THE QUANTUM LAWS AND THE UNCERTAINTY PRINCIPLE OF HEISENBERG

Abstract

thermoelectric action made years ago with no reference to the problem of electronic emission. As to the value of the constant A', usually written A and often called a "universal constant," I predicted3 a year or two ago that it would prove to be different in different metals. Du Bridge says, regarding this matter, "On computing the value of A from carefully taken emission data on several out-gassed platinum specimens .... values 200 times or more as great as the theoretical were obtained," the "theoretical" value being that suggested by Richardson and Dushman and confirmed, approximately, by Dush-man's study of tungsten, tantalum and molybdenum. 1 Proc. Nat. Acad. Sci., 13, 56, 1927. 2 This is not a gratuitous or a new assumption. See my note on the Temperature Relations of Photo-Electric Emission and Thermionic Emission. Ibid., 12, 486, 1926. 3 Ibid., 13, 325, 1927. In preceding papers' we have shown how the second and third laws of thermodynamics may be deduced from a single statistical principle which implied that the properties of a system can be described by assuming a finite number of possible states. This number was called U. It is our purpose in this paper to justify and to interpret this assumption, to restate the fundamental laws upon which quantum theory is based, and to show how this restatement leads directly to the uncertainty principle of Heisenberg.2 In our previous work, although we endeavored to say nothing that was contrary to the new mechanics, we did not use its phraseology. Indeed, for our statistical purpose, it made no difference whether we considered the number of ways in which certain particles may be distributed among the cells of a phase space, or the number of ways in which the same number of particles with the same energy may be assigned the various discrete solutions of the mechanical equations. The same value is obtained for Q, for it has been shown by Schr6dinger3 that between any given limits the number of such solutions coincides with the number of cells formerly employed, in the simple cases which have so far been investigated. Vow,. 15, 1929