Symmetry: A ‘Key to Nature’s Secrets’

Mike King
The five regular polyhedra. Steven Weinberg writes that ‘they satisfy the symmetry requirement that every face, every edge, and every corner should be precisely the same as every other face, edge, or corner…. Plato argued in Timaeus that these were the shapes of the bodies making up the elements: earth consists of little cubes, while fire, air, and water are made of polyhedra with four, eight, and twenty identical faces, respectively. The fifth regular polyhedron, with twelve identical faces, was supposed by Plato to symbolize the cosmos.’

When I first started doing research in the late 1950s, physics seemed to me to be in a dismal state. There had been a great success a decade earlier in quantum electrodynamics, the theory of electrons and light and their interactions. Physicists then had learned how to calculate things like the strength of the electron’s magnetic field with a precision unprecedented in all of science. But now we were confronted with newly discovered esoteric particles—muons and dozens of types of mesons and baryons—most existing nowhere in nature except in cosmic rays. And we had to deal with mysterious forces: strong nuclear forces that hold partiicles together inside atomic nuclei, and weak nuclear forces that can change the nature of these particles. We did not have a theory that would describe these particles and forces, and when we took a stab at a possible theory, we found that either we could not calculate its consequences, or when we could, we would come up with nonsensical results, like infinite energies or infinite probabilities. Nature, like an enemy, seemed intent on concealing from us its master plan.

At the same time, we did have a valuable key to nature’s secrets. The laws of nature evidently obeyed certain principles of symmetry, whose consequences we could work out and compare with observation, even without a detailed theory of particles and forces. There were symmetries that dictated that certain distinct processes all go at the same rate, and that also dictated the existence of families of distinct particles that all have the same mass. Once we observed such equalities of rates or of masses, we could infer the existence of a symmetry, and this we thought would give us a clearer idea of the further observations that should be made, and of the sort of underlying theories that might or might not be possible. It was like having a spy in the enemy’s high command.1


I had better pause to say something about what physicists mean by principles of symmetry. In conversations with friends who are not physicists or mathematicians, I find that they often take symmetry to mean the identity of the two sides of something symmetrical, like the human face or a butterfly. That is indeed a kind of symmetry, but it is only one simple example of a huge variety…

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