Correspondence Principle

The correspondence principle is generally known as the Bohr correspondence principle (CP), for Niels Bohr. It is considered one of Bohr's greatest contributions to physics, along with his derivation of the Balmer formula. Bohr's leading idea is that classical physics, though limited in scope, is indispensable for the understanding of quantum physics. The idea that old science is “indispensable” to the understanding of new science is in fact the main theme in using the concept of correspondence; therefore, the CP can be defined as the principle by which new theories of science (physics in particular) can relate to previously accepted theories in the field by means of approximation at a certain limit. Historically, Max Planck had introduced the concept in 1906. Bohr's first handling of the concept was in his first paper after World War I, in which he showed that quantum [Page 279]formalism would lead to classical physics when n→∞, where n is the quantum number. Although there were many previous uses of the concept, the important issue here is not to whom the concept can be attributed, but an understanding of the various ways that it can be used in scientific and philosophic research.

The principle is important for the continuity in science. There are two ways of thinking about such continuity. A theory T covers a set of observations S. A new observation s1 is detected. T cannot explain s1. Scientists first try to adapt T to be able to account for s1. But if T is not in principle able to explain s1, then scientists will start to look for another theory, T∗, that can explain S and s1. The scientist will try to derive T∗ by using CP as a determining factor. In such a case, T∗ should lead to T at a certain limit.

Nonetheless, sometimes there may be a set of new observations, S1, for which it turns out that a direct derivation of T ∗ from T that might in principle account for S1 is not possible or at least does not seem to be possible. Then the scientist will try to suggest T∗ separately from the accepted set of boundary conditions and the observed set of S and S1. But because T was able to explain the set of it is highly probable that T has a certain limit of correct assumptions that led to its ability to explain S. Therefore, any new theory T∗ that would account for S and S1 should resemble T at a certain limit. This can be obtained by specifying a certain correspondence limit at which the new formalism of T∗ will lead to the old formalism of T.

These two ways of obtaining T∗ are the general forms of applying the correspondence principle. Nevertheless, the practice of science presents us with many ways of connecting T∗ to T or parts of it. Hence it is important to discuss the physicists’ different treatments of the CP. Moreover, the interpretation of CP and the implications of using CP will determine our picture of science and the future development of science; hence, it is important to discuss the philosophical implications of CP and the different philosophical understandings of the concept.

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