Page:Deux Mémoires de Henri Poincaré.djvu/9

 x, y, z and $$t\sqrt{-1}$$ are considered as the coordinates of a point in four-dimensional space, the transformations of relativity are reduced to rotations in this space. He also had the idea of adding to the three force-components X, Y, Z the magnitude

$$T = X\xi + Y\eta + Z\zeta\,$$

which is nothing but the work of the force per unit time and which we can (to some extent) regard as a fourth component. When we ask after the force that a body experiences per unit volume, the magnitudes X, Y, Z, T$$\sqrt{-1}$$ are affected by a transformation of relativity in the same way as the magnitudes x, y, z, t$$\sqrt{-1}$$.

I recall these ideas of Poincaré because they are similar to methods that Minkowski and other scientists have later used to facilitate mathematical operations that arise in the theory of relativity.



Let us pass now to the paper on the quantum theory. Towards the end of 1911 Poincaré had attended the meeting of the Council of Physics convened in Brussels by Mr. Solvay, in which we had especially dealt with the phenomena of the calorific radiation and the hypothesis of the elements or quanta of energy imagined by Mr. Planck to explain them. In the discussions, Poincaré had shown all the promptness and the penetration of his spirit and we had admired the facility with which he could enter the most difficult questions of Physics, even in those which were new for him. At the return to Paris, he did not cease dealing with the problem of which he felt the high importance. If the hypothesis of Mr. Planck were true, "the physical phenomena would cease obeying laws expressed by differential equations, and it would be, undoubtedly, the greatest and most profound revolution that natural philosophy suffered since Newton".

But are these new conceptions really inevitable and is there no way to arrive at the radiation law without introducing these discontinuities which are in direct opposition with the notions of traditional mechanics? Here is the question that Poincaré poses in his paper and to which he gives an answer that I will allow myself to briefly summarize.