, this money allowed him to live and study in Cambridge. There, he studied general relativity and quantum physics, guided by Ralph Fowler. From 1925 to 1928, he held an 1851 Research Fellowship from the Royal Commission for the Exhibition of 1851. In June 1926, he completed his Ph.D. with the first thesis on quantum mechanics ever submitted. Afterward, he continued his research in Copenhagen and Göttingen. In the spring of 1929, he worked as a visiting professor at the University of Wisconsin–Madison.

Personal life

In 1937, Paul Dirac married Margit Wigner, the sister of physicist Eugene Wigner. Margit had previously been married. Dirac raised Margit’s two children, Judith and Gabriel, as if they were his own. Paul and Margit Dirac also had two daughters together, Mary Elizabeth and Florence Monica.

Margit, known as Manci, visited her brother in 1934 in Princeton, New Jersey, from Hungary. During a dinner at the Annex Restaurant, she met Paul Dirac, who was described as a "lonely-looking man at the next table." A Korean physicist, Y. S. Kim, later said that Manci’s care helped Dirac continue his work. During the years 1939–46, Dirac published eleven scientific papers. He was able to focus on his research because Manci managed other responsibilities.

Dirac was known by his friends and colleagues as unusual in personality. In a 1926 letter to Paul Ehrenfest, Albert Einstein wrote about a Dirac paper, "I am toiling over Dirac. This balancing on the dizzying path between genius and madness is awful." In another letter, Einstein said, "I don’t understand the details of Dirac at all." Dirac was known for being very precise and speaking very little. His colleagues in Cambridge jokingly created a unit called a "dirac," which meant one word spoken every hour. When Niels Bohr said he did not know how to finish a sentence in a scientific article, Dirac replied, "I was taught at school never to start a sentence without knowing the end of it." Dirac criticized physicist J. Robert Oppenheimer’s interest in poetry, saying, "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." Bohr called Dirac "a complete logical genius" and also "the strangest man" who had ever visited his Institute.

Dirac wrote in his diary during his postgraduate years that he focused only on his research. He stopped working only on Sundays, when he took long walks alone.

An anecdote from a 2009 biography describes a 1929 trip to Japan by Werner Heisenberg and Dirac on an ocean liner. Both were young and unmarried. Heisenberg, who enjoyed socializing, danced and flirted with others. Dirac, described as "an Edwardian geek" by biographer Graham Farmelo, avoided socializing. When Heisenberg asked why he danced, Dirac replied, "But, Heisenberg, how do you know beforehand that the girls are nice?"

Margit Dirac told scientists George Gamow and Anton Capri in the 1960s that her husband once introduced her to a visitor as "Wigner’s sister, who is now my wife."

Another story says that when Dirac first met young physicist Richard Feynman at a conference, he asked after a long silence, "I have an equation. Do you have one too?"

After Dirac gave a lecture, a colleague raised his hand and said, "I don’t understand the equation on the top-right-hand corner of the blackboard." After a long pause, the moderator asked Dirac if he wanted to answer. Dirac replied, "That was not a question, it was a comment."

Dirac was known for his personal modesty. He named an equation for the time evolution of a quantum-mechanical operator after physicist Werner Heisenberg, calling it the "Heisenberg equation of motion." Most physicists refer to Fermi–Dirac statistics for half-integer-spin particles (fermions) and Bose–Einstein statistics for integer-spin particles (bosons). Dirac later called the former "Fermi statistics" and the latter "Bose statistics" for reasons of "symmetry."

During a visit to Moscow State University in 1956, Dirac was asked to summarize his philosophy of physics. He wrote on the blackboard, "Physical laws should have mathematical beauty." This phrase, like those left by other distinguished visitors, has never been erased.

Dirac believed that mathematical beauty was important in physics. He thought that physicists should aim for beauty when creating laws of nature and that beauty could help decide whether a theory was worth accepting. In a 1939 lecture, he said that the mathematical beauty of the general theory of relativity was one reason it was accepted.

Dirac did not focus on the interpretation of quantum theory. In a paper published in a book honoring him, 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."

Werner Heisenberg recalled a conversation at the 1927 Solvay Conference about religion. Dirac criticized the political purpose of religion, which Bohr found clear when Heisenberg later described it. Heisenberg was tolerant, while Wolfgang Pauli, raised as a Catholic, finally said, "Well, our friend Dirac has got a religion and its guiding principle is 'There is no God, and Paul Dirac is His prophet.'" Everyone, including Dirac, laughed.

Later in life, in an article about God in the May 1963 issue of Scientific American, Dirac wrote:

In 1971, at a conference, Dirac discussed the possibility of scientifically answering the question of God. He explained:

Research

Paul Dirac discovered the equation that describes how electrons behave at very high speeds, now known as the Dirac equation. His work introduced the idea that every particle has an opposite, called an antiparticle, such as the positron, which is the opposite of the electron. Dirac also created quantum field theory, which is the foundation for understanding how tiny particles, like electrons and protons, interact. He also helped develop quantum electrodynamics and introduced the terms "fermion" and "boson" to describe particles based on their spin. Fermions have half-integer spin, while bosons have whole-number spin.

Dirac believed that mathematical beauty was the most important guide for understanding physics. His professors praised his ability to solve complex problems and create new mathematical tools. He made many important contributions to mathematics, including the Dirac delta function, Dirac algebra, and the Dirac operator.

In 1925, Dirac studied a paper by Werner Heisenberg that described a new way to understand quantum mechanics. He noticed that the mathematical structure in Heisenberg’s work was similar to a concept from classical physics called Poisson brackets. Using this connection, Dirac developed a new way to describe quantum mechanics, leading to a major breakthrough in the field. His work was published in 1926, and he earned his PhD from Cambridge University.

After Wolfgang Pauli proposed the Pauli exclusion principle, which states that two electrons cannot share the same energy level, Dirac and Enrico Fermi realized this principle changed how scientists studied electron systems. Their work led to Fermi-Dirac statistics, which describes how groups of identical particles, like electrons, behave in materials such as solids and liquids.

In 1928, Dirac used spin matrices to create the Dirac equation, which explained how electrons move at high speeds. This equation predicted the existence of the positron, an antiparticle of the electron. The positron was discovered in 1932 by Carl Anderson. Dirac’s equation also explained how quantum spin arises from relativity.

Dirac’s work on quantum field theory helped explain how particles like electrons are created and destroyed in processes such as beta decay. His equation became a key part of modern physics, describing all matter particles, including quarks and leptons. He is considered the founder of quantum electrodynamics and introduced the idea of vacuum polarization.

Dirac’s book, The Principles of Quantum Mechanics, published in 1930, became a standard textbook. It combined earlier ideas from Heisenberg and Schrödinger into a single mathematical framework. The book also introduced the Dirac delta function and the bra-ket notation, which are widely used in physics today.

Dirac’s version of quantum electrodynamics included problems with infinite energy values. He disagreed with the solution called renormalization, which ignored these infinities. This disagreement caused his work to fall out of favor, while others like Schwinger and Feynman developed a more successful version of quantum electrodynamics, which earned them the 1965 Nobel Prize.

In the 1950s, Dirac worked on improving quantum electrodynamics. He developed a theory of constraints and solved problems related to particle fields, including the description of mesons and photons.

In 1931, Dirac suggested that a single magnetic monopole—a particle with only a magnetic charge—could explain why electric charges are quantized. No magnetic monopole has been found, despite many searches.

Dirac also contributed to the Tube Alloys project, which was part of the British effort to develop atomic bombs during World War II.

Career

On August 19, 1929, Dirac traveled with Werner Heisenberg on the Graf Zeppelin LZ 127 during its first round-the-world flight to Tokyo. Both scientists gave lectures there.

From 1932 to 1969, Dirac held the position of Lucasian Professor of Mathematics at the University of Cambridge. In 1934, he created the Helikon vortex isotope separation process. In 1937, he proposed a model about the universe based on the large numbers hypothesis. During World War II, he worked on theoretical methods to enrich uranium using gas centrifuges. He introduced the separative work unit (SWU) in 1941. He also contributed to the Tube Alloys project, which was the British effort to develop atomic bombs during the war.

Dirac’s work on the Hamiltonian for constrained systems is one of his most important achievements. This theory expands Hamiltonian principles to apply to curved spacetime. The equations for the Hamiltonian use six degrees of freedom described by g_rs and p_rs for each point on a surface. The g_m0 (m = 0, 1, 2, 3) appear in the theory only through variables like g_r0 and (−g_00)^−1/2, which act as coefficients in motion equations. There are four constraints or weak equations for each point on the surface where x⁰ = constant. Three of these constraints, H_r, form a four-vector density on the surface. The fourth, H_L, is a three-dimensional scalar density on the surface, with H_L ≈ 0 and H_r ≈ 0 (r = 1, 2, 3).

In the late 1950s, Dirac used his Hamiltonian methods to rewrite Einstein’s general relativity in Hamiltonian form. This helped complete the problem of quantizing gravity and made it more connected to other areas of physics, as noted by Salam and DeWitt. In 1959, he gave a talk on "Energy of the Gravitational Field" at the American Physical Society meeting in New York. In 1964, he published Lectures on Quantum Mechanics, which discusses the dynamics of nonlinear systems and the quantization of curved spacetime. He also wrote a paper titled "Quantization of the Gravitational Field" for the 1967 ICTP/IAEA Trieste Symposium on Contemporary Physics.

Dirac’s lectures on quantum field theory from 1963–1964 at Yeshiva University were published in 1966 as part of the Belfer Graduate School of Science Monograph Series, Number 3.

Many of Dirac’s students included Homi J. Bhabha, Fred Hoyle, John Polkinghorne, and Freeman Dyson. In 1930, Subrahmanyan Chandrasekhar attended Dirac’s quantum mechanics course four times and described it as "just like a piece of music you want to hear over and over again."

Later life

In 1969, Dirac had to retire from his position at Cambridge University because he was 67 years old. Before retiring, he was invited to work at the University of Miami in Coral Gables, Florida. He agreed to join the newly created Center for Theoretical Studies there. In September 1970, he also accepted a visiting professor job at Florida State University in Tallahassee, Florida. He moved his family to Tallahassee and became a full professor at FSU in 1972.

People who knew Dirac during his time in Tallahassee said he was generally happy, though he found the hot summers uncomfortable and often returned to Cambridge to escape the heat. He walked about a mile each day to work and enjoyed swimming in one of the two nearby lakes, Silver Lake or Lost Lake. He was more friendly and social at FSU than at Cambridge, where he mostly worked from home. At Florida State, he usually had lunch with his colleagues before taking a nap.

During his last twelve years, Dirac wrote over 60 papers at FSU, including a short book about general relativity. His final paper, published in 1984 and titled "The inadequacies of quantum field theory," expressed his belief that quantum field theory was not fully correct. He wrote, "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 ended with, "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."

In 1975, Dirac gave five lectures at the University of New South Wales. These lectures were later published as a book called Directions in Physics (1978). He donated the money he earned from the book to the university to create the Dirac Lecture Series. The Silver Dirac Medal for the Advancement of Theoretical Physics is given by the University of New South Wales to honor these lectures.

Dirac died on October 20, 1984, in Tallahassee, Florida, at the age of 82. He was buried at Roselawn Cemetery in Tallahassee.

Commemorations

Paul Dirac’s childhood home in Bishopston, Bristol, is honored with a blue plaque. A nearby street, Dirac Road, is named to recognize his connection to Bristol. A commemorative stone was placed in a garden in Saint-Maurice, Switzerland, the town where his father’s family came from. This happened on August 1, 1991. On November 13, 1995, a memorial made of Burlington green slate and featuring the Dirac equation was placed in Westminster Abbey. The Dean of Westminster, Edward Carpenter, first refused permission for the memorial, thinking Dirac was anti-Christian. However, after five years, he agreed to allow it.

After Dirac’s death, two groups of physicists created annual awards in his memory. The Institute of Physics, the UK’s organization for physicists, gives the Paul Dirac Medal for important work in theoretical physics. The first three winners were Stephen Hawking (1987), John Stewart Bell (1988), and Roger Penrose (1989). Since 1985, the International Centre for Theoretical Physics has given the Dirac Medal of the ICTP each year on August 8, Dirac’s birthday.

The Dirac–Hellman Award at Florida State University was created by Bruce P. Hellman in 1997 to recognize excellent work in theoretical physics by researchers at the university. The Paul A.M. Dirac Science Library at Florida State University, opened in December 1989, is named in his honor. His papers are kept there. A statue of Dirac, made by Gabriella Bollobás, is outside the library. The street where the National High Magnetic Field Laboratory in Tallahassee, Florida, is located is called Paul Dirac Drive. In addition to Bristol, a road named Dirac Place in Didcot, Oxfordshire, honors him. The Dirac-Higgs Science Centre in Bristol is also named in his honor.

The BBC named a video codec Dirac in his honor. An asteroid discovered in 1983 was named after him. The Distributed Research utilising Advanced Computing (DiRAC) and Dirac software are also named in his honor.

Dirac is often compared to Isaac Newton, James Clerk Maxwell, and Albert Einstein. Einstein wrote that Dirac provided the most logically perfect explanation of quantum mechanics. On the 100th anniversary of Dirac’s birth, Richard Dalitz stated that Dirac’s work became more important over time, and physicists use daily the ideas and equations he developed.

On a scale created by Lev Landau to measure the genius and productivity of physicists, with 0 being the highest, Dirac was ranked 1, along with other pioneers of quantum mechanics like Erwin Schrödinger and Werner Heisenberg. John Polkinghorne wrote that Dirac was the greatest theoretical physicist he knew personally. He also noted that Dirac’s strong moral character and modest nature made him an inspiring and respected figure in science.

Books

• The Principles of Quantum Mechanics (1930): This book explains the ideas of quantum mechanics using the modern method that Dirac helped create. At the end of the book, he also describes the relativistic theory of the electron, known as the Dirac equation, which he developed. This work does not mention other books about quantum mechanics that were available at the time.
• Lectures on Quantum Mechanics (1966): Much of this book focuses on how quantum mechanics works in curved space-time.
• Lectures on Quantum Field Theory (1966): This book introduces the basics 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, explains the basics of spinors starting with a real Hilbert space formalism.
• General Theory of Relativity (1975): Based on Dirac's 1975 lectures at Florida State University, this 69-page book describes Einstein's general theory of relativity.