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1. jimbokun · 1789667116 · focus · HN ↗

   Did Dirac’s prediction that studying “beautiful” mathematics would lead to breakthroughs in the understanding of Physics pan out?

   1. lacker · 1789670512 · focus · HN ↗

      Yes, quite well in fact. This lecture was in 1939. In the 50's, Lie groups (previously just a pure, beautiful mathematics) were used in particle physics. Gell-Mann used SU(3) to predict some new particles before anyone observed them.

      And then similar stuff happened later in quantum mechanics, with gauge theory, but I understand that only at a handwavy level. I think overall the "standard model" is a perfect example of what Dirac predicted.

      Whether this still holds up in the past 40 years is another question. I don't have a great example from my lifetime.

      1. skew-aberration · 1789724345 · focus · HN ↗

         Also a layman but I have a different read of it.

         1) Dirac actually developed big parts of Lie Theory and its application in relativistic particle physics, without using the mathematical formalisms at all (until later on).

         His work was subsumed/beautified by mathematicians after the fact (30s), an 'optimization' really which helped to extend and understand it further, not to discover it. The Gell-Mann prediction mirrors Dirac's own positron (non)prediction closely but was done without Lie formalisms.

         The applications of Lie theory in relativistic fields theories began even earlier, with the Noether/Klein/Hilbert/Einstein collaboration in 1910s.

         2) Continuous symmetries are a convenience and not essential to particle physics IMHO.

         e.g. It's obvious we can swap positive and negative charge and get the same physics. That's a discrete symmetry. But in gauge theories the symmetry is not +ve <-> -ve, but rather the continuous rotation of the unit circle in a complex plane. electron becomes positron via complex numbers. It doesn't mean there's a complex electron with +-ie charge, but it does work better with relativistic Lagrangian fields theories where phase changes are continuous and frame dependent. Noether's methodology of using an invariant action integral leverages the Lie theory very effectively, but there are other ways to skin that cat though.

         3) Beauty is in the eye of the beholder, but I doubt the standard model and the perturbative methods (renormalization, etc) underpinning it would be to Dirac's liking.

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