The Classical Limit as an Approximation
Benjamin H. Feintzeig
Abstract
I argue that it is possible to give an interpretation of the classical <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:c="http://cambridge.org/core/content" xmlns:m="http://cambridge.org/core/metadata"><mml:mrow><mml:mi>ℏ</mml:mi><mml:mo>→</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math> limit of quantum mechanics that results in a partial explanation of the success of classical mechanics. The interpretation is novel in that it allows one to explain the success of the theoretical structure of classical mechanics. This interpretation clarifies the relationship between physical quantities and propositions in quantum theories and provides a precise notion of a quantum theory holding “approximately on certain scales.”