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?
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?