D O C U M E N T 2 J U N E 1 9 2 7 2 7 1. From Leo Kohn[1] [London, between 1 June and 31 July 1927][2] [Not selected for translation.] 2. From Werner Heisenberg[1] Copenhagen, 10 June 1927 Dear and honored Professor, A hearty thanks for your kind letter [2] although I indeed have no new ideas, I would like to write once again, giving my reasons for believing that indeterminacy, that is the invalidity of strict causality, is in fact necessary, and not simply possible without introducing contradictions. If I have understood your point of view correctly, you are of the opinion that, in fact, all experiments would yield the same results as those required by statistical quantum mechanics, but that over and above that, it will later prove possible to speak of the determinate trajectories of a particle. As a particle, I don’t mean, for example, a wave packet as described by Schrödinger,[3] but instead an object with a predetermined “size” (independent of its velocity), i.e., with a determinate force field, independent of the velocity. My principal objection is now as follows: Think of free electrons with a constant, low velocity, so low that their De Broglie wavelengths are much greater than their sizes i.e., their force fields are practically zero at distances from the particles of the order of their De Broglie wavelengths. Electrons of this description approach a grid whose lattice spacing is of the order of the De Broglie wavelength mentioned. Ac- cording to your theory, the electrons will be reflected in certain discrete directions in space. If you now know the precise position of a particle, i.e., what its trajectory was, you could calculate where it strikes the grid, and could set up an obstacle that would reflect that particle in some arbitrary direction, quite independently of the other lattice lines. You could do this if the forces of the particle on the obstacle and vice versa act only over short distances, which are small compared to the lattice constant. In reality, the electron will be reflected in the particular discrete direc- tions, independently of the obstacle. One could avoid this only by again consider- ing the motions of the particle in direct relation to the behavior of the waves. This, however, means that one must assume that the size of the particle, i.e., its forces of interaction, depend on its velocity. With that assumption, one abandons the word “particle” and loses, in my opinion, any understanding of the fact that in the Schrödinger equation, or in the Hamiltonian matrix representation, only the simple potential energy enters. If you use the word “particle” in such a liberal fashion, I