The idea tha taking the limit of the non-classical theories for certain parameters (relativity and quantum mechanics) should lead to the classical theory.
It appears that classical limit is only very strict for relativity. For quantum mechanics it is much more hand-wavy thing. See also: Subtle is the Lord by Abraham Pais (1982) page 55.
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The classical limit is a regime in which quantum corrections or occupation-number discreteness become negligible and classical equations describe the relevant observables.
The classical limit is a concept in physics that refers to the behavior of quantum systems as they transition to classical systems, typically as certain parameters approach appropriate limits. It describes the conditions under which quantum mechanical systems can be approximated by classical mechanics. Here are a few key points about the classical limit: 1. **Planck's Constant**: One of the most important factors in the classical limit is Planck's constant (h).