Some of the most powerful equations in science look deceptively simple. The above equation is one of those. It’s discover is Paul Dirac, an enigmatic Englishman of very few words. A story goes that the preeminent physicist, Richard Feynman, met Dirac at the 1946 Princeton bicentennial celebration. At the time, Feynman was trying to reformulate quantum mechanics using the analogy of the “principle of least action” in classical mechanics. Feynman wanted to ask Dirac if he knew that his analogy could be made exact by a simple constant factor of proportionality. This is how Feynman recalled the conversation with Dirac [1]:

Feynman: “Did you know that they were proportional?”

Dirac: “Are they?”

Feynman: “Yes.”

Dirac: “Oh, that’s interesting.”

Born in 1902, Dirac had an almost religious belief that nature’s fundamental laws are described by equations that are mathematically beautiful. These equations, he believed, would remain predictive everywhere and for all time. And in an uncanny way, this turned out to be true, and in spectacular fashion.

Dirac discovered his beautiful equation in 1927, when he was a 25-year-old fellow at St John’s college, Cambridge. By combining quantum theory with the special theory of relativity, it sensationally explained the electron’s spin (observed experimentally two years before), as well as its magnetism. But there was more.

After three years of studying puzzling properties of the equation, Dirac concluded in 1931 that it predicted a new particle (which he named positron) that had exactly the same mass as the electron but with the opposite electric charge. A year later in California, the experimenter Carl Anderson discovered a particle with precisely these properties in cosmic ray showers that rained down from outer space. But there is still more.

Anyone who has been examined by doctors on a positron emission tomography (PET) scanning machine has Dirac to thank. A PET scan machine is used to construct images for checking things such as blood flow, brain function, metastasis, or the body’s response to a cancer treatment. When positrons collide with electrons, gamma rays are formed. By using radioactive ‘tracers’ to emit positrons doctors can use PET scans to trace the resultant build-up of gamma rays inside the body, thus aiding the detection of malfunctioning tissues and organs. All this would not have been possible without the discovery of the positron and the physical properties of positron annihilation almost 100 years ago, thanks to the genius of an enigmatic Englishman of very few words.

Notes:

[1] Quoted in Krauss, Lawrence, R, Quantum Man, New York: Norton, 2011, 61.