D O C U M E N T 2 9 O P T I C A L E X P E R I M E N T 4 9 lens with the particle moving within its focal plane. The wave planes will of the same phase are then fanned out behind the lens slightly obliquely from each other. The larger the variability of λ in a direction crosswise from the direction of propa- gation, the greater the molecule’s velocity and the closer the smaller the lens’s focal distance. So in this case even radiation at a great distance from the emitting molecule has a trait accessible in principle to observation that is characteristic of the state of motion of the emitting particle. Does the radiation emitted from a mov- ing particle really possess this property? One might think that this has already been verified by Stark’s observation of the Doppler effect of light emitted by moving canal-ray particles.[6] Such a conclusion would be unjustified, however. For the existence of the Doppler effect does not prove that the same particle sends out light radiation of differing color frequency simultaneously in various directions, rather only that when a particle sends out any radiation at all in one direction, it then has a color frequency in accord with Doppler’s principle. This could also occur if in an elementary process of emission the entire radiant energy were emitted in a single direction, e.g., according to Newton’s emission theory of light. Before we go into the question of the demonstrability of the fan-like structure of emitted radiation from moving particles required by the undulatory theory, let us consider the emission process from the point of view of quantum theory. This requires the following: 1) The energy of the molecule is only capable of certain energy values . (Judged from a system of coordinates relative to the molecule). 2) In the transition from the state with the greater energy to the smaller energy , the difference is emitted at frequency v, whereby . . . (2) 3) The emission time is small against the time that, according to the undulatory theory, the emission should take in order to be able to explain the empirically found interference capability of spectral light light for great path differences. On one hand, one knows from Wien’s experiments on the light emission of canal rays in high vacuum that the average lingering period in the state of greater energy and the emission time together is of order of magnitude seconds [7] on the other hand, quantum statistics demands that the transition times be very small com- pared to the lingering periods in Bohr’s “stationary” orbits. The emission times must therefore be smaller than seconds, which is not reconcilable with an in- terpretation of the observed interference capability of spectral light in the sense of the undulatory theory. The quantum theory hence comes into conflict with the un- dulatory theory. [p. 3] E1, E2 . . . Em En Em En – Em En – hv = 10 8– 10 10–