#8 – Paul Dirac
Dirac was a physicist of incredible brilliance even by the standards of the great physicists. You can’t turn a corner in quantum physics without bumping into something he discovered.
Solve the ubiquitous and vitally important quantum harmonic oscillator problem using the wave equation method and you’ll get a complicated and not especially enlightening differential equation and its solution. Solve it using the elegant and clear operator method and you’ll have taken a first step into a larger and richer view of the quantum world. Dirac was the first one to notice that this was possible, and physics has been following his lead ever since. He’s one of those people for whom a Nobel (his was in 1933) seems an inadequate honor.
That’s not even the barest fraction of his contributions. In 1928 he developed the Dirac equation. The equation below his picture is the manifestly covariant form of his equation, which describes the quantum mechanics of relativistic spin-1/2 particles. Its solution contains negative energy states, which seemed physically impossible. Dirac was not quite brave enough to interpret those states as antiparticles, but nonetheless it turns out that his equation both requires and predicts antiparticles. By itself that’s worth a spot in the top ten. We’re just getting warmed up.
His eponymous equation and other work resulted in a description of vacuum polarization and some of the first quantum field theory, specifically quantum electrodynamics. Though it remained plagued with difficulties until Feynman and others developed the modern version of QED, his work was the first to establish a beachhead on the difficult problem of quantizing the electromagnetic field. He discovered that a single magnetic monopole would explain the quantization of electric charge. Unfortunately none have yet been discovered, but either way he revealed the importance of the still-open problem of the possible existence of magnetic charge. He also established the connection between the various formalisms of quantum mechanics into a coherent whole built around the idea of operators acting on vectors in Hilbert space. He extended the classical idea of Poisson brackets into quantum physics, resulting in the both important and useful concept of canonical quantization.
Like no one since Leibniz, he revolutionized the way mathematical physics is written. He invented bra-ket notation and the Dirac delta function. I can hardly imagine trying to do physics without them.
He died in 1984, a legend in his own time.
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