Book contents
- Frontmatter
- Contents
- Preface
- 1 Quantum mechanics and its interpretation
- 2 Hamilton–Jacobi theory
- 3 Elements of the quantum theory of motion
- 4 Simple applications
- 5 Interference and tunnelling
- 6 The classical limit
- 7 Many-body systems
- 8 Theory of experiments
- 9 Spin ½: the Pauli theory
- 10 Spin ½: the rigid rotator
- 11 The Einstein–Podolsky–Rosen experiment and nonlocality
- 12 Relativistic quantum theory
- References
- Index
6 - The classical limit
Published online by Cambridge University Press: 20 January 2010
- Frontmatter
- Contents
- Preface
- 1 Quantum mechanics and its interpretation
- 2 Hamilton–Jacobi theory
- 3 Elements of the quantum theory of motion
- 4 Simple applications
- 5 Interference and tunnelling
- 6 The classical limit
- 7 Many-body systems
- 8 Theory of experiments
- 9 Spin ½: the Pauli theory
- 10 Spin ½: the rigid rotator
- 11 The Einstein–Podolsky–Rosen experiment and nonlocality
- 12 Relativistic quantum theory
- References
- Index
Summary
Conceptual and formal problems
Many of the problems surrounding the interpretation of quantum mechanics stem from the absence of a sufficiently general and physically transparent analysis of the connection with the domain in which classical concepts are assumed to apply. It is the purpose of this chapter to describe with the aid of a few examples how the quantum potential approach provides a context within which the conceptual and formal issues raised by this problem may be clarified. A key question is to explain how the state or context dependence which is so characteristic of the quantum domain turns into state independence at a certain level, characterized as ‘classical’.
To illustrate one aspect of the conceptual problem we recall that in Bohr's interpretation the validity of classical concepts is already presupposed since, it is suggested, it is only in terms of these that one can unambiguously communicate the results of experiments in the quantum domain. Thus, classical physics must be considered as prior to quantum mechanics and the latter is a generalization of the former in that it provides a new set of laws governing the application of classical concepts. According to this view, any procedure by which classical mechanics is recovered from quantum mechanics as a mathematical limit can only be a demonstration of consistency with the already postulated epistemological relation between the two theories and not as a ‘derivation’ of classical mechanics from quantum mechanics (George, Prigogine & Rosenfeld, 1972).
- Type
- Chapter
- Information
- The Quantum Theory of MotionAn Account of the de Broglie-Bohm Causal Interpretation of Quantum Mechanics, pp. 218 - 276Publisher: Cambridge University PressPrint publication year: 1993