Hostname: page-component-848d4c4894-mwx4w Total loading time: 0 Render date: 2024-06-24T18:19:31.142Z Has data issue: false hasContentIssue false

Chaos and Fundamentalism

Published online by Cambridge University Press:  01 April 2022

Gordon Belot*
Affiliation:
New York University
*
Send requests for reprints to the author, Department of Philosophy, New York University, New York, NY 10003.

Extract

It is natural to wonder what our multitude of successful physical theories tell us about the world—singly, and as a body. What are we to think when one theory tells us about a flat Newtonian spacetime, the next about a curved Lorentzian geometry, and we have hints of others, portraying discrete or higher-dimensional structures which look something like more familiar spacetimes in appropriate limits?

Type
Philosophy of Physics and Chemistry
Copyright
Copyright © 2000 by the Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

I would like to thank Bob Batterman for insightful comments on an earlier draft.

References

References

Batterman, R. (1995), “Theories Between Theories: Asymptotic Limiting Intertheoretic Relations”, Synthese 103: 171201.CrossRefGoogle Scholar
Belot, G. and Earman, J. (1997), “Chaos Out of Order: Quantum Mechanics, the Correspondence Principle and Chaos”, Studies in History and Philosophy of Modern Physics 28: 147182.CrossRefGoogle Scholar
Benatti, F. (1993), Deterministic Chaos in Infinite Quantum Systems. New York: Springer-Verlag.CrossRefGoogle Scholar
Cartwright, N. (1999), The Dappled World: A Study of the Boundaries of Science. New York: Cambridge University PressCrossRefGoogle Scholar
Casati, G. and Chirikov, B. V. (1995a), “Comment on ‘Decoherence, Chaos, and the Second Law’ “, Physical Review Letters 75: 350.CrossRefGoogle Scholar
Casati, G. and Chirikov, B. V. (1995b), “The Legacy of Chaos in Quantum Mechanics”, in Casati, G. and Chirikov, B.V. (eds.), Quantum Chaos: Between Order and Chaos. New York: Cambridge University Press, 353.CrossRefGoogle Scholar
De Bièvre, S., Esposti, M. Degli, and Giachetti, R. (1996), “Quantization of a Class of Piecewise Affine Transformations on the Torus”, Communications in Mathematical Physics 176: 7394.CrossRefGoogle Scholar
Degli Esposti, M., Graffi, S., and Isola, S. (1995), “Classical Limit of Quantized Hyperbolic Toral Automorphisms”, Communications in Mathematical Physics 167: 471507.CrossRefGoogle Scholar
Emch, G., Narnhofer, H., Thirring, W., and Sewell, G. (1994), “Anosov Actions on Noncommutative Algebras”, Journal of Mathematical Physics 35: 55825599.CrossRefGoogle Scholar
Ford, J., Mantica, G., and Ristow, G. H. (1991), “The Arnold's Cat: Failure of the Correspondence Principle”, Physica D 50: 493520.CrossRefGoogle Scholar
Lesniewski, A., Rubin, R., and Salwen, N. (1998), “Classical Limits for Quantum Maps on the Torus”, Journal of Mathematical Physics 39: 18351847.CrossRefGoogle Scholar
Liu, C. (1998), “Explaining the Emergence of Cooperative Phenomena”, Philosophy of Science 66 (Proceedings): S92S106.CrossRefGoogle Scholar
Neilson, D. (1989), “Electronic Properties of Two-Dimensional Systems and the Quantum Hall Effect”, in Mahanty, J. and Das, M. P. (eds.), Condensed Matter Physics. Singapore: World Scientific, 263291.Google Scholar
Peter, I. and Emch, G. (1998), “Quantum Anosov Flows: A New Family of Examples”, Journal of Mathematical Physics 39: 45134539.CrossRefGoogle Scholar
Sussman, G. and Wisdom, J. (1992), “Chaotic Evolution of the Solar System”, Science 257: 5662.CrossRefGoogle ScholarPubMed
Toulmin, S. (1953), The Philosophy of Science: An Introduction. New York: Harper and Row.Google Scholar
Van Fraassen, B. and Sigman, J. (1992), “Interpretation in Science and in the Arts”, in Levine, G. (ed.), Realism and Representation: Essays on the Problem of Realism in Relation to Science, Literature, and Culture. Madison: The University of Wisconsin Press, 7399.Google Scholar
Vitali, D. and Grigolini, P. (1998), “Chaos, Thermodynamics and Quantum Mechanics: an Application to Celestial Dynamics”, Physics Letters A 249: 248258.CrossRefGoogle Scholar
Wisdom, J. (1987), “Chaotic Behaviour in the Solar System”, in Berry, M., Percival, I., and Weiss, N. (eds.), Dynamical Chaos. Princeton: Princeton University Press, 109129.Google Scholar
Zurek, W. (1998), “Decoherence, Chaos, Quantum-Classical Correspondence, and the Algorithmic Arrow of Time”, Physica Scripta 76: 186198.CrossRefGoogle Scholar