Abstract
The ongoing debates about the interpretation of quantum mechanics have often taken place in forums such as the measurement problem and Schrödinger’s cat paradox. I urge that we move beyond those old forums, and consider instead the more general problem of how classical properties emerge from quantum mechanics. Quantum chaos appears as a special case of this general problem, being the study of the emergence of classical chaos from QM. Such a study quickly leads to the following conclusion: the classical limit of a quantum state is typically an ensemble of classical orbits, and not a single classical orbit. This fact enables us to understand the relation between several quantum and classical dynamical models. This study also reveals interesting connections between old and new problems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. E. Ballentine, Int. J. Theor. Phys. 27, 211–218 (1988).
L. E. Ballentine, Found. Phys. 20, 1329–1343 (1990).
L. E. Ballentine, Quantum Mechanics (Prentice-Hall, Englewood Cliffs, New Jersey, 1990 ).
L. E. Ballentine, Yumin Yang, and J. P. Zibin, Phys. Rev. A (to be published).
A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics ( Springer, New York, 1991 ).
G. Casati, editor, Chaotic Behavior in Quantum Systems ( Plenum, New York, 1985 ).
H. A. Cerdeira, R. Ramaswamy, M. C. Gutzwiller, and G. Casati, editors, Quantum Chaos ( World Scientific, Singapore, 1991 ).
P. Cvitanovic, I. Percival, and A. Wirtzba, editors, Quantum Chaos - Quantum Measurement ( 1992, Kluwer, Dordrecht ).
L. E. Ballentine, Phys. Rev. A 44, 4126–4132 (1991).
L. E. Ballentine, Phys. Rev. A 44, 4133–4141 (1991).
L. E. Ballentine, Phys. Rev. A 47, 2592–2600 (1993).
J. E. G. Farina, Am. J. Phys. 45 1200 (1977). This paper gives a simple example in which the symmetrized correlation between the position and momentum operators arises, and is the natural analog of the corresponding classical correlation.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Ballentine, L.E. (1995). The Emergence of Classical Properties from Quantum Mechanics: New Problems from Old. In: Ferrero, M., van der Merwe, A. (eds) Fundamental Problems in Quantum Physics. Fundamental Theories of Physics, vol 73. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8529-3_3
Download citation
DOI: https://doi.org/10.1007/978-94-015-8529-3_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4608-6
Online ISBN: 978-94-015-8529-3
eBook Packages: Springer Book Archive