D O C U M E N T 5 1 3 A P R I L 1 9 2 7 5 0 9 stems from the limitation on the observing time, is of order of magnitude , with v being the atom’s velocity and a the width of the slit. This is in conformity with the fact that the light diffraction through the slit causes the light, emitted from a moving atom within a certain finite directional domain , to arrive in the direc- tion vertical to the motion for observation one again finds for each frequency range, determined by the Doppler effect, . On the other hand, if we consider the balance of energy, we find that the possibility (offered by the broadened frequency range) to detect a somewhat larger or smaller quantum by means of the photoelectric effect may be connected with the circumstance that ki- netic energy can be removed from or introduced to the atom by radiation recoil in a direction that deviates from the vertical direction of observation. The fact that not only a statistical balance of energy is observable, but an individual one as well, has to do with the fact that, as you indicate in your footnote,[5] a possible “light- quantum description” can never explicitly do justice to the geometrical conditions of the “course of the radiation.” Heisenberg shows in an exceedingly inspired way how his uncertainty relation can be used not only in actually developing the quantum theory but also for assess- ing its intuitive content. Insofar as this relation is a direct consequence of the for- malism of quantum mechanics, the whole thing does form a very closed system, at least if limited to mechanical phenomena. With such a pedagogically colored con- cept as intuitiveness, however, it does seem to me instructive, given the current state of science, always to remember how indispensable the concepts of continuous field theory are. If we only speak about particles and quantum jumps, it is difficult to find a simple introduction into the theory pointing to the basic limitations of ob- servation, because the mentioned uncertainty is not exclusively related to the exis- tence of discontinuities but precisely to the impossibility of their precise description: accordingly, those properties of material particles and of light that find their expression in the wave theory. The representation of an electron by a group of De Broglie waves is in fact entirely analogous to the one of a light quantum by a group of electromagnetic waves. Thus all the above relations hold in this case as well. From the uncertainty that corresponds to the uncertainty of the electrons’ im- petus with the group velocity, it directly follows that the group broadens, also in the direction of propagation over time all exactly in the manner Heisenberg presents it on the basis of quantum mechanics, in continuation of Dirac’s theory of matrix transformations.[6] Δν v a -=-- λ a -- - Δν ν v c -- λ a -- - ⋅ v a -- - = =