Symmetry is a very important idea in physics; it lies behind basic laws such as the conservation of energy, and behind the state-of-the-art theory of particle physics, the Standard Model.



If a system is symmetric under some change, it means it looks the same after the change... so the change is in some sense no change. For example: A circle is symmetric with respect to rotations around its centre - it looks the same no matter what angle you rotate it through. A square is also symmetric, but only under rotations by 90, 180, 270 or 360 degrees. Any other angle and the sides will have changed direction, they won’t line up with the original. To leap from simple shapes to the edge of physics, supersymmetry is the idea that the world is symmetric under the “rotation” in which all fermions are swapped for bosons, and vice versa.



I think one reason, perhaps the reason, that symmetry is so powerful in solving problems in physics is that it is connected to the attempt to be objective. 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. Translational symmetry is the statement that the laws of physics are the same wherever you happen to be and, via Noether’s theorem, it leads directly to conservation of momentum. But also more metaphorically... what would physics look like from a different angle? Or if we were all made of antimatter instead of matter? Or...? 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.

The model in the photograph at the top of this article is what got me thinking about this again. It is on display at the Physics Institute of Heidelberg University, which I visited on Friday last week. The metal arrows represent the dipole magnets of atoms in a ferromagnet, and the arrows themselves are in fact magnetic. 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. 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. 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.) Just as a cold ferromagnet hides the spherical symmetry inherent in electromagnetism. It remains important for the the theory, and its predictive power, that the symmetry remains in the underlying equations. The reason it features in my talk above is that this is exactly the trick used by Brout, Englert and Higgs to make the Standard Model work for massive particles.



Part of me wants to add that this is quite a good way of thinking about people and politics... the same basic human impulses can lead to very different results in everyday life, depending on the local conditions or something. If I’m honest I do find that a helpful analogy sometimes when I’m struggling to keep my temper and/or see some else’s point of view. But I guess that kind thing is why they only let religious types do ‘Thought for the Day’ on BBC Radio Four.

Jon Butterworth has written a book about being involved in the discovery of the Higgs boson, Smashing Physics, available here, and in the US and Canada as “Most Wanted Particle”. Some interesting events where you might be able to hear him talk about it etc are listed here. Also, Twitter.