Curie Symmetry Principle: Does It Constrain the Analysis of Structural Geology?

Curie symmetry principle, the causality relation between the symmetry of the causes and the resultant effect, has often been invoked to infer the composite deformation history of geological bodies in the Earth’s crust. This principle provides a powerful constraint for predicting an unavailable past physical condition; the effects at the macroscopic level must be the same or higher symmetry than the intersection of the causes. However, in nonlinear phenomena, it is shown that the resultant effect selects a lower symmetry than the intersection of causes, which logically opposes the principle. Here, we introduce a symmetry breaking principle where the symmetry group of the effect is included in the intersection of the causes, and derive a new nonlinear phenomenological equation to formulate the symmetry breaking phenomena. The new principle suggests that the anisotropic pattern may not be necessary to consider the anisotropic causes or the multiple deformation history under nonlinear phenomena.