Skip to main content

The National MagLab is funded by the National Science Foundation and the State of Florida.

Paul Dirac

Paul Adrien Maurice Dirac was an outstanding twentieth century theoretical physicist whose work was fundamental to the development of quantum mechanics and quantum electrodynamics.

Paul Dirac

He was awarded the Nobel Prize in Physics jointly with Erwin Schrödinger in 1933 for his contributions to atomic theory, Dirac’s prediction of the existence of antimatter having been experimentally proven by that time. Though he spent most of his life concerned with theoretical science, he had initially intended to pursue a more practical career, earning his bachelor's degree in electrical engineering.

Dirac was born on August 8, 1902, in Bristol, England, though he was registered at birth as Swiss because his father, Charles Adrien Ladislas Dirac, was a Swiss immigrant. His mother, Florence Hannah Holten, was English, and Dirac would himself gain British citizenship in 1919. The younger Dirac had two siblings and studied in his youth at the Merchant Venturer's Technical College, the same school where his father taught French. Dirac excelled in mathematics and science, but his father apparently wished him to excel in French as well, for Dirac reported later in his life that his father would not respond to him unless he spoke in that language. It has been commonly quipped that this habit of his father’s was the reason that Dirac became a man of few words who generally enjoyed solitude.

When he was 16, Dirac began his undergraduate career at Bristol University. Following graduation three years later, he was unable to find employment as an electrical engineer, an understandable problem considering the economic depression experienced by Great Britain after World War I. Consequently, he decided to remain at Bristol, where a scholarship enabled him study in the mathematics department for two years free of charge. During that time Dirac appears to have discovered his true calling, for when his scholarship ended, instead of looking for a job in electrical engineering, he applied to be a research assistant in the mathematics department at St. John’s College, Cambridge. He was awarded the position, and there he came to focus his studies on mathematics as it applied to atomic theory.

Having already developed an interest in Albert Einstein’s< theories as an undergraduate, Dirac became very familiar at Cambridge with the works of Niels Bohr, Max Born, Werner Heisenberg, Arnold Summerfeld and other great theoretical minds, some of which he was privileged enough to hear speak at the university. Dirac was awarded his Ph.D. in physics in 1926, but had already made his first notable contributions to the field before he ever received the degree. Dirac’s doctoral research supervisor, Ralph Fowler, received a preview copy of a paper written by Heisenberg in 1925 and recommended that Dirac examine it carefully. In the course of doing so, Dirac became intrigued by an equation developed by Heisenberg, who was working out a new type of quantum mechanics, and later realized that its form was analogous to that of the Poisson Brackets, an operation used in classical mechanics. This Dirac interpreted as a direct link between quantum and classical physics, and the discovery helped him develop a formulation of quantum mechanics that surpassed all others in its generality and logic. Dirac’s generalized quantum mechanics immediately placed him in the same ranks of other illustrious physicists working in the field, though he was only in his mid-twenties and had not yet received his doctorate. More importantly, the formulation enabled him to make several other key theoretical advances.

By applying quantum mechanics to James Clerk Maxwell’s theory of electromagnetism, Dirac established the groundwork of quantum field theory. He also utilized his version of quantum mechanics to develop the transformation theory, which not only united the opposing views of quantum mechanics proposed by Heisenberg and the Austrian physicist Erwin Schrödinger, but also established that other possible versions of quantum mechanics were possible as well. This momentous achievement, which allowed a much deeper understanding of quantum mechanics than had been previously possible, was made through the use of mathematics alone. Even when he presented the theory in his seminal text The Principles of Quantum Mechanics, which was published in 1930, he did not provide visual analogies or mental pictures in his explanation because he believed that to do so would “introduce irrelevancies.” Indeed, this philosophy seems to have served Dirac very well, for in 1927 he successfully predicted the existence of new subatomic particles solely utilizing mathematical arguments. The theoretical deduction of the new particles, however, was only a byproduct of another landmark undertaking.

Believing that quantum mechanics should take into account Einstein’s theory of special relativity and being unhappy with the results of other physicists that had attempted to achieve this, Dirac decided to develop an equation of the motion of a quantum particle that would not ignore relativistic effects, as did Schrödinger’s wave equation. For his starting point Dirac used only the most basic information known about the electron, its charge and mass. From this simple beginning, he mathematically arrived at a wave equation for a single electron that respects all the requirements of special relativity and quantum mechanics, and was able to predict the properties of the electron, including its spin and magnetic charge, with incredible precision. The importance of Dirac’s work in this area was recognized by the Nobel Foundation in 1933, when he was awarded the physics prize jointly with Schrödinger. By the time he received the honor, an initially controversial prediction that Dirac made based on his own equation, that there existed a positive counterpart to the electron, had been experimentally verified.

In analysis of his own mathematical equations, Dirac found that electrons could have either positive or negative kinetic energy. This could only be possible, he deduced, if an unidentified particle with the same mass and charge as the electron but positive rather than negative existed. Suggesting that something exists that no one has ever seen evidence of has always been a risky venture, and Dirac was at first hesitant to draw the conclusion his mathematical arguments seemed to lead him to in case others considered it a sign of an error in his work. His fear appears to have been well grounded, as indicated in a letter from Heisenberg, with whom Dirac was on friendly terms, to Wolfgang Pauli, written after Heisenberg had become acquainted with Dirac’s notions of the anti-electron (or positron as it is now called). Heisenberg wrote, “The saddest chapter of modern physics is and remains the Dirac theory.” Presumably Heisenberg had a change of heart regarding the matter when shortly after, in 1932, Carl Anderson experimentally observed the particle of antimatter that Dirac had theoretically anticipated. Years later the anti-proton and anti-neutron, which could be predicted by extension of Dirac’s work, were also proven to exist.

After receiving his doctorate, Dirac traveled for two years before returning to St. John’s College, where he was elected a fellow in 1928. A few years later, in 1932, he became Lucasian Professor of Mathematics at Cambridge. While on an extended trip to the United States in 1934 and 1935, he met Margit Wigner, the sister of physicist Eugene Wigner. He married her in 1937, and the couple made their home in England until 1969, when Dirac retired from Cambridge. Subsequently they moved to the United States, where Dirac worked for a short time at the University of Miami’s Center for Theoretical Studies before being appointed professor emeritus at Florida State University. He died in Tallahassee on October 20, 1984, following a long illness.

Though most of Dirac’s most famous work was completed in the first part of his life, he was active in theoretical physics until shortly before his death. He was particularly interested in his later years in possible interrelations between certain large numerical constants and their potential cosmological significance. More precisely, according to Dirac’s large numbers hypothesis, these particular numbers are only thought to be constants, but in reality are gradually changing with the increasing age of the universe. Dirac’s attraction to cosmology, a field focused upon developing a unified understanding of the universe, seems fitting for a man who played such an important role in unifying different views of quantum mechanics.

No matter what aspect of physics he focused upon, Dirac seems to have been guided by his belief that “physical laws should have mathematical beauty.” The beauty of his own work has been remarked upon by many and can be seen in Westminster Abbey, carved in stone.