In the prelude to his quantum mechanics textbook Principles of Quantum Mechanics, R. Shankar describes several features of the progression from older scientific theories to newer ones, and how the older ones are related to the newer ones:
- There is a domain of phenomena described by the new theory and a sub-domain wherein the old theory is reliable (to a given accuracy).
- Within the sub-domain either theory may be used to make quantitative predictions. It might often be more expedient to employ the old theory.
- In additional to numerical accuracy, the new theory often brings about radical conceptual changes. Being of a qualitative nature, these will have a bearing on all of .
This is a nice way of thinking about it, I think.