Maths and Physics #3: Dirac's Influence

The next part of the physics-maths story starts with quantum mechanics. When Heisenberg tried to explain things, he ran into mathematical array with strange properties. To him, they were strange. Mathematicians, however, had known it for long by the name of array matrices.

 

Dirac entered the quantum mechanical story late. He was more mathematician than physicist. When he investigated Heisenberg’s and Schrodinger’s equations, he “bent the rule of mathematics”. He made extensive use of a “mathematical function that made purists blanch”. Dirac didn’t care. If the physics worked (as quantum mechanics did), then any mathematical implication of it, however weird it may seem, must be true, argued Dirac. Dirac was reversing the directionality – so far, maths had helped physics; but now Dirac was saying physics could lead to new maths too. Oh, that function that made purists blanch? Decades later, other mathematicians would prove the function was correct.

 

Dirac wasn’t done yet. He tried combining the maths of general relativity and quantum mechanics. His results showed that two properties of electrons that had been a mystery were a consequence of the maths. Another consequence of Dirac’s unified maths was what sounded like science fiction – the existence of anti-matter. However outlandish it may sound, Dirac insisted it must be true if it flowed from the maths. It would take decades, but anti-matter would change the course of physics – so many areas like particle physics, the idea of what is in a vacuum, how a black hole can radiate away, are all based on anti-matter.

 

By now, the experimental setups were getting very complicated, costly… and often led to erroneous findings. This put off Dirac. His faith in experimental findings fell – they seemed to make too many errors, and physicists seemed to over-react to every new strange finding. Forget experiments, Dirac urged, just go where the maths takes you – that must be the truth of nature. “Mathematical beauty” was the only true North Star, he declared. But there was a key difference to remember, reminded Dirac:

“The mathematician plays a game in which he himself invents the rules, while the physicist plays a game in which the rules are provided by nature.”

 

Many physicists were put off by Einstein and Dirac: the traditional, data driven approach had worked so well for centuries, why change the approach? The enthusiasm for maths seemed overdone. The seeds for what would be called the “long divorce” between physics and maths were now sown.