spontaneous symmetry breaking

Imagine a pencil balanced perfectly on its sharpened tip. While it stands, every direction around it looks the same — the situation is perfectly symmetric. But that balance is unstable, and the pencil must fall. The moment it topples, it points one particular way, say northeast, and the perfect rotational symmetry is gone. Nothing forced it to choose northeast over north or west; the law of gravity treated all directions equally. The symmetry was broken not by the laws, but by the system settling into one of many equally-good lowest-energy states. That is spontaneous symmetry breaking: the rules stay symmetric, but the actual state of the world does not.

More precisely, a symmetry is spontaneously broken when the equations governing a system are unchanged under some transformation, yet the lowest-energy configuration (the ground state, or 'vacuum') is not. There are many possible ground states related to each other by the symmetry, and the system simply picks one. A magnet is the textbook example: above a certain temperature its atomic spins point every which way and there is no preferred direction. Cool it down, and the spins all line up into one direction, breaking the rotational symmetry — even though the underlying physics had no built-in preference for that direction. The symmetry is hidden in the laws but invisible in the outcome.

This idea is the heart of how particles get mass. In particle physics the role of the 'fallen pencil' is played by the Higgs field, whose lowest-energy state is not zero but a particular nonzero value everywhere in space. The electroweak symmetry of the underlying equations is still exactly true, but the vacuum we live in has selected one state, and that hidden, broken symmetry is what lets the W and Z bosons and the matter particles acquire mass. The common misconception to avoid: spontaneous breaking does not mean the symmetry is destroyed or false — it is still there in the laws, merely not displayed by the ground state.