The emergence of the principle of symmetry in physics

Abstract

In 1894 Pierre Curie formulated rules for relations between physical phenomena and their symmetry. The symmetry concept originated in the geometrical study of crystals, which it served as a well-defined concept from the 1830s. Its extension as a rule for all physics was a gradual and slow process in which applications, though often partial, preceded the formulation and clear conceptualization of the rules. Two traditions that involved ““interdisciplinary”” study were prominent in applying consideration of symmetry to physics. One is a French tradition of physical crystallography that linked crystalline structure and form to their physical, chemical and even biological qualities, which drew back to Haüüy, and included Delafosse, Pasteur, Senarmont, and Curie. This tradition (until Curie) employed qualitative argument in deducing physical properties. A mathematical approach characterizes the second tradition of Franz Neumann and his students. During the 1880s two members of this tradition, Minnigerode and Voigt, formulated rules of symmetry and implicitly recognized their significance. Yet, until 1894 both traditions studied only crystalline or other asymmetric matter. Then, Curie, who drew on the two traditions, extended the rules of symmetry to any physical system including fields and forces. Although originated in a specific idealistic ontological context, symmetry served also adherents of molecular materialism and was eventually found most effective for a phenomenological approach, which avoided any commitment to a specific view of nature or causal processes. Therefore, the rule of symmetry resembles the principles of thermodynamics. Its emergence suggests parallels to the history of energy conservation.

Magnon-polarons in cubic collinear antiferromagnets

“…We will however disregard rotations in our analysis, and couple therefore the spins exclusively to R γλ i j . The number of coefficients B αβγλ i j appearing in the Hamiltonian (22) can be reduced considerably by applying Neumann's principle, stating that the Hamiltonian must be invariant under symmetry operations of the material itself [57,58]. NiO forms the FCC structure above its Néel temperature, and its structure therefore belongs to the cubic symmetry group O h .…”

Time, Equilibrium, and General Relativity

“…Pierre Curie) principle [Curie,3]. Discussion of Curie's principle in relation to the Higgs mechanism can be found in [Katzir,4] and [Earman,5]. In qm field theories group representations of symmetries are applied to derive particle properties, and the absence of symmetries gives clues to derive differences between properties and for transitions and changes [Veltman,6].…”

Tensors

“…The fact that physical properties of crystals should remain the same when the system of coordinates to which the properties are referred are rotated to a new set of coordinates by a symmetry operation was first appreciated by Franz Neumann, who applied this principle to elastic coefficients of crystals in a course in elasticity at the University of Königsberg in 1873/4 [3,4]. In order for this to be true for particular symmetry elements, limitations are imposed upon the components of T ij when representing a property of a crystal.…”

“…4 We shall show in Chapter 6 that when second-rank tensors are used to represent stresses and small strains, they too are always symmetric. We shall now restrict our discussion to symmetrical second-rank tensors, so that T ij = T ji .…”