Editing Correspondence principle (section)

==Modern view==
While Bohr viewed "correspondence" as principle aiding his description of quantum phenomena, fundamental differences between the mathematical structure of quantum and of classical mechanics prevents correspondence in many cases. Rather than a principle, "there may be in some situations an approximate correspondence between classical and quantum concepts," physicist [[Asher Peres]] put it.<ref name=Peres1993>{{citation |last=Peres |first=Asher |author-link=Asher Peres |title=Quantum Theory: Concepts and Methods |title-link=Quantum Theory: Concepts and Methods |publisher=Kluwer |year=1993 |isbn=0-7923-2549-4}}</ref>{{rp|298}} Since quantum mechanics operates in a discrete space and classical mechanics in a continuous one, any correspondence will be necessarily fuzzy and elusive.<ref name=Peres1993/>{{rp|229}}

Introductory quantum mechanics textbooks suggest that quantum mechanics goes over to classical theory in the limit of high quantum numbers<ref>{{Cite book |last=Levine |first=Ira N. |title=Quantum chemistry |date=1991 |publisher=Prentice Hall |isbn=978-0-205-12770-2 |edition=4 |location=Englewood Cliffs, N.J}}</ref>{{rp|27}} or in a limit where the Planck constant in the quantum formula is reduced to zero, <math>\hbar \rightarrow 0</math>.<ref name=Messiah_vI/>{{rp|214}} However such correspondence is not always possible. For example, classical systems can exhibit chaotic orbits which diverge but quantum states are unitary and maintain a fixed overlap.<ref name=Peres1993/>{{rp|347}}

===Generalized correspondence principle===

The term "generalized correspondence principle" has been used in the study of the history of science to mean the reduction of a new [[scientific theory]] to an earlier scientific theory in appropriate circumstances.<ref name="SEP"/> This requires that the new theory explain all the phenomena under circumstances for which the preceding theory was known to be valid; it also means that new theory will retain large parts of the older theory. The generalized principle applies correspondence across aspects of a complete theory, not just a single formula as in the classical limit correspondence.<ref name=PostInFrench>{{Cite book |last=Post |first=H. R. |url=http://link.springer.com/10.1007/978-94-017-1185-2_1 |title=Correspondence, Invariance and Heuristics: In Praise of Conservative Induction |date=1993 |publisher=Springer Netherlands |isbn=978-90-481-4229-3 |editor-last=French |editor-first=Steven |volume=148 |location=Dordrecht |pages=1–43 |doi=10.1007/978-94-017-1185-2_1 |editor-last2=Kamminga |editor-first2=Harmke}}</ref>{{rp|17}} For example, [[Albert Einstein]] in his 1905 work on relativity noted that classical mechanics relied on Galilean relativity while electromagnetism did not, and yet both work well. He produced a new theory that combined them in a way that reduced to these separate theories in approximations.
Ironically the singular failure of this "generalized correspondence principle" concept of scientific theories is the replacement of classical mechanics with quantum mechanics.<ref name=PostInFrench/>{{rp|21}}