Paul Adrien Maurice Dirac Essay, Research Paper

Paul Adrien Maurice Dirac

Patrick Ennis

Mrs. Carter

Research

Monday, December 9, 1996

“Physical Laws should have mathematical beauty.” This statement was Dirac’s

response to the question of his philosophy of physics, posed to him in Moscow in

1955. He wrote it on a blackboard that is still preserved today.[1]

Paul Adrien Maurice Dirac (1902-1984), known as P. A. M. Dirac, was the

fifteenth Lucasian Professor of Mathematics at Cambridge. He shared the Nobel

Prize for Physics in 1933 with Erwin Schrodinger.[2] He is considered to be the

founder of quantum mechanics, providing the transition from quantum theory. The

Cambridge Philosophical Society awarded him the Hopkins Medal in 1930. He was

awarded the Royal Medal by the Royal Society of London in 1939 and the James

Scott Prize from the Royal Society of Edinburgh. In 1952 the Max Plank Medal

came from the Association of German Physical Societies, as well as the Copley

Medal from the Royal Society. The Akademie der Wissenschaften in the German

Democratic Republic presented him with the Helmholtz Medal in 1964. In 1969 he

received the Oppenheimer Prize from the University of Miami. Lastly in 1973, he

received the Order of Merit.[3]

Dirac was well known for his almost anti–social behavior, but he was a

member of many scientific organizations throughout the world. Naturally, he was

a member of the Royal Society, but he was also a member of the Deutsche Akademie

der Naturforsher and the Pontifical Academy of Sciences. He was a foreign member

of Academie des Sciences Morales et Politiques and the Academie des Sciences,

the Accademia delle Scienze Torino and the Accademia Nazionale dei Lincei and

the National Academy of Science. He was an honorary member and fellow of the

Indian Academy of Science, the Chinese Physical Society, the Royal Irish Academy,

the Royal Society of Edinburgh, the National Institute of Sciences in India, the

American Physical Society, the Tata Institute for Fundamental Research in India,

the Royal Danish Academy, and the Hungarian Academy of Sciences. He was a

corresponding member of the USSR Academy of Sciences.[4] The world wide respect

he earned for his work was well deserved.

A prolific writer, Dirac published over two hundred works between 1924

and 1987, mainly papers in physics journals on topics relating to quantum

mechanics. His book Principles of Quantum Mechanics , published in 1930, was the

first textbook in the discipline and became the standard.[5] Some predictions

made by Dirac are still untested because his theoretical work was so far

reaching, but many other predictions have been verified, assuring him of a

special place in the history of physics.[6]

Dirac was three years old when Einstein published his famous papers on

relativity in 1905 and a year old when his predecessor Joseph Larmor began his

tenure as Lucasian professor. Physics had just begun its incredible

transformation of the twentieth century when Dirac arrived on the scene.

Dirac came to Cambridge as a graduate student in 1923 after graduating

from the University of Bristol. As a student in mathematics in St. John’s

College, he took his Ph.D. in 1926 and was elected in 1927 as a fellow. His

appointment as university lecturer came in 1929.[7] He assumed the Lucasian

professorship following Joseph Larmor in 1932 and retired from it in 1969. Two

years later he accepted a position at Florida State University where he lived

out his remaining years. The FSU library now carries his name. [8]

While at Cambridge, Dirac did not accept many research students. Those

who worked with him generally thought he was a good supervisor, but one who did

not spend much time with his students. A student needed to be extremely

independent to work under Dirac.[9] One such student was Dennis Sciama, who

later became the supervisor of Stephen Hawking, the current holder of the

Lucasian Chair. Dirac’s lectures were attended by Sir M. J. Lighthill while he

was a student at Cambridge and Lighthill was Dirac’s successor to the Lucasian

Chair.

Dirac offered the first course in quantum mechanics in Britain, entitled Quantum

Theory (Recent Developments) . Among his students was J. R. Oppenheimer, an

American, who later on was in charge of the Manhattan Project, which created the

first atomic bomb.[10]

Dirac’s work should be understood in the context of the development of

quantum physics. The theoretical work had been underway for several years before

his entry into the field. It was plagued with difficulties, in part because of

the radical change in the way one thought about the world around us, and in part

because it was a difficult problem. The important developments of the beginning

of this century were carried out by Max Plank, Max Born, Niels Bohr, Albert

Einstein, Werner Heisenberg, Erwin Schrodinger, and Wolfgang Pauli. Quantum

mechanics was brought to life during the few short years of 1925 through 1927 by

most of these men.[11]

Dirac was the first to apply quantum mechanics to an electromagnetic

field, using the method of second quantization. This work contained the basis

for quantum field theory,[12] which Dirac called quantum electrodynamics.[13]

The singular delta function was invented by Dirac in order to prove two problems

were equivalent. He was working with the problems of “diagnolizing the energy

matrix in the Born–Heisenberg-Jordan theory” and “finding the energy

eigenvalues of Schrodinger’s wave equation.”[14] The delta function is now used

in many different areas of mathematics and physics and is considered basic. In

1926 he derived Balmer-spectrum energy levels of the hydrogen atom. He was the

first to derive the Lorentzian shape of spectral lines using quantum mechanics.

He introduced the terms bra and ket from the word bracket to denote the use of

parts of the bracket. The half brackets were for state vectors and their

eigenvalues. One of his major breakthroughs was the use of an algebraic version

of quantum mechanics based on Poisson brackets.

Dirac’s life was dedicated to physics with no interests outside of his

work, but, besides quantum mechanics, he did work on isotope separation,

magnetic monopoles, large-number hypothesis and other physics areas. The large-

number hypothesis was based on Dirac’s belief that very large constants should

not exist in nature. Somehow these large constants that did exist were a

consequence of the age of the universe.[15] One of the interesting implications

of his work that predicted the positron was the prediction of a magnetic

monopole. It is common knowledge that a magnet has a north and a south pole,

where opposites attract and sameness repels. The idea that a pole could exist in

isolation is quite foreign. Although theory predicts its existence, none has

ever been found. His work in isotope separation was a step from his theoretical

world into the world of experimental physics. He had done some work in the 1930s,

but stopped when his colleague, Peter Kapitza, found himself unable to leave the

Soviet Union, because Stalin had revoked the necessary exit permit.[16]

In the 1940s the war effort dragged Dirac back into isotope separation. A

group at Oxford was looking for an efficient means to do it. Dirac’s method

worked, but it was not considered the most cost effective. However, he did

continue to contribute to the effort, and even wrote a report on the statistical

method of isotope separation that contained concepts still used today.[17]

Dirac views on religion were very restricted. He seemed to have believed

that nothing was as important as his physics. Heisenberg related a story of an

exchange between Dirac and Wolfgang Pauli where Dirac expressed his agnostic

views. Pauli responded with “Dirac has a new religion. There is no God and Dirac

is his prophet.”[18] Dirac was a member of the Pontifical Academy of Sciences at

the Vatican, having written many papers for them. He was not anti-religious. His

wife maintained that he was deeply religious, but he has shown no evidence for

it.[19]