“Of all the equations of physics, perhaps
the most magical is the Dirac equation.” Remarked MIT physics professor Frank Wilczek. Paul Dirac believed that the
fundamental laws governing the universe could be expressed
through “pretty mathematics” When he wrote down an equation to describe
the electront, he noticed something odd. His equation predicted the existence of
antimatter - the mirror image of matter. If matter is like the salt flats
of the Salar de Uyuni in Bolivia, antimatter emerges as its reflection, revealing
the mysterious symmetry of the universe. Dirac predicted the existence of the antimatter
counterpart to the electron, the positron. Subatomic particles with the same
mass as electrons that carry a positive electric charge in contrast
to the electron’s negative charge. If the two come into contact, they annihilate
each other, converting both particles into energy. For a man best described as
an agnostic, he remarked, “God is a mathematician of a very high order.” Dirac was a lonely man who grew up
a lonely boy and this had a profound impact on his personality and possibly
also his work as a theoretical physicist. He told a colleague, “I never
knew love or affection when I was a child,” as described in the book
“The Strangest Man” by Graham Farmelo. Paul Dirac’s father, Charles, insisted his three
children speak to him in his native French. At dinner, Paul would sit in the living room
eating with his father, while his older brother Felix and younger sister Betty ate in the kitchen,
having dinner with their British mother Florence. When Paul mispronounced a word
in French or misgendered a noun, his father punished him by making him stay
put, even if he felt like throwing up. Paul Dirac reflected, “Since I found
that I couldn’t express myself in French, it was better for me to stay silent.” He remained quiet into adulthood.
Preferring to work alone. He spoke so little that his
colleagues jokingly defined a unit called a "Dirac" as one word per hour. Charles’ strict educational regime at
home mirrored how he taught French at the Merchant Venturer’s School in
Bristol, where Paul was a student. World War One indirectly benefited Paul; as the
older students left for military service, it freed up space and resources for him to advance through
the upper classes, accelerating his learning. His father insisted that he and his brother
study engineering at Merchant Venturer’s College, which was eventually absorbed
by the University of Bristol. However, Paul was not cut out for
such a life; one summer spent as a trainee engineer in a factory resulted in a
report describing him as a “positive menace” When he failed to find employme nt upon
graduation owing to the serious post-war economic depression, his father suggested
he study at the University of Cambridge. Dirac secured a spot, but couldn’t get
a big enough scholarship to attend. Instead, the head of Bristol University’s
mathematics department arranged for him to get an applied mathematics degree
which he finished in two years. When he applied to Cambridge again, he
was able to secure the financial aid that he needed, allowing him to enroll
as a graduate research student in 1923. He was lucky to study under Ralph Fowler, a
distinguished physicist who introduced Dirac to the cutting-edge field of quantum mechanics, the
science of the very small, atoms and particles. Dirac lived and breathed science, even while
taking long walks by himself on Sundays. Fowler’s lectures on Niels Bohr’s
theory of the atom fascinated Dirac. Much like planets orbiting
the sun in a fixed path, Bohr suggested that electrons orbit at
certain distances from the nucleus of an atom. However, Dirac noticed that Bohr's ideas
didn't fully explain how electrons behaved in atoms more complex than hydrogen,
nor did it consider how electrons act when moving very fast, as described by
Einstein's special theory of relativity. While Paul was developing his
own theories at Cambridge, his brother Felix was toiling
away at a factory in Birmingham. Wondering would might have been had he
followed his own dream of becoming a doctor. Instead, his father forced him into engineering. Miserable, and making little money, Felix’s body was found beside a
bottle of poison in January 1925. He was 24 years old. Paul was surprised by his parents’ grief, telling
a friend decades later: “I didn’t know they cared so much…I never knew that parents ought to care
for their children, but from then on I knew.” Charles Dirac was in such deep grief that his
doctor advised him to take a year off work. Paul carried on at Cambridge. In the summer of that year, his supervisor,
Fowler, introduced him to a groundbreaking paper by German theoretical physicist Werner
Heisenberg that would change Dirac’s life. Heisenberg proposed a new way of
understanding atoms, challenging Bohr’s model of electrons in fixed orbits.
Since the exact paths of electrons cannot be measured, he suggested
focusing on what can be measured, such as the energy levels of electrons.
Heisenberg developed matrix mechanics, a mathematical framework to describe
the jumps between energy levels. Imagine your car going from 0 to 60 miles
per hour instantly without moving through intermediate speeds, akin to an electron skipping
steps as it transitions between energy states. Shortly after, Austrian physicist Erwin
Schrödinger presented a different view, depicting particles as waves
spread through space. This model accounts for strange phenomena
like the double-slit experiment, where electrons act like waves rather than
particles, creating interference patterns. Heisenberg’s matrix mechanics and Schrodinger’s
wave mechanics are different ways of describing the same quantum phenomena, like
reading the same book in two languages. Author Farmelo described their impact
this way: “Heisenberg and Schrödinger had knifed a sack of gemstones, and the
race was on to pick out the diamonds.” Dirac took both their ideas and ran with them.
Published in January 1928, the Dirac equation accurately describes the behavior
of electrons moving at any speed. The equation introduced spin - a
quantum property providing particles with intrinsic angular momentum, much
like the spin of a planet on its axis. American theoretical physicist John Van
Vleck likened Dirac’s explanation of spin to Yet, within the beauty of the
Dirac equation lay an anomaly. It allowed for electrons
to have negative energy. This baffled scientists
because, in classical physics, the energy of electrons, like that
of all objects, is always positive. Dirac proposed a bold solution to this conundrum. He suggested the existence of a “sea” of
negative energy states filled with electrons. Should an electron escape the
sea by gaining sufficient energy, it transitions to a positive energy
state, leaving behind a “hole”. The hole isn’t filled by another electron
due to the Pauli exclusion principle, which prevents two electrons
from occupying the same state. This “hole” behaves like a
positively charged particle, identical in mass but opposite in charge to the
electron, acting as its antimatter counterpart. So Dirac’s theory not only resolved the negative
energy puzzle but predicted the existence of antimatter, based purely on mathematical
logic rather than empirical evidence. His hypothesis was met with skepticism. Farmelo, in his book, describes
how: “...the critical chorus had swelled from a whisper to a roar.”
Heisenberg was concerned he might be wrong. So was physicist Wolfgang Pauli. Bohr was among those who were
skeptical of the hole theory, and he confronted Dirac directly,
asking, “Do you believe all that stuff?” Dirac simply responded: “‘I don't think anyone
has put a conclusive argument against it.’” He would be proved right a few years later. In 1932, Carl Anderson at Caltech
was observing the effects of cosmic rays within his cloud chamber.
He captured a photo of a charged particle, curving in a manner that
indicated a positive charge. Anderson had stumbled upon the positron, the antiparticle to the electron, providing the
empirical evidence to support Dirac’s theory. When asked later why he did not speak
out more boldly to predict the positron, Dirac said it was because of “pure cowardice”. He was ecstatic about his theory but
was also afraid of being proved wrong. Anderson’s confirmation of the existence
of the positron catapulted Dirac to fame. The following year, 1933, he was
awarded the Nobel Prize in Physics alongside Schrodinger for their
contributions to atomic theory. Dirac was initially reluctant to
accept the Prize as he hated publicity, but when others pointed out he’d receive even
more publicity for turning it down, he accepted. At 31, he stood atop the scientific world, his contributions defying the
expectations of his peers. His personal life was also
poised to defy expectations. He was so quiet and awkward that there was
never any expectation that he would find love. Dirac once asked Heisenberg why he danced,
to which Heisenberg replied it was a pleasure to dance with nice girls.
Dirac responded: 'Heisenberg, how do you know beforehand that the girls are
nice?'" as described by Farmelo in his book. Despite his social awkwardness, he managed to
find a partner who understood his unique mind. In the 1930s, during his sabbatical at the
Institute for Advanced Study in Princeton, New Jersey, his colleague,
physicist Eugene Wigner, introduced him to his sister
Manci who was visiting. What began as a friendship blossomed into more, despite Dirac’s initial hesitation,
articulated in this letter to Manci: “You should know that I am not in love
with you. It would be wrong for me to pretend that I am. As I have never been in
love I cannot understand fine feelings.” This didn’t deter Manci. They later married, and Dirac
raised Manci’s two children from her first marriage and together,
they welcomed two more children. They settled in Cambridge, where Dirac held
the Lucasian Professorship of Mathematics at the University of Cambridge, one
of the world's most prestigious academic posts for over three decades.
By the late sixties, his scientific work began to take a backseat to his home life,
where he began to focus on his gardening. It was time for a change. Dirac had always enjoyed his visits to America and now sought to settle there
with his wife permanently. When he was appointed professor of physics at
Florida State University, a department then ranked 83rd in the U.S., the department head likened it
to the English faculty recruiting Shakespeare. Despite such high praise, Dirac did
not view himself in the same light. In a candid conversation with physicist
Pierre Ramond of the University of Florida, Dirac confided: “My life has been a failure!” That shocked Ramond.
Author Farmelo described it this way: “Ramond would have been less stunned if Dirac had
smashed him over the head with a baseball bat.” Dirac’s dissatisfaction stemmed from the
failure of quantum mechanics to explain something as simple as the interaction
between a n electron and photon without resorting to infinite values, making
him view his work as unsatisfactory. Ramond was shattered by Dirac’s assessment,
remarking: “I could hardly believe that such a great man could look back on his life as a
failure. What did that say about the rest of us?” Yet, in the eyes of the world,
Dirac is far from a failure. In a testament to his enduring legacy,
Dirac’s equation—a cornerstone of quantum mechanics—was immortalized on the
stone floor of Westminster Abbey. Dirac lived out the rest of his
years in Tallahassee, Florida. On October 20, 1984, he died of heart
failure at home with his wife by his side. He was 82 years old. One of the most profound implications of Dirac’s
work is the asymmetry in matter and antimatter. According to standard physics models,
the Big Bang should have produced equal amounts of matter and antimatter, meaning
they would have annihilated each other, leaving a universe filled only with energy. And yet, our universe is dominated by matter,
which makes possible the formation of stars, galaxies, and everything we
see, including ourselves. It remains one of the great mysteries in physics. Paul Dirac unlocked the mysteries of the
universe through his profound understanding of the fundamental principles
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