By Chen T.Q.

This paintings provides the development of an asymptotic strategy for fixing the Liouville equation, that's an analogue of the Enskog-Chapman method for the Boltzmann equation. as the assumption of molecular chaos has now not been brought, the macroscopic variables outlined via the mathematics technique of the corresponding microscopic variables are random typically. for that reason, it truly is handy for describing the turbulence phenomena. The asymptotic approach for the Liouville equation finds a time period exhibiting the interplay among the temperature and the rate of the fluid flows, as a way to be misplaced less than the idea of molecular chaos.

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This paper was taken as decisive proof that the old quantum atomic theory, with integral quantum numbers, failed for the helium atom. 32 Meanwhile, late in 1922, Bohr had already anticipated that Born's perturbation theory approach must fail, if only because the perturbations were themselves of the same order as the unperturbed results. 33 And in his major survey paper on the foundations of quantum theory he had expressed strongly his conviction that classical mechanics, and with it the existing quantum atomic theory, must fail.

The positivistic attitude in the choice of orbits was thus continued, and strengthened, in the treatment of quantum numbers. But still the theory rested upon the very classical concepts it spurned. The orbits were restricted to those that, given the absence of any continuous radiation from the orbiting electrons, were possible according to the classical theory. The quantum numbers, to be accepted, had ultimately to be interpretable in terms of the classical concepts. Even if it were recognised that the planetary model was too naive to be a genuine structural representation, there was simply no alternative visualisation.

Bohr was cautious. But there can be little doubt that he was already heading towards the abandonment of a causal space-time description for atomic processes. 43 Von Mises's rejection of causality in 1921 appears to have been directly related to Bohr's views as they were expressed in his paper to the Solvay congress that year. 44 And in 1923 H. A. "45 Moreover, he drew the conclusion that in this case the principle of causality, expressed as "Given a situation A in space-time we can determine a later situation B", was simply inappropriate: we were not given such a situation A.