Dirac Equation
Where should one start to discuss the contribution of this Giant? Dirac started as an Engineer, graduating from Bristol University before moving to Cambridge, contributing (and initiating) quantum electrodynamics (QED), the Relativistic Quantum Field theory. In particle physics, the Dirac equation is a relativistic version of the Schrödinger equation. Dirac was looking for a linear equation, specifically guided by the Schrödinger equation, but that was relativistically invariant.
He could not find one that did not involve taking the square root of an operator. However, he devised a technique that allowed the linearisation that was required. However, this introduced a noncommutative algebra, from which he realized that the factors needed were matrices.
Determining the square root of an operator-led Dirac to consider both the positive and negative roots. Instead of conceding that there might be an error in his work. He proposed that these solutions must correspond to anti-matter (positron when considering the anti-particle of the electron).
Dirac, as Mathematics Professor at Cambridge
Dirac became the Lucasian Professor of Mathematics at Cambridge, arguably the most prestigious post in all of Mathematics, made famous by “Giants,” including I. Newton, C. Babbage, and G.G. Stokes.
I was fortunate to study the full equation of viscous flow in fluid dynamics that he is intimately involved with as one half of the Navier (1785-1836) – Stokes equation. Navier, by the way, can be found with his name “up in lights” (as it should be) as one of the legendary 72 names on the Eiffel Tower.
Dirac Preciseness
He was famous for his preciseness, and I often recount a famous event like this. While delivering a lecture at a conference, a member of the audience raised his hand and said:
“I don’t understand the equation on the top-right-hand corner of the blackboard.”
There was a silence in the room! After a long cessation, the session chair approached Dirac and quietly asked him if he wanted to answer the question.
“That was not a question; it was a comment – Dirac Replied.“
Dirac was brave enough to include matrices in his work. Matrices were just being admitted into mainstream Physics after the pioneering work of W. Heisenberg (1901-76) and before him by M.Born (1882-1970). On a related issue, matrices have their origins with the “Prince of Mathematics,” namely J.C.F.Gauss (1777-1855) and the Senior Wrangler, A. Caley (1821-95), but this is not the time to discuss them; I will have to wait for an appropriate date to do this.
Never ignore Negative Solutions
Let’s get things right. The positron was predicted by the great Mathematical Physicist P.A.M. Dirac (1902-84) when he was at St John’s, Cambridge, commencing his education as an Engineer at Bristol University. He took the bold step to NOT ignore the negative solution to the relativistic Schrodinger equation and predicted the anti-electron (now called a positron).
Dirac was mischievous rather like Euler (1707-83) when he (Euler) substituted $ix$ for (x) in the Maclaurin series expansion for (exp(x)), leading to Euler’s beautiful formula. A great book on Dirac is “The Strangest Man: The hidden Life of Paul Dirac, Quantum Genius” by Graham Farmelo.
