4 9 8 D O C . 3 2 9 F U N D A M E N T A L C O N C E P T S OF P H Y S I C S established which permit the exact calculation of the possible arrange- ments of such structures and the con- ditions under which changes occur in the arrangement. But these theories are characterized by their making a sacrifice, on principle, of strict caus- ality: they are statistical theories on principle. What Is meant thereby Is next to be made clear. In earlier physics, too. statistical laws had their Important place. If I have a gas under very low pressure in a hollow vessel provided with a minute aperture connecting It with empty space, then from time to time— for instance, every 10 seconds on the average—a molecule of the gas will pass Into space. The probability that during a given observed second a molecule will leave Is, therefore. 1-10. This Is a statistical statement. But up to the present It was held to he certain that orderliness of such type was supported by exact laws con- cerning mutual collisions between molecules and with the walls of the vessel. Should these laws be fully understood, and also the circumstances of motion of all the molecules at some given time, it ought. on principle, to be open to mathematical calculation to predirt exactly when a molecule would leave the'hollow vessel In this case the statistical law would be merely the result of a combination of a strictly causal law with Incomplete knowledge or Imperfect estimate of the true Initial condition of the system under consideration. On the contrary, according to these modem theories, the natural law foundations are themselves not causal, to begin with, but statistical. For example: if I hare certain atoms in a given condition. "A." they may pass, with the emission of light, into the condition "B " spontaneously. There exists definite probability that a giv- en observed atom will, at a given ob- served second, actually make the transition. These theories maintain: were I to know with all Imaginable precision the circumstances of an atom, it would nevertheless, in prin- ciple. be impossible for me, on the bnsls of natural laws, to calculate when the atom will really go over Into condition "B." This means waiving causality "In principle." All natural laws are. therefore, claimed to he "In principle" of the statistical variety and our imperfect observation prac- tices alone have cheated us into a be- lief In strict causality. In Itself, It is already sufficiently Interesting that a reasonable science can exist at all after dispensing with rigorous causality. It Is furthermore not to be denied that this surrender has really led to Important achieve- ments in theoretical physics, but nevertheless I must confess that my scientific Instinct reacts against fore- going the demand for strict causality. But. In any case, it must be admitted that today we are far away from the realization of this demand which ap- peared so self-evident to our forefa- thers. One achievement In recent times of the development referred to I must mention, because It is decisive and of lasting Importance. The properties of radiation hinted at above have led to comparing radiation with a gas whose molecules fly In the direction of prop- agation of the rays and carry with them energy depending entirely on the color. I.e .. the frequency. There is the question, therefore, of a combination of the wave theory with the corpuscu- lar theory of light. Analogously, a wave theory of matter has arisen which, conversely, co-ordinates an no- dulatory field with the flying par- ticles. This analogy leads to endow- ing a stream of particles with prop- erties which correspond to those ob- served In the Interference phenomena of light and Roentgen rays. This view has been confirmed by experiment. It was shown that a beam of cathode rays, I. e.. an aggregation of flying electrical particles, la deflected by the molecular lattice of a crystal after a fashion which is entirely analogons to the deflection of Roentgen rays, or to that of a pencil of light by an optical diffraction grating. We stand here before a new property of matter for which the strictly causal theo- ries hitherto in vogue are unable to account. PD. Published in St. Louis Post-Dispatch, 9 December 1928, Supplement, 7: 1-4. Translation of Doc. 156, except for a few lines at the end of the German draft, which were omitted. [1] Einstein 1917a. [2] Henry J. de Laak was retired from the position of Professor of Physics and Mathematics at the St. Louis University. For all subsequent notes, see notes of the same number in Doc. 156. [11] [9] [10]