optical and electrical phenomena in moving bodies; this theory was based upon the atomistic conception (vorstellung) of electricity, and on account of its great success appears to have justified the bold hypotheses, by which it has been ushered into existence. In his theory[1], Lorentz proceeds from certain equations, which must hold at every point of "Æther"; then by forming the average values over "physically infinitely small" regions, which however contain large numbers of electrons, the equations for electro-magnetic processes in moving bodies can be successfully built up.
In particular, Lorentz's theory gives a good account of the non-existence of relative motion of the earth and the luminiferous "Æther"; it shows that this fact is connected with the covariance of the original equation, at certain simultaneous transformations of the space and time co-ordinates; these transformations have obtained from H. Poincaré[2] the name of Lorentz-transformations. The covariance of these fundamental equations, when subjected to the Lorentz-transformation, is a purely mathematical fact; I will call this the Theorem of Relativity; this theorem rests essentially on the form of the differential equations for the propagation of waves with the velocity of light.
Now without recognizing any hypothesis about the connection between "Æther" and matter, we can expect these mathematically evident theorems to have their consequences so far extended — that thereby even those laws of ponderable media which are yet unknown may anyhow possess this covariance when subjected to a Lorentz-transformation; by saying this, we do not indeed express an opinion, but rather a conviction, — and this conviction I may be permitted to call the Postulate of Relativity. The position of affairs here is almost the same as when the Principle of Conservation of Energy was postulated in cases, where the corresponding forms of energy were unknown.
Now if hereafter, we succeed in maintaining this covariance as a definite connection between pure and simple observable phenomena in moving bodies, the definite connection may be styled the Principle of Relativity.
- ↑ See. Encyklopädie der math. Wissenschaften, Vol. 2, Art. 14. Weiterbildung der Maxwellschen Theorie. Elektronentheorie.
- ↑ Rend. Circ. Matem. Palermo, t. XXI (1906), p. 129.
