Paul Adrien Maurice Dirac is regarded as one of the greatest theoretical
physicists of the 20th century. In fact he will always rank one
of the greatest scientists of all time. Dirac’s work was mainly
concerned with a branch of science known as quantum mechanics. It
takes considerable time and effort to develop familiarity with quantum
mechanics. However, it is not something beyond comprehension. It
is quantum mechanics which has provided us the best model we have
of the physical reality. We find the use of quantum mechanics in
many technological applications including quantum optics and nanoelectronics.
It may not be very far away when computers will be developed based
on quantum logic. The present article does not attempt to explain
Dirac’s contribution in quantum mechanics but merely states
his accomplishments and briefly touches upon his other aspects of
life.
Dirac was a founder of quantum mechanics. In 1926,
slightly later than Max Born (18821970) and Pascual Jordan (190280)
in Germany, Dirac developed a general theoretical structure (formalism)
for quantum mechanics. By applying the ideas of Einstein’s
special theory of relativity to quantum mechanics, Dirac unified
the theories of quantum mechanics and relativity. This gave birth
to the relativistic form of quantum mechanics. His relativistic
quantum mechanics described the properties of the electron and corrected
the failure of Schrodinger’s theory to explain electron spin,
discovered by George Eugene Uhlenbeck (190088) and Samuel Abraham
Goudsmit (190278) in 1925. In his attempt to unify quantum mechanics
and relativity theory he came up with an elegant equation, which
is called Dirac equation. While working out the solution of his
equation in 1930, Dirac predicted the existence of antiparticle
of electron—a particle with the same properties as electron
but with positive charge. Carl David Anderson (190591) confirmed
Dirac’s prediction in 1932 by discovering a positively charged
electron, which he called positron. Dirac’s argument applies
all particles, and not just electrons. It meant wherever matter
existed its mirror or antimatter must also exist. Werner Heisenberg
termed Dirac’s prediction of antimatter as “the most
decisive discovery in connection with the properties or nature of
elementary particles.” Dirac’s vision of quantum mechanics
was marked by its generality and simplicity. Thus Albert Einstein
(18791955) said: “Dirac, to whom in my opinion we owe the
most logically perfect presentation of quantum mechanics.”
Niels Bohr (18851962) said: “Of all physicists, Dirac had
the purest soul”. Though Dirac’s work mainly concerned
with the mathematical and theoretical aspects of quantum mechanics,
but he also made outstanding work on the magnetic monopole, fundamental
length, the delta function, etc.
According to Dirac the principle of mathematical
beauty is the key concept in the relationship between mathematics
and physics. He said: “The research worker, in his efforts
to express the fundamental laws of Nature in mathematical form,
should strive for mathematical beauty. I should still take simplicity
into consideration in a subordinate way to beauty.”
Dirac had a scintillating academic career. He wrote
his first research paper at 22. At the age of 28 Dirac was elected
a Fellow of Royal Society of London. He became a Lucasian Professor
(a chair once held by Isaac Newton) at the Cambridge University
at 31. He received the Nobel Prize at 33. He produced about 200
research papers. Of these about 90 were devoted to the development
of quantum theory. All his papers were truly original and contained
pathbreaking ideas. N. Mukunda wrote: “The number of scientific
papers that Dirac wrote is not particularly great. A bibliography
compiled at the time of his 70th birthday contained a little over
one hundred publications; in all it may run to some 200 papers or
so. But the number and variety of entirely original and trailblazing
ideas in these papers are truly stupendous.” Dirac was something
more than a genius. The mathematician Mark Kac divided geniuses
into two classes—the ordinary geniuses and the “magicians”.
While one can imagine that the achievements of the first category
of geniusesthat is the ordinary geniuses, might be emulated by
others with enormous hard work and a bit of luck but the achievements
of the second category of geniuses or the so called the “magicians”
are so astounding that one fails to see how any human mind imagined
them. Dirac was truly a “magician”.
Dirac was born on August 08, 1902 in Bristol England.
His father Charles Adrien Ladislas Dirac taught French at the secondary
school attached to the Merchant Ventures College in Bristol. Charles
Dirac was a Swiss citizen and he was educated at the University
of Geneva. He came to England around 1888. Dirac’s mother
was Florence Hannah Holten, the daughter of a Master Mariner of
a Bristol Ship. Before her marriage, Florence was working in a library.
Dirac was one of three children. He had an older brother and a younger
sister. Dirac’s childhood was not a happy one. Dirac’s
father Charles was very strict with his children. He insisted that
only French be spoken at the dinner table. As there was no exception
to the rule, Dirac was the only person to dine with his father.
The other members of the family dined in the kitchen. Since Dirac
had to speak with his father only in French, he spoke very little.
He took lot of time to frame proper sentences. Perhaps this was
the reason for Dirac’s pronounced tendency to speak very little
and the utmost care he took in choosing words while speaking. Dirac
once said: “I had no social life at all as a child…My
father made a rule that I should talk to him in French. He thought
it would be good for me to learn French that way. Since I found
I could not express myself in French, it was better for me to stay
silent than talk English. So I became very silent from an early
age.” Because of his father’s dominating personality
hardly anybody came to meet the Diracs. Dirac’s elder brother
Reginald Charles Felix Dirac wanted to become a physician but his
father forced him to study mechanical engineering at Bristol. He
obtained a third class degree and he started working as a draftsman
with an engineering firm. Reginald committed suicide at 24. After
this incident Dirac was totally elienated with his father. Perhaps
Dirac thought his father was in some way responsible for his brother’s
suicide.
The first school, which Dirac attended, was Bishop
Primary School. Dirac’s exceptional mathematical ability showed
itself at an early age. In his school he was given rather advanced
books on mathematics for independent study. His father also encouraged
his son to develop his mathematical ability. At the age of 12 Dirac
entered the Merchant Ventures Secondary School. Commenting on his
school Dirac wrote: “The Merchant Ventures was an excellent
school for science and modern languages. There was no Latin or Greek,
something of which I was rather glad, because I did not appreciate
the value of old cultures. I consider myself very lucky in having
been able to attend the school…I was rushed through the lower
forms, and was introduced at an especially early age to the basis
of mathematics, physics and chemistry in the higher forms. In mathematics
I was studying from books, which mostly were ahead of the rest of
the class. The rapid advancement was a great help to me in my latter
career.”
After completing his secondary school education
in 1918, Dirac decided to study electrical engineering at the University
of Bristol. This is in spite of the fact that his favourite subject
was mathematics. However, in those days the only possible career
for a mathematician was school teaching. As Dirac wanted to avoid
the profession of a school teacher, he ended up in studying electrical
engineering. He obtained his degree in electrical engineering in
1921. However, he could not find a permanent job as an engineer.
In the meantime his interest in mathematics had become more intense.
He unsuccessfully attempted to study mathematics at Cambridge. The
reason for his not been able to study mathematics at Cambridge was
financial. Though he obtained a scholarship to study mathematics
at St John’s College at Cambridge but it was not enough for
meeting his financial needs. He failed to get additional support
from the local education authority. He was not given the additional
support because his father had not been a British citizen long enough
for his son to be eligible for such support. However, Dirac got
an opportunity to study mathematics at the Bristol University without
paying fees.
As a student of electrical engineering he did hardly
any experimental work. In any case Dirac was not good at practical
work. He did not appreciate the fact that topics such as atomic
physics and Maxwell’s electromagnetic theory were excluded
from electrical engineering course. However, his engineering studies
had a bearing on his future work in mathematical physics. Particularly
the use of approximations that he learnt while studying engineering
exerted a strong influence on his later work. The use of approximation
strengthened his confidence in the intuitive approach to problem
solving and which in turn led him to believe that to construct a
theory expressing fundamental law of nature one need not have the
exact knowledge of actualities. It can be done being guided by intuition.
He was of the opinion that a physicist must be satisfied to work
only with approximate knowledge of reality—the actual phenomena
were too complex to be understood in a precise way. On the influence
of engineering studies on his work in mathematical physics Dirac
himself said : “If I had not this engineering training I should
not have had any success with the kind of work that I did later
on, because it was really necessary to get away from the point of
view that one should deal only with results which could be deduced
from known exact laws, in which one had implicit faith.”
He obtained a first class honours degree in mathematics in 1923
and he was awarded a grant to undertake research at Cambridge. Because
of his fascination with the general theory of relativity, Dirac
was interested in working with Ebenezer Cunningham. But Cunningham
had as many students as he was prepared to take and so Dirac started
working under the supervision of Ralph Howard Fowler(18991944),
who had collaborated with Niels Bohr in his pioneering work in atomic
physics. R. H. Dalitz and R. Peierls while writing on Dirac in Biographical
Memoirs of Fellows of the Royal Society of London, wrote: “Fowler
was then the leading theoretician in Cambridge, well versed in the
quantum theory of atoms; his own research was mostly on statistical
mechanics. He recognized in Dirac a student of unusual ability.
Under his influence Dirac worked on some problems in statistical
mechanics. Within six months of arriving in Cambridge he wrote two
papers on these problems. No doubt Fowler aroused his interest in
the quantum theory, and in May 1924 Dirac completed his first paper
dealing with quantum problem. Four more papers were completed by
November 1925.”
It was after going through the proofs of Werner
Heisenberg’s paper on uncertainty principles that Dirac got
a clue to formulate for the first time a mathematically consistent
general theory of quantum mechanics in correspondence with Hamiltonian
mechanics. The paper was sent to Fowler and who in turn passed it
to Dirac. After reading the paper for the second time Dirac realized
“that it (Heisenberg’s paper) provided the key to the
problem of quantum mechanics. Dirac’s work on quantum mechanics
became the basis for his Doctoral thesis on Quantum Mechanics. It
is important to note that before submission his doctoral thesis,
Dirac had published eleven papers. Dirac was awarded a PhD degree
in 1926. He then went to Copenhagen to work with Niels Bohr. From
Copenhagen he moved to Gottingen in February 1927 where he interacted
with J. Robert Oppenheimer (190467), Max Born, James Franck (18821964)
and Igor Yevgenevich Tamm (18951971). He also spent a few weeks
in Leiden before he returned to Cambridge.
In 1927 Dirac was elected a Fellow of St John’s
College, Cambridge. In 1930 Dirac was elected a Fellow of Royal
Society of London. He was only 28 years old. What is more Dirac
was given the honour on the very first occasion his name was put
forward. This was an indication of the extremely high opinion that
Dirac’s fellow scientists had of him. In 1930 Dirac published
The Principles of Quantum Mechanics. In this book Dirac developed
the socalled transformation theory of quantum mechanics that furnished
a machinery for calculating the statistical distribution of certain
variables when others are specified. Commenting on the book one
reviewer wrote: “ Dirac was not influenced by the feeding
frenzy in experimental phenomenology of the time. This has given
Dirac’s book …a lasting quality that few works match.”
This book confirmed Dirac’s stature as the 20th century Newton
in the minds of many physicists. Thus N. Mukunda wrote: “
This book is often compared for its spirit and style to the Principia
of Isaac Newton.” It has guided several generations of physicists.
His other published works include Lectures on Quantum Mechanics
(1966), The Development of Quantum Theory (1971), Spinors in Hilbert
Space (1974), and General Theory of Relativity (1975 ).
In 1932, Dirac was appointed Lucasian professor
of mathematics at the Cambridge University. He held this post for
37 years. The post was once held by Isaac Newton. Stephen Hawking
succeeded Dirac.
In 1937 Dirac married Eugene Paul Wigner’s
sister Margit, whom she met at Priceton. This was second marriage
for Margit. She had two children Judith and Gabriel Andrew from
her first marriage. Both the children adopted the name of Dirac.
Dirac was an extremely modest man. He never talked
about the importance of his own work. He was ever ready to acknowledge
his debt to others. Once commenting on his work Dirac said: “Well,
from the initial idea of Heisenberg, one could make fairly rapid
development, and I was able to join in it. I was just a research
student at that time. I was lucky enough to be born at the right
time to make it possible for that to be so.” On another occasion
he said: “It was very easy in those days for any secondrate
physicist to do firstrate work. There has not been such a glorious
time since then. It is very difficult now for a first rate physicist
to do secondrate work”.
Dirac had an unusual personality. He was extremely shy. He avoided
company. Dirac spent most of his time alone in libraries. His only
pastime was solitary walk. He was reluctant to take part in conversation.
Dirac is wellknown for clarity and simplicity in his writing. Bohr
commenting on Dirac’s style of writing said: “Whenever
Dirac send me a manuscript, the writing is so neat and free of corrections
that merely looking at it is an aesthetic pleasure. If I suggest
even minor changes, Paul becomes terribly unhappy and generally
changes nothing at all.”
Like many other great personalities innumerable
stories have become attached to Dirac. Most of these stories had
to do with Dirac’s unusual logic and precision that he adopted
while interacting with world. Often such stories do not represent
the true facts. But in case of Dirac all the stories are claimed
to be true. George Gamow in his Thirty Years that Shook Physics
wrote: “Now it often happens that ‘absent minded professor’
stories grow up around famous scientists. In most cases these stories
are not true, merely inventions of wags, but in case of Dirac all
the stories are really true, at least in the opinion of this writer…
Being a great theoretical physicist, Dirac liked to theorise about
all the problems of daily life, rather than to find solutions by
direct experiment. Once at a party at Copenhagen, he proposed a
theory according to which there must be a certain distance at which
a woman’s face looks its best. He argued that at d=infinite
one cannot see anything anyway, while at d=0 the oval of the face
is deformed because of the small aperture of the human eye, and
many other imperfections (such as small wrinkles) become exaggerated.
‘Tell me, Paul,’ I asked, ‘how close you have
seen a woman’s face?’ ‘Oh’, replied Dirac,
holding his palms about two feet apart, ‘about that close’”.
After Dirac delivered a lecture at the University of Toronto, somebody
in audience asked during the question period; “Professor Dirac,
I do not understand how you derived the formula on the top left
side of the blackboard.” Dirac did not reply. He simply said:
“This is not a question, it is a statement. Next question,
please.” As mentioned earlier that Dirac’s writing was
marked for its clarity and simplicity. Niels Bohr, while writing
a paper with many hesitations and redrafting once remarked in Dirac’s
presence : “ I do not know how to finish this sentence.”
To this Dirac replied: “I was taught at school that you should
never start a sentence without knowing the end of it.” Once
Leonidovich Pjotr Kapitza (18941984) had given an English translation
of Dostoevski’s Crime and Punishment. When Dirac went to return
the book, Kaptza asked: “Well, how do you like it?”
Dirac’s only comment was: “It is nice, but in one of
the chapters the author made a mistake. He describes the Sun rising
twice on the same day.” An interesting interaction with Dirac
was narrated by his colleague Jagdish Mehra: “The weather
outside was very bad, and since in England it is always respectable
to start a conversation with the weather, I said to Dirac, ‘t
is very windy, Professor.’ He said nothing at all, and a few
seconds later he got up and left. I was mortified, as I thought
that I had somehow offended him. He went to the door, opened it,
looked out, came back, sat down, and said, ‘Yes.’”
Dirac traveled extensively and studied at various
foreign universities including Copenhagen, Gottingen, Leyden, Wisconsin,
Michigan and Princeton. Dirac visited the erstwhile Soviet Union
a number of times. During 1973 and 1975 Dirac lectured on the problems
of cosmology in the Physical Engineering Institute in Leningrad.
Dirac also visited India. After retiring from the Lucasian Chair
of Mathematics at Cambridge in 1969, Dirac went with his family
to Florida in United States of America. He held visiting lecturership
at four US universities before he was appointed Professor of Physics
at Florida State University in 1971.
Dirac received the Nobel Prize in Physics 1933
at the age of 33. He shared the Prize with Erwin Schrodinger (18871963).
At the first instance Dirac was contemplating to turn down the Prize
on the grounds that he did not relish publicity. But on being pointed
out that he would receive far more publicity in case he decided
to refuse the Prize, he accepted it. Though Dirac could invite his
parents but he only invited his mother and not his father, a reflection
of his strained relation with his father. Some of the other honours
that Dirac received are: Fellow of the Royal Society of London (1930),
the Order of Merit (1933), Royal Society Royal Medal (1939), Royal
Society Copley Medal (1952), Royal Socity Bakerian lecturer (1941).
While Dirac refused to accept honorary degrees but he accepted membership
of academic societies. Among these academic bodies included USSR
Academy of Sciences (1931), Indian Academy of Sciences (1939), Chinese
Physical Society (1943), Royal Irish Academy (1944), Royal Society
of Edinburgh (1946), Instut de France (1946), National Institute
of Science of India (1947), American Physical Society (1948), Pontifical
Academy of Sciences, Vatican City (1958), Royal Danish Academy (1962)
and Academy of Sciences Paris (1963).
Dirac died on October 20, 1984 in Tallahassee, Florida, USA. In
November 1995 a plaque was unveiled in Westminster Abbey commemorating
Paul Dirac. The memorial address was present by Stephen Hawking.
We would like to end this article by quoting Dirac
on what he had to say about quantum mechanics: “… the
present form of quantum mechanics should not be considered as the
final form. There are great difficulties…with the present
quantum mechanics. It is the best that one can do up till now. But
one should not suppose that it will survive indefinitely into the
future. And I think that it quite likely that at some future time
we may get an improved quantum mechanics in which there will be
a return to determinism and which will, therefore, justify the Einstein
point of view.”
References
 Dirac: A Scientific Biography by Cambridge: Cambridge University
Press, 1990.
 Reminiscences About a Great Physicist: Paul Adrien Maurice
Dirac. Edited by Behram N. Kursunoglu and Eugene P. Wigner. Cambridge:
Cambridge University Press, 1987.
 Images of Twentieth Century Physics by N. Mukunda. Hyderabad:
Universities Press India Limited, 2000. (Published in collaboration
with Jawaharlal Nehru Centre for Advanced Scientific Research,
Bangalore).
 The Oxford Companion to the History of Modern Science J. L.
Heilborn (edited by). Oxford: Oxford University Press, 2003.
 The Cambridge Dictionary of Scientists (Second edition) by
David, Ian, John and Margaret Millar. Cambridge: Cambridge University
Press, 2002.
 A Dictionary of Scientists. Oford: Oxford University Press,
1999.
 The History of Science from 1895 to 1945 by Ray Spangenburg
and Diane K. Moser. Hyderabad: Universities Press (India) Limited,
1999.
 Chambers Biographical Dictionary. New York: Chambers Harrap
Publishers Ltd., 1997.
 Paths of Innovators by R. Parthasarathy. Chennai: East West
Books (Madars) Private Ltd., 2000.
1. Paul Dirac
2. Max Born
3. Pascual Jordan
4. George Eugene Uhlenbeck
5. Samuel Abraham Goudsmit
6. Carl David Anderson
7. Niels Bohr
8. Albert Einstein
9. Ralph Howard Fowler
10. Robert Oppenheimer
11. James Franck
12. Igor Yevgenevich Tamm
13. Eugene Paul Wigner
14. Kapitza Leonidorvich Pjtr
15. Erwin Schrodinger
