4 5 6 D O C U M E N T 4 6 4 J A N U A R Y 1 9 2 7 appropriate. The sole difference from the ancients is that we are thoroughly con- vinced that this construct cannot be found by reason alone, rather, that without sub- tle empiricism it is impossible to discover a useful basis for the deduction. Kind regards, your (signed) A. Einstein Best regards to Meyerson, whom I value so highly. 464. From Paul Ehrenfest Leyden, 24 January 1927 Dear Einstein, Yesterday we spoke a great deal about you here once again. Namely, Professor Mahalanobis from Calcutta, Tagore’s companion, was visiting us with his remark- ably beautiful young wife. A few of hours of amusing chatting about all sorts of things. (Especially what they told me about your friend Mendel, the cancer special- ist and his wife, made me very very much want to get to know them.) — What a pity that they both, like a large proportion of Indians schooled in Europe, aren’t suf- ficiently calm people. They’re “genuinely Jewish” and consequently it’s no coin- cidence that throughout their whole trip, they actually almost always became particular friends with Jews. At any rate, those were a few interesting happy hours that Galinka and I spent with them. Permit me to send you a piece that Uhlenbeck and I sent out a few days ago to the Zeitschrift für Physik. A short while ago I sent you a letter destined for the Naturwissenschaften, in which I showed that in the attempt to quantize ideal gases with IMPENETRABLE molecules CONSISTENTLY AND EXACTLY on the basis of wave mechanics, one is led to the Heisenberg-Dirac antisymmetric solutions as the ONLY solutions compatible with impenetrability. (For an instant I thought that my proof fails if the transition is from a one-dimensional gas to a three- dimensional gas but very soon I saw that everything is in good order, just provided that the gas vessel has a nondegenerate form, and that in the case of specific forms, entirely inessential, purely formal complications arise.) Now Uhlenbeck and I have shown that if on this basis one consistently does the statistics, YOUR MIXTURE PARADOX VERY CERTAINLY DOES NOT OCCUR. For a gas with completely identical molecules that are impenetrable, one obtains Fermi’s result. For a mixture of IMPENETRABLE molecules, we could not determine the spectrum of the eigenfrequencies anymore and settled for only showing that the mixture paradox certainly does not occur. For wholly penetrable molecules, one would simply get the Boltzmann statis- tics, which also doesn’t yield any mixture paradox.