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Symmetries in Science II Proceedings, Southern Illinois Univ., Carbondale, 1986

In some sense, the use of symmetry allows us to ask whether things would look the same from somewhere else. This is literally true, in fact.

But also more metaphorically Or if we were all made of antimatter instead of matter? If physical laws are describing the objective nature of the universe, then, well, they damn well should be the same, whatever our subjective point of view.

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The model in the photograph at the top of this article is what got me thinking about this again. The metal arrows represent the dipole magnets of atoms in a ferromagnet, and the arrows themselves are in fact magnetic.

Symmetry (physics) - Wikipedia

They can rotate freely, each orienting itself according to the interactions between its own magnetic field and those of its neightbours. The array on the right represents a magnet above its Curie temperature.

Symmetries in Mathematics and Physics II - On some interesting Lie algebras

The high temperature agitates the atoms, and the dipoles are not aligned - they are arranged irregularly despite the magnetic forces between them. The whole things looks pretty much the same from any direction - it is roughly symmetric under any rotation about the centre of the plane. The array on the left represents a magnet below the Curie temperature.

Now they are supposed to be cooler, the dipoles are in a regular array.

1. The Concept of Symmetry

Because of this, the individual magnetic forces all pull in the same directions, and the whole array becomes globally aligned. This breaks the original rotational symmetry into a more limited symmetry - it is only symmetric under rotations by multiples of 60 degrees. This happens in real magnets. I demonstrated the effect in my Friday evening discourse Royal Institution a while ago:. This idea of broken symmetry is just as important as the idea of symmetry.

It is fundamental to physics is that there are symmetries, present in the underlying laws governing the behaviour of particles and forces, which are hidden in low energy states, meaning that in general they are not apparent in everyday life. Everyday life generally corresponds to a low energy state. Like most of the works on display at ….

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