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Paul Dirac: The most beautiful equation

The godfather of Modern Quantum Mechanics

Paul Dirac was one of the most significant — and curious — characters in the annals of physics. His contributions to both quantum mechanics and mathematics are both varied and considerable, from the Dirac equation, to early work on quantum field theory that forms the backbone of superstring theories, to experimenting with uranium enrichment for the Manhattan Project. He proposed the existence of both antimatter and magnetic monopoles as natural consequences of equations he derived. He had a very mathematical approach to theoretical physics that continues to inspire and awe researchers around the world to this day.

Dirac was nearly as famous among his colleagues in the academic elite for his quirky personality as he was for his research. Taciturn in the extreme, his fellow researchers at Cambridge went so far as to define a new unit called a dirac, which was equal to one word an hour. Indeed, during his postgraduate years, he has stated that he worked every day except Sunday, when he took long walks by himself.

Furthermore, he was known to lack social graces: during their first meeting, Dirac said to a young Richard Feynman in an attempt to break the ice after a long, awkward silence: “I have an equation named after me, do you?” Einstein struggled with him as well, writing in a letter, “I have trouble with Dirac. This balancing on the dizzying path between genius and madness is awful.” Despite these issues, he got married in 1937 to Margit Wigner, the sister of Nobel Prize winning Eugene Wigner, adopting her two children from a previous relationship and fathering two more. As a couple, they were complete opposites, and it worked, as sometimes it does.

The Dirac Equation

In a lifetime of scientific achievement, Dirac’s greatest accomplishment is, without a doubt, the Dirac equation. 

Erwin Schrödinger’s famous equation, describing the wave function of a quantum mechanical system, was itself an amazing discovery. However, it is limited in that it only encompasses the non-relativistic world. Many physicists had tried their hand at marrying the quantum world of Schrödinger with the relativistic one of Einstein without success — and without it, the wave function of relativistic particles, such as the electron, could never be understood.  

Story has it that one evening Dirac, who loved to play with equations, was staring into his fireplace in his home in Cambridge when a new approach to the problem occurred to him: to take the square root of the operator at the core of Schrödinger’s equation. This immediately led to a solution with four matrices, implying that the wave function must have four components.

The result gave new insight into Wolfgang Pauli’s two component hypothesis of spin, which had been based on observation rather than theory and which Pauli himself could not explain. Indeed, its prediction of the spin of the electron was a perfect match with experiment. 


The theory made other predictions as well. One of the implications of the four component solution was the fact that the electron must have a shadow particle with negative energy. This sent off a shock wave through the physics community, which suddenly struggled to explain things as basic as the stability of the hydrogen atom. After a few years, it became clear that a new particle must exist, one with the same mass as an electron but the opposite charge, with the added quality that if this particle, which Driac dubbed an “anti-electron”, should ever meet an electron, they would annihilate each other in a burst of radiation. It came as almost a relief to the science community when, in 1932, just such a particle was discovered by Carl D. Anderson.

The Magnetic Monopole:

The last major implication of this theory is one that still motivates experimental research today, defying all efforts to resolve it for nearly a century now. It theorizes the existence of a particle known as a magnetic monopole — that is to say, it is a “north” magnetic pole without “south” one, or vice versa. For decades, physicists have created more and more sensitive experiments to detect this elusive entity without success, making it almost like the Bigfoot of theoretical physics. As Dirac’s equation is part of Grand Unified Theorems, this presents a bit of a problem, as some theories predict they should in fact have been created in large quantities in the early Universe and should have persisted until the current day. Their apparent absence has left cosmologists and theoretical physicists looking for new ways to create a Universe without them.


Dirac was awarded the Nobel Prize for this work in 1933 and went on to have a long life doing the things that he loved best: playing with equations, teaching, and being with his family. He continued his work on quantum electrodynamics, rejecting the “renormalization” techniques that neatly excised the troubling infinities that were the natural consequence of the formalization, trying to place them on “logical foundations”. He ultimately moved from Cambridge to Florida late in life, in order to be closer to his children. He died there in 1984, aged 82, still playing with equations, hoping to find a Hamiltonian that could remove the need for the renormalizations he detested yet nevertheless agreed so well with observation.

The Many Worlds of Hugh Everett III


Dr. Hugh Everett III was one of the more compelling and even bizarre figures in physics, someone was scorned and even ridiculed during their lifetime, only for the influence of their theories to grow beyond science and becoming a pop culture phenomenon after their death. Moreover, he truly and deeply believed in the consequences of his theories, which likely contributed to his death and the later suicide of his daughter.


Basic concepts via Schrodinger’s cat

The many worlds interpretation (MWI) of quantum mechanics was in truth first proposed by Schrödinger himself, though Everett developed it independently and much more fully. The Schrödinger’s Cat thought experiment presents a perfect way to describe the similarities and differences between the “conventional” interpretation of QM and MWI. 

In the first, the fate of the cat is uncertain, in essence both alive AND dead, until the box is opened, at which point the quantum uncertainty collapses – the act of observing destroys the uncertainty. 

In MWI, the act of opening the box creates two parallel universes, one where the cat is dead and one where it is alive. The universe has in essence split into two nearly identical versions of itself, where the only difference is the state of the cat. The catch is that these two universes are utterly separate, there is no observing one from the other. The fate of the cat is sealed. And just because you can’t see the other universes, doesn’t mean they aren’t there.

Early negative reception

Disappointed and frustrated with the reception his work received, he left academia after finishing his dissertation and went to work at the Pentagon on a secret Cold War project based on game theory – in fact, some of his work is still classified.

Hugh in Copenhagen

He did ultimately visit Niels Bohr in Copenhagen to discuss the principles of his theory. 

Growing influence

Over time, though, MWI has gained in influence, particularly among cosmologists. The Universe as we see it is simply incredibly unlikely: even tweaking the values of some universal constants by a tiny amount would be enough to make sure that we would never have had a chance to evolve.

It boggles the mind that everything has worked out exactly the way it has by, in essence, dumb luck. It makes far more sense that uncountably many Universes have existed or do exist and we inhabit one of the lucky few.


Themes quite similar to MWI have been employed in fiction for centuries, long before the development of quantum mechanics. One could argue that ancient mythologies, for example the Norse, with Valhalla and Jondheim, do as well. However, these generally involved crossing into alternative realities or different planes of existence, which isn’t really what WMI is about. Some authors, such as Michael Moorcock, cite MWI specifically as an inspiration but again lack certain fundamental insight.

The idea of exploring multiple futures from a specific moment in time, with different events unfolding based on different choices, does come closer to the true spirit of MWI. This thematic element has shown up repeatedly in both literature and movies. The 1998 movie “Sliding Doors”, for example, follows two separate outcomes of a woman’s life, depending on whether or not she made a particular train. Another interesting example can be found in the last two chapters of the Avengers movies: Infinity War and End Game. In these movies, one character searches many different future timelines in order to find a course of action that allows the highest chance of successfully overcoming the antagonist.


Quantum Immortality

As a consequence of MWI, another thought experiment along the lines of Schrödinger’s cat was developed, more bordering on a philosophical principle than anything else: the idea of quantum immortality. 

Let’s think of it as Schrödinger’s Roulette. If you spun the barrel of the gun, held it to your head, and pulled the trigger, your awareness would only continue in the universes where the chamber was not loaded. No matter how many times you repeated this act, this would be the result, although in an increasingly smaller fraction of all possible universes. Thus, in a way, one has obtained a type of immortality.

The death of Hugh Everett and suicide of his daughter Elisabeth

Hugh Everett III died at the age of 51 of a heart attack. He had been known to discuss the concept of quantum immortality with colleagues and friends, stating that his awareness would continue in whichever parallel universe where he did not die. Perhaps this explains some of his life choices — chain smoking and eating and drinking to excess — which inevitably contributed to his early demise. A firm atheist, he has asked that his ashes be thrown out with the trash. After a few years, they were.

Unfortunately, this story does not end here. Hugh Everett III’s daughter and oldest child Elisabeth committed suicide 14 years after his death after a long bout with mental illness. In her suicide note, she wrote that she wanted her ashes to be thrown out in the trash, like her father’s, in the hope that she would “end up in the correct parallel universe with Daddy”. 

The Eels album Electroshock Blues

Hugh Everett III’s one surviving child is critically acclaimed musician Mark Everett, leader of the band the Eels. His album “Electroshock Blues”, released in 1998, is greatly inspired by his sister and his father. Furthermore, he was involved with an award-winning documentary called “Parallel worlds, parallel lives” (available on Vimeo) that details his pursuit of his father and his father’s work.

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