WAVE NATURE OF ELECTRON 247 On the other hand the determination of the stable motions of the electrons in the atom involves whole numbers, and so far the only phenomena in which whole numbers were involved physics were ose of interference selves could not be represented as simple corpuscles either, but that a Pen and of eigenvibration. That suggested the idea to me that electrons then odicity had also to be assigned to them too. thus arrived at the following overall concept which guided my studies for both matter and radiations, light in particular, it is necessary to introduce the corpuscle concept and the wave concept at the same time. In other words the existence of corpuscles accompanied by waves has to be assumed in all according to Bohrs expression, they constitute two complementary forces of reality, it must be possible to establish a certain parallelism between the motion of a corpuscle and the propagation of the associated wave. The first objective to achieve had, therefore, to be to establish this correspondence. With that in view I started by considering the simplest case: that of an isolated corpuscle, i.e. a corpuscle free from all outside influence. We wish to associate a wave with it. Let us consider first of all a reference syster oxoyozo in which the corpuscle is immobile: this is the intrinsic" system of the corpuscle in the sense of the relativity theory. In this system the wave will be stationary since the corpuscle is immobile: its phase will be the same at every point; it will be represented by an expression of the form sin 2Zvol(to-To); to being the intrinsic time of the corpuscle and to a constant. In accordance with the principle of inertia in every Galilean system, the orpuscle will have a rectilinear and uniform motion. Let us consider such Galilean system and let v=Bc be the velocity of the corpuscle in this system; we shall not restrict generality by taking the direction of the motion as the x-axis. In compliance with Lorentz' transformation, the time t used by an observer of this new system will be associated with the intrinsic time to by the relation -B2 and hence for this observer the phase of the wave will be given by √1-B( BxWAVE NATURE OF ELECTRON 247 On the other hand the determination of the stable motions of the electrons in the atom involves whole numbers, and so far the only phenomena in which whole numbers were involved in physics were those of interference and of eigenvibrations. That suggested the idea to me that electrons them￾selves could not be represented as simple corpuscles either, but that a peri￾odicity had also to be assigned to them too. I thus arrived at the following overall concept which guided my studies: for both matter and radiations, light in particular, it is necessary to introduce the corpuscle concept and the wave concept at the same time. In other words the existence of corpuscles accompanied by waves has to be assumed in all cases. However, since corpuscles and waves cannot be independent because, according to Bohr’s expression, they constitute two complementary forces of reality, it must be possible to establish a certain parallelism between the motion of a corpuscle and the propagation of the associated wave. The first objective to achieve had, therefore, to be to establish this correspondence. With that in view I started by considering the simplest case: that of an isolated corpuscle, i.e. a corpuscle free from all outside influence. We wish to associate a wave with it. Let us consider first of all a reference system o~~y~z~ in which the corpuscle is immobile: this is the "intrinsic" system of the corpuscle in the sense of the relativity theory. In this system the wave will be stationary since the corpuscle is immobile: its phase will be the same at every point; it will be represented by an expression of the form sin ZZV~(~~~~) ; to being the intrinsic time of the corpuscle and to a constant. In accordance with the principle of inertia in every Galilean system, the corpuscle will have a rectilinear and uniform motion. Let us consider such a Galilean system and let t, = ,dc be the velocity of the corpuscle in this system; we shall not restrict generality by taking the direction of the motion as the x-axis. In compliance with Lorentz’ transformation, the time t used by an observer of this new system will be associated with the intrinsic time to by the relation: and hence for this observer the phase of the wave will be given by