Curie's principle

Curie's principle states that the symmetries of an effect must include the symmetries common to its causes. It also implies that an effect with lower symmetry signals a symmetry-breaking cause or condition.

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Symmetry (physics): A transformation is a symmetry when it leaves a system or its governing laws unchanged. The principle compares the transformations that leave causes and effects unchanged.
Pierre Curie: Pierre Curie was a French physicist whose research included crystallography, magnetism, and radioactivity. He formulated the symmetry principle that bears his name.
Piezoelectricity: Piezoelectricity is the generation of electric polarization by mechanical stress in certain materials. Crystal symmetry rules out piezoelectric response in centrosymmetric crystals.
Noether's theorem: Noether's theorem connects continuous symmetries of an action to conserved quantities in physical systems. It derives conservation laws from symmetries, unlike Curie’s constraint on effects from causes.
Symmetry breaking: Symmetry breaking occurs when a system or outcome has less symmetry than its governing laws or conditions. An effect can have lower symmetry when an additional condition breaks a symmetry shared by the causes.
Symmetry in physics: Symmetry in physics describes transformations that preserve physical laws or properties of systems. Curie’s principle belongs to the broader use of symmetry to constrain physical phenomena.
Pyroelectricity: Pyroelectricity is the change in electric polarization of a material as its temperature changes. Only crystals with a polar symmetry axis can show a pyroelectric response.
Neumann's principle: Neumann's principle states that a crystal’s physical properties must be invariant under its point-group symmetries. It constrains crystal properties using crystal symmetry rather than common symmetries of causes.
Boundary condition: A boundary condition specifies constraints on a system at its spatial or temporal limits. A boundary can supply an extra cause that lowers an effect’s symmetry.
Curie's law: Curie's law states that a paramagnet’s magnetic susceptibility is inversely proportional to its absolute temperature. The shared name can obscure that this is a distinct result by Pierre Curie.