In the study of the physical properties of crystalline matter it is necessary to take account of the symmetry of such matter. This is, in general, anisotropic; that is to say, it has not the same properties in all directions. On the other hand, media such as glass or water are isotropic, having equivalent properties in all directions. It was the study of optics which first showed that the propagation of light in a crystal is dependent upon the elements of symmetry in that crystal. The same thing is true for the conduction of heat or electricity, for magnetization, for polarization, etc.
It was in reflecting upon the relations between cause and effect that govern these phenomena that Pierre Curie was led to complete and extend the idea of symmetry, by considering it as a condition of space characteristic of the medium in which a given phenomenon occurs. To define this condition it is necessary to consider not only the constitution of the medium but also its condition of movement and the physical agents to which it is subordinated. Thus a right circular cylinder possesses a plane of symmetry perpendicular to its axis in its position, and an infinity of planes of symmetry pass through its axis. If the same cylinder is in rotation on its axis, the first plane of symmetry persists, but all the others are suppressed. Furthermore, if an electric current traverses the cylinder lengthwise, no plane of symmetry remains.
In every phenomenon the elements of symmetry compatible with its existence may be determined. Certain elements can coexist with certain phenomena, but they are not necessary to them. That which is necessary is that certain ones among these elements shall not exist. It is dissymmetry that creates the phenomenon. When several phenomena are superposed in the same system, the dissymmetries are added together. "Works of Pierre Curie," page .
It was from the above considerations that Pierre Curie announced the general law whose text, already cited, attains the highest degree of generalization. The synthesis thus obtained seems complete, and all that was further needed was to deduce from it all the developments of which it admits.
For this it is convenient to define the particular symmetry of each phenomenon and to introduce a classification which makes clear the principal groups of symmetry. Mass, electric charge, temperature, have the same symmetry, of a type called scalar, that of the sphere. A current of water and a rectilineal electric current have the symmetry of an arrow, of the type polar vector. The symmetry of an upright circular cylinder is of the type tensor. All of the physics of crystals can be expressed in a form in which the particular phenomena in question are not specified, but in which are examined only the geometrical and analytical relations between the types of quantities where certain ones are considered as causes and the other as effects.
Thus, the study of electrical polarization by the application of an electric field becomes the examination of the relation between two systems of vectors, and the writing out of a system of linear equations having coefficients. The same system of equations holds for the relation between an electric field and an electric current in crystalline conductors; or for that between the temperature gradient and the heat current, except that the meaning of the coefficients must be changed. Similarly, a study of the general relations between a vector and a system of tensors can reveal all the characteristics of piezo-electric phenomena. And all the rich variety of the phenomena of elasticity depends on the relation between two sets of tensors which require, in principle, coefficients.
The foregoing brief exposition reveals the high philosophic import of these conceptions of symmetry which touch all natural phenomena, and whose profound significance Pierre Curie so clearly set forth. It is interesting in this connection to recall the relation which Pasteur saw between these same conceptions and the manifestations of life. "The universe," he said, "is a dissymmetric whole. I am led to believe that life, as it is revealed to us, must be a function of the dissymmetry of the universe, or of the consequences that it involves."
As his organization of his work in the School progressed, Pierre Curie could begin to dream of going forward again with his experimental research. He could do so, however, only under most precarious conditions, for he had not even a laboratory for his personal work, nor a room of any kind entirely at his disposition. Besides, he possessed no funds to support his investigations. It was only after he had been several years at the School that he obtained, thanks to the influence of Schützenberger, a small annual subvention for his work. Up to that time the materials necessary for him were provided, thanks to the kindness of his superiors, to the extent possible, by drawing upon a very limited general fund of the teaching laboratory. As for a place to work in, he had to content himself with very little. He set up certain of his experiments in the rooms of his pupils when these were not in use. But more frequently he worked in an outside corridor running between a stairway and a laboratory. It was there that he conducted, in particular, his long research on magnetism.
