This blog post examines how Paul Dirac opened new horizons in quantum mechanics with his cold, rational mind and explores the impact of his achievements on modern physics.
“If you pluck a flower on Earth, the stars at the edge of the universe will move.”
This statement was made by British-born theoretical physicist Paul Dirac regarding gravity. At first glance, it seems an incredibly romantic and poetic expression, hardly what one would expect from a physicist. Yet he is also famous for the following anecdote. One day, Dirac was waiting for someone at a castle. When another guest remarked, “Ghosts appear at midnight in this castle,” Dirac asked, “Is midnight based on Greenwich Mean Time or daylight saving time?” This anecdote makes Dirac seem like a cold, unfeeling person. Yet he was a scientist who achieved extraordinary accomplishments in physics, particularly quantum mechanics, and had many episodes in his life. What kind of person was he, and what impact did he have on physics, especially quantum mechanics?
Paul Dirac was born in England in August 1902. The early 20th century, when he was born, was a time when the established order of classical physics, solidified since Newton, was being completely overturned, and new theories and laws were emerging. Problems with classical physics were being reported one after another across Europe, and physicists were grappling with how to solve them. Dirac grew up under a very strict father. His father insisted he speak only French at home, but Dirac, who did not know French well, naturally developed a quiet and isolated personality. He later recalled that it was only when he saw his father grieving after his brother’s suicide that he first realized parents should love their children.
Dirac studied electrical engineering at Bristol University but found little interest in it. He later studied physics at Cambridge University. In 1925, after reading Heisenberg’s paper sent by mail from Professor Fowler, he published his life-changing quantum theory. Dirac’s quantum theory stated that visually representing atomic models was meaningless; they could only be described through mathematical calculations. This developed Heisenberg’s theory and served to connect quantum theory, which had only recently emerged, with classical mechanics. After gaining recognition from authoritative physicists, Dirac accelerated his research.
At the time, the physics community was struggling to find a connection between the theory of relativity and quantum theory. Relativity applied when an object’s speed approached the speed of light, while quantum theory was introduced to understand physical phenomena at the atomic scale that classical mechanics couldn’t explain. These two great theories had developed independently for about 30 years without any significant connection being found. Before Dirac, Schrödinger had attempted this process first but failed to describe the motion of electrons, resulting in the publication of a non-relativistic equation. While studying Schrödinger’s equation, Dirac discovered a method in 1928 to apply relativity to describe the structure of electrons, ultimately proposing the Dirac equation. The Dirac equation described the physical behavior of fermionic particles with half-integer spin, such as electrons, protons, and neutrons, and predicted the existence of anti-particles, a concept unfamiliar at the time.
In the quantum mechanics developed by Dirac, the physical state of a single particle or a system of multiple particles could be represented as a function of space and time. This state contained all information about the system obtainable through observation. Dirac treated the electromagnetic field as a collection of oscillators, each of which could represent a single photon. Through this method, Dirac transformed classical Maxwell’s electromagnetic field into quantum mechanical oscillators, demonstrating that each oscillator satisfies its own Schrödinger wave equation. This groundbreaking achievement marked the beginning of what is now called ‘quantum field theory’ and is extensively utilized by high-energy particle physicists today. By introducing distinct oscillators to represent the electromagnetic field, Dirac replaced a continuous quantity—difficult to handle in quantum mechanics—with a discrete one. According to anecdote, Dirac conceived the correct equation while gazing at a fireplace, pondering what would happen if the coefficients in Schrödinger’s equation were matrices instead of numbers. He advanced Schrödinger’s six months of research in just a few hours. In 1932, the experimental discovery of the positron, one of the antiparticles predicted by Dirac’s equation, sent shockwaves through the physics community. The discovery of antiparticles opened new horizons for physics studying the nature of matter and set a new milestone for theoretical research in particle physics exploring smaller fundamental particles.
Dirac made a major contribution to the development of quantum mechanics through his prediction of antiparticles and the discovery of a new physical form capable of describing atomic theory. In recognition of these achievements, he was awarded the Nobel Prize in Physics in 1933 at the young age of 31. When he heard he would receive the Nobel Prize, he initially intended to decline it, disliking media attention. However, Rutherford’s advice that refusing the prize would draw even more attention ultimately led him to accept it. In 1932, he was appointed to the Lucasian Professorship of Mathematics at Cambridge University, succeeding Joseph Lammer. This position, previously held by Newton and Stephen Hawking, is one of the most prestigious university professorships in Britain. He continued his prolific research in Fermi-Dirac statistics, quantum field theory, and quantum electrodynamics, which statistically describe the properties of subatomic particles with half-integer spin. In 1971, he moved to the United States, conducting research at the University of Miami’s Center for Theoretical Physics. He later devoted himself to research and teaching at Florida State University, passing away on October 20, 1984, at the age of 82. To honor his achievements, the International Centre for Theoretical Physics (ICTP) awards the Dirac Medal to theoretical physicists.
Richard Feynman, a Nobel laureate in physics renowned for his popular lectures, reportedly said after becoming famous for quantum electrodynamics: “Dirac had already done everything! I don’t know why I’m making such a fuss!” Another paper states: “Dirac’s achievements are on par with Bohr’s, and only Einstein surpasses him!” Dirac did not seek attention and possessed a reserved personality. Perhaps because of this, he is not a widely famous scientist. Yet, Dirac is undoubtedly one of the founders of quantum mechanics, which dominates modern physics, and a great scientist who opened a new world in physics—a figure unlikely to be seen again in human history.
