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I was taking an introductory course in quantum mechanics when I came across the Bohr's correspondence principle. According to Wikipedia, the correspondence principle states that the behavior of systems described by the theory of quantum mechanics reproduces classical physics in the limit of large quantum numbers. However it seemed to me as nothing more than the requirement that a theory should agree with experiments. Since the classical physics is formed so as to have its results agree with the experiments isn't it obviously necessary for a new theory to give the same results or atleast not contradict the original ones? Can someone make this clear to me?

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  • $\begingroup$ Can you make a more descriptive title for this question? $\endgroup$ – user191954 Aug 15 '18 at 12:58
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    $\begingroup$ The devil is in the details. Nobody I know perorates on the principle in the abstract: They always focus on the how of a specific situation, and try to connect the detail of a particular quantum setup to a suitable classical limit. I strongly believe this question belongs to the sibling SE and is wasted here. $\endgroup$ – Cosmas Zachos Aug 15 '18 at 18:57
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In hindsight the correspondence principle seems obvious, but nature didn't have to behave this way. What the CP shows is that the transition from quantum to classical behavior is continuous rather than discrete for an individual quantum system as the energy scale increases. For example, the quantum behavior of individual systems may have persisted for all energies and classical behavior may have emerged only when averages over large ensembles of systems were studied.

To put this in modern perspective, consider the situation at the Planck scale. No one expects quantum physics to be a complete description of nature at this scale. Since we do not have a theory that describes nature at the Planck scale, we cannot know whether the transition between quantum theory to the eventual Planck scale theory will be continuous or discrete. If, for example, space-time becomes discrete (think about a cellular automaton model) at the Planck scale will the transition still look continuous?

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  • $\begingroup$ Thanks for the answer. "For example, the quantum behavior of individual systems may have persisted for all energies and classical behavior may have emerged only when averages over large ensembles of systems were studied." So you are saying that it is only average of the processes in quantum level need to produce the same results as classical theory but however the principle states that somehow produce the same results without even averaging, isn't it? $\endgroup$ – Deepakms Aug 16 '18 at 3:52
  • $\begingroup$ You are correct $\endgroup$ – Lewis Miller Aug 16 '18 at 14:33
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    $\begingroup$ The C P shows that averaging is not necessary for the emergence of classical behavior $\endgroup$ – Lewis Miller Aug 16 '18 at 14:34
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    $\begingroup$ I was only saying that nature may have dictated a different transition, but didn't. $\endgroup$ – Lewis Miller Aug 16 '18 at 14:37

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