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Paul Dirac and the Origins of Quantum Mechanics

Written by Kat Jivkova. Quantum Mechanics is as mystifying as it is precise, able to produce predictions with a high degree of accuracy. But where did some of its ideas originate?

Quantum mechanics in abstract terms is an intricate theory which explains how the microscopic world underpins the macroscopic one. It depends on three main principles: (1) granularity, meaning that the universe is built from discrete chunks of matter or energy; (2) indeterminacy, the idea that elementary particles are in infinitely many states and one is realised only when they interact with something; and (3) relationality, which suggests the universe depends on how things interact and ensue. The counterintuitive yet precise theory of quantum mechanics has been developed, particularly over the first half of the twentieth century, by several physicists, from Max Planck and Niels Bohr to Erwin Schrödinger and Werner Heisenberg. The strangest and perhaps most significant contributor, however, is Paul Dirac, who established the first and most widely used mathematically rigorous formulation of the theory.

Dirac himself was a bizarre man and a misfit. Farmelo’s biography of Dirac titled The Strangest Man delves into the physicist’s life beyond his scientific achievements, uncovering his character in a raw form. He struggled greatly with human engagement and was enormously reticent, usually found responding to his peers in a monosyllabic manner. While others may have channelled their angst through poetry or painting, Dirac expressed himself through mathematical equations. As a young student, he studied engineering in Bristol while his free time was used to read up on physics; at this stage, physics was still a very evolving field of study, with physicists hunting for the meaning of reality. It was undoubtedly Britain’s solar eclipse expeditions that stimulated Dirac’s passion, for this had predicted Einstein’s shift in the stars adjacent to the Sun’s occulted disc. Therefore, physics had been transformed from a traditional Newtonian study to a relativistic one. Dirac wrote, “A wonderful thing happened. Relativity burst on the world.” This revelation set the tone for Dirac’s work in the progression of quantum mechanics.

Dirac’s impetus into research on quantum mechanics began with his enrolment at Cambridge in 1923 and meeting with series of prominent physicists. He first met Niels Bohr in 1925 during a talk given by the latter on the faults of quantum theory. Dirac was quick to criticise Bohr, stating that his arguments were not supported by facts, but by qualitative statements. In the same year, he met Heisenberg, who had published his own paper on quantum mechanics, and upon reading this, Dirac’s interest for the field was reasserted. Unquestionably, these two physicists exacerbated Dirac’s desire to challenge the current notions of quantum theory and he did this in a way which certainly reflected his own character; it, therefore, comes as of no surprise that Dirac used mathematics to create a new insight into quantum physics.

Notably, when Heisenberg published his first paper on quantum mechanics, Dirac was initially left stunned, and he later centred the concept of his own work around Heisenberg’s findings. He quickly admitted that it was truly “the most important idea that was introduced by Heisenberg” – Heisenberg won the Nobel Prize in Physics in 1932 for the creation of quantum mechanics. In Dirac’s first paper on the subject, he invented his own notations which are still currently used, where q stands for quantum and c stands for classical, while also using the equation pq — qp = h/2i. Interestingly, this equation was composed by Heisenberg and later developed by Jordan and Born in 1925, which created the foundations of matrix multiplication and the matrix mechanics formulation. It was nicknamed “the sharpened quantum condition.”

A significant milestone in Dirac’s work was undoubtedly achieved in Copenhagen. Dirac completed a thesis titled “Quantum Mechanics” in 1926, thus receiving his PhD, and was therefore free to travel around Europe upon completing his doctorate, meeting scientists such as Einstein and Schrödinger in the process. In Copenhagen, he worked with a series of recognised transformations in quantum theory, later acknowledged to comprise the transformation theory; this referred to the fluctuations of a quantum state in its infinite Euclidian space through a series of vectors. He explored the use of vectors beautifully, describing the transformation theory as his “darling”. One further importance marked by his Copenhagen visit was his development of quantum electrodynamics, which describes the interactions between light and matter. In his papers written on the subject, he managed to create an eminent description of light quanta by quantising the electromagnetic field, thus formulating a very elaborate theory of radiation.  

Dirac’s most famous advancements in quantum theory stemmed from his electron equation, which described the spin of the electron.  Physicist Frank Wilczek referred to the equation as “achingly beautiful.” This relativistic equation united quantum mechanics and Einstein’s Theory of Special Relativity, building a foundation for the later Quantum Field Theory and the Standard Model of Particle Physics. Crucially, the equation relied on the existence of a, previously unknown, positively charged partner to the negatively charged electron. This explains Dirac’s model of a vacuum-sealed sea of negatively charged electrons, whereby any “hole” within this would appear positively charged. At first, it was thought that the positively charged particles (the holes) pervading this vacuum were protons. However, Wolfgang Pauli argued that the protons would need to have the same mass as electrons for the equations to work. Further, previous experiments had not revealed such a particle.

In 1931, Dirac coined the term “anti-electron” to fit his equation, though its existence was doubted by other physicists. Dirac’s luck drastically changed the following year with Carl Anderson’s discovery of the “positron”, which confirmed the existence of a positively charged particle with an electron’s mass. Dirac’s theoretical work on this antielectron was validated, though he himself acknowledged that this position could have easily been found “in a single afternoon” had it not been for his cowardice in failing to push experimentalists to hunt for the particle. These theories paved the way for the study of an entirely avant-garde realm of physics: antimatter. Antimatter is identical to matter in every way but has an opposing charge – a positron (antimatter) has the same mass but opposite charge to the electron (matter). Contact between matter and antimatter annihilates both particles. Research into antimatter continues, particularly at CERN (European Council for Nuclear Research) where an Antiproton Decelerator is being used to investigate the properties of antiprotons.

Paul Dirac was certainly a genius of his time. He helped to pioneer the emerging field of quantum mechanics, winning the Nobel Prize in Physics alongside Schrödinger in 1933 for advancements in atomic theory. Aged 31, Dirac was the youngest to have been awarded the prize. However, it was his dedication to quantum mechanics which should be recognised as his most important achievement. While the origins of quantum mechanics can be traced back to Heisenberg, it was Dirac who opened a gateway for new branches within quantum theory to be researched through his mathematical expression. His equation authenticated the study of theoretical physics and predicted the existence of antimatter, as proven by the discovery of the positron. Nevertheless, there are still foundational problems concerning quantum physics which physicists face today, mainly the unification of loop quantum gravity with general relativity. Dirac managed to combine quantum mechanics and special relativity within a single equation – who will be the next physicist to unify the two current theories?

Written by Kat Jivkova

Bibliography

CERN. ‘Antimatter’ [Online]. [Accessed on 4 November 2020]. https://home.cern/science/physics/antimatter

Close, Frank. ‘Paul Dirac: a physicist of few words: a detailed biography argues that the Nobel prizewinner’s notorious reticence delayed experimentalists from discovering the antimatter that would confirm his elegant theory.’ Nature Publishing Group Vol.459 (2009): 326.

Hirshfeld, Alan. “The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom.’ American Journal of Physics 78 (2010): 445-446.

Pais, Abraham, Maurice Jacob, David I. Olive, and Michael F. Atiyah. “Paul Dirac: Aspects of His Life and Work.” In Paul Dirac: The Man and His Work, 1–45. Cambridge: Cambridge University Press, 1998.

Sack, Harald. “Carl David Anderson and the Discovery of the Positron.” [Online]. [Accessed on 4 November 2020]. http://scihi.org/carl-david-anderson-positron/.

Vervloet, Alex. “Quantum Mechanics and Existentialism: Removing my Fear of Death.” [Online]. [Accessed on 4 November 2020]. https://medium.com/@alexvervloet/quantum-mechanics-and-existentialism-removing-my-fear-of-death-e58931c03d14

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