Rule 13 of 36 · Chapter II — Symmetry & Conservation
Break a symmetry, pay a price
Why this rule exists
When a system settles into a state less symmetric than its underlying laws, that broken symmetry is not free: it forces a physical consequence. A liquid freezing into a crystal picks out particular directions its equations never preferred, and paying for that choice shows up as latent heat released and, often, as new low-energy excitations. The deep reason is that a continuous symmetry, once spontaneously broken, leaves behind soft modes — Goldstone's theorem — so the price of ordering is a family of gentle restoring motions.
In practice
When a system chooses one outcome among many that the laws treat alike — a magnet's north direction, a buckled beam's bend — expect a cost and look for where it is paid. Watch for latent heat at the transition, for a new massless or low-frequency mode (sound in a solid, spin waves in a magnet), and for a domain structure where different regions made different choices. The symmetry is not gone; it reappears as the ease of moving between the equivalent states.
When it doesn't apply
Explicit breaking, where the laws themselves are only approximately symmetric, gives the would-be soft mode a small mass instead of leaving it exactly gapless. In gauge theories the Goldstone mode is absorbed by a gauge field and the count changes, as in the Higgs mechanism. Discrete symmetries break without producing soft modes at all.