1 4 4 D O C U M E N T 1 2 3 D E C E M B E R 1 9 2 5 In essence the only alteration compared to my first note to you[3] is that even when a region is retained in an energy-free state, the usual gas laws remain very precisely the same, down to very low temperatures. The “degeneracy temperature” only increases in the proportion e : 1 and the degeneracy obtains the character of a condensation, similar to your theory of “undulatory molecules.”[4] Nevertheless, I reject this possibility because in the present case the last energy level gains a mac- roscopic order of magnitude (see §5, end). I left the author’s name blank and marked a few places in red along the margin that would have to be altered purely stylistically if you do cosign, so that, e.g., “I” would be substituted by “one of us” or by “we.” But at the same time, there will be passages that you will perhaps not immediately agree with in substance, especially in §1, §6, and the end of §5, and furthermore, the absolutely neutral standpoint I assume as regards the weighting (1 or N!). (If N! is taken, then the zero-point en- tropy klg (N!) must, of course, be ascribed to the cooled solid, since even at the low- est temperature a vapor pressure, if ever so small, is positioned above the body, and in this way, as time passes, an exchange really does occur between the molecules of the solid.) Please feel free to do as you please now. The idea of regarding you as an “ex- ploiter” would not have occurred to me even in jest. To continue with the sociolog- ical work analogy, one could rather say: When a sovereign builds, carters have plenty to do. In any event, I was thinking of asking you to present the paper at the Academy if it appears to you of sufficient interest. At the moment I am busy with some “carter’s work” on your “wave theory of gases.”[5] The purpose: better not change the kind of statistics, but instead ex- change the concepts “material substrate” and “energy content.” The phase space cells—similar to the Jeans-Debye[6] “ether-block quantization”—are the material substrate, the molecules are the energy content. It is clear that as soon as the old statistics are applied, your results must reappear. I managed to do that as well—en- tirely by the usual Planck state summation method. In this conception the condition of a constant number of molecules, so trivial in the normal gas theory, appears ex- tremely strange and almost a little mysterious. It would almost be preferable to be allowed to omit it, which would simplify the calculation very much but would nat- urally lead to quite distorted results. This condition of a constant number of mole- cules is the main difference between your theory of gases and radiation theory.[7] (The other difference is that in the theory of radiation, the energy of a quantum is proportional to s1/3, in gas theory it is proportional to s2/3. This is connected to the
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