Scott, things aren’t as happy as they used to be down here at the Unemployment Office
Theorists began in the 1960s to consider the possibility of symmetries that are “broken.” That is, the underlying equations of physics might respect symmetries that are nevertheless not apparent in the actual physical states observed. The physical states that are possible in nature are represented by solutions of the equations of physics. When we have a broken symmetry, the solutions of the equations do not respect the symmetries of the equations themselves.
The elliptical orbits of planets in the solar system provide a good example. The equations governing the gravitational field of the sun, and the motions of bodies in that field, respect rotational symmetry—there is nothing in these equations that distinguishes one direction in space from another. A circular planetary orbit of the sort imagined by Plato would also respect this symmetry, but the elliptical orbits actually encountered in the solar system do not: the long axis of an ellipse points in a definite direction in space.
At first it was widely thought that broken symmetry might have something to do with the small known violations of symmetries like mirror symmetry or the eightfold way. This was a false lead. A broken symmetry is nothing like an approximate symmetry, and is useless for putting particles into families like those of the eightfold way.
But broken symmetries do have consequences that can be checked empirically. Because of the spherical symmetry of the equations governing the sun’s gravitational field, the long axis of an elliptical planetary orbit can point in any direction in space. This makes these orbits acutely sensitive to any small perturbation that violates the symmetry, like the gravitational field of other planets. For instance, these perturbations cause the long axis of Mercury’s orbit to swing around 360° every 2,254 centuries.
In the 1960s theorists realized that the strong nuclear forces have a broken symmetry, known as chiral symmetry.
