D O C U M E N T 4 6 4 J A N U A R Y 1 9 2 7 4 5 7 For two sorts of molecules where the molecules of the same sort are impenetra- ble to each other but molecules of a different sort would be PENETRABLE to each other, our statistics would provide Fermi-type formulas WITH THE MIXTURE PARADOX but then it wouldn’t be a paradox anymore, if for masses becoming alike all molecules are just SUDDENLY allowed to become impenetrable to one another, because that would suddenly produce a large reduction in the freedom to vibrate, so to speak. Can Bose-Einstein statistics be gained at all from our 3N-dimensional oscilla- tion basis? NEITHER FOR IMPENETRABLE MOLECULES NOR FOR PENE- TRABLE ONES. If, pursuant to Schrödinger’s older paper in PHYSIKALISCHE ZEITSCHRIF[T],[10] for instance, the THREE-DIMENSIONAL oscillation com- putation is taken as a basis, then for a gas WITH THOROUGHLY SIMILAR mol- ecules that exert ABSOLUTELY NO MUTUAL INTERACTIONS, which are therefore also penetrable to one another, one does in fact obtain the Bose-Einstein statistics. BUT: I/ THIS method cannot possibly be applied to a gas mixture, because, of course, only ONE M can occur in the THREE-DIMENSIONAL oscillation equation. II/ This method cannot possibly be applied to impenetrable molecules, because, of course, the interaction between TWO molecules cannot be expressed by THREE VARIABLES. Therefore, as soon as one is dealing with a mixture of molecules that are impen- etrable to one another or have differing masses, one must relinquish the three- dimensional basis and therefore Bose-Einstein statistics. For “light corpuscles,” however, one gets by with the Rayleigh-Jeans-Planck statistics of the characteristic oscillations of the UNIQUE three-dimensional lumi- nous ether and doesn’t have to think at all about a mutual impenetrability of the cor- puscles, either./ We also already believe we can see where some limits of the Pauli exclusion principle lie. First, why two electrons orbiting around two different nuclei are allowed to nat- urally have equivalent quantum orbits. Second, why can even two electrons peacefully possess the same translatory quantum number in the same atom, provided only that they don’t also have the same spin[11] as well? One could thus cheat and set this in relation with the impen- etrability: If just the spin is “counterposed,” then the two electrons greatly attract each other magnetically at the last moment. For the same spin, however, the “elec- tric impenetrability is also supported by magnetic repulsion.” This is cheating, of course. But “cheating in accordance with the present state of science.”
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