A Short Course in General Relativity by J. Foster, J. Nightingale

By J. Foster, J. Nightingale

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Their argument, recall, is that we don’t need quantum mechanics to describe the motions of planets because decoherence is supposed to ensure that the predictions of quantum mechanics will be indistinguishable from the predictions of classical mechanics. One of the central theses of this book, however, is that we do need a quantum planetary dynamics, or rather what might better be described as a planetary quantum dynamics. In other words, while we might not need quantum dynamics to describe planetary systems, we do need planetary dynamics to describe quantum systems.

58). This is evident both in his 1925 matrix mechanics paper and in his 1927 uncertainty paper, where he is still in the process of constructing the new quantum theory. 20 In calling Heisenberg a realist about quantum theory, what I mean is that he believed that quantum mechanics is an accurate, final, and true description of the way the world really is. An important part of Heisenberg’s defense of realism is the sharp distinction he draws between, on the one hand, phenomenological theories along with what he calls the “the pragmatic philosophy” and, on the other hand, closed theories and his own philosophy.

Many textbooks on quantum mechanics give the impression that Ehrenfest’s theorem adequately characterizes the classical limit. 9) only holds under highly restricted circumstances. In order to use this characterization of the classical limit, one must be able to replace the mean values of functions, such as hFðq^Þi, with a function of the means, Fðhq^iÞ. This substitution is legitimate only if the Hamiltonian of the system is a polynomial of second degree or less, such as in the case of linear or harmonic oscillator potentials.

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