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Paul Adrien Maurice Dirac

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.

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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

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