Size matters (click to enlarge)|
The classical limit of quantum mechanics
Given that there is no sharp boundary separating "classical" and "quantum" phenmomena there should be a classical limit of QM which explains the classical appearance of every-day life. The intuition behind this is clear: QM is more fundamental and should "explain" why classical physics provides such an excellent description of macro objects. Most people think that classical physics should be viewed as a "special" or "limiting" case of QM. The examination of this relation has developed into an industry and faces both, technical and conceptual problems.
According to common wisdom it essentially needs some limit (like h goes to 0 or the "quantum numers" to infinity), the Ehrenfest theorem or the WKB approximation to recover classical physics as a limiting case of QM. However, on a closer look one realizes, that it is far from obvious what "classical" limit is supposed to mean. Does one just require, that classical "predictions" can be reproduced or does a proper limit requires that the mathematical structure of classical physics emerges out of the quantum formalism? How then shall real functions on phase space emerge out of Hermitian operators on Hilbert space?
Yet other questions are related to the interpretation of QM. If, as many believe, quantum mechanics teaches us that "reality" is very different than we used to think in pre-quantum times, how than does the classical and the quantum world relate in this respect?
A selected list of references: