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The Emergence of the Macroworld: A Study of Intertheory Relations in Classical and Quantum Mechanics

Published online by Cambridge University Press:  01 January 2022

Malcolm R. Forster  and
Alexey Kryukov
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Abstract

Classical mechanics is empirically successful because the probabilistic mean values of quantum mechanical observables follow the classical equations of motion to a good approximation (Messiah 1970, 215). We examine this claim for the one-dimensional motion of a particle in a box, and extend the idea by deriving a special case of the ideal gas law in terms of the mean value of a generalized force used to define “pressure.” The examples illustrate the importance of probabilistic averaging as a method of abstracting away from the messy details of microphenomena, not only in physics, but in other sciences as well.

Type
Reduction and Structure of Theories
Information
Philosophy of Science , Volume 70 , Issue 5: Proceedings of the 2002 Biennial Meeting of The Philosophy of Science Association. Part I: Contributed Papers , December 2003 , pp. 1039 - 1051
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

‡

We are thankful for the criticisms and comments of two anonymous referees and the participants at the PSA meetings in Milwaukee, November, 2002.

References

Batterman, Robert W. (1998), “Why Equilibrium Statistical Mechanics Works: Universality and the Renormalization Group”, Why Equilibrium Statistical Mechanics Works: Universality and the Renormalization Group 65:183–208.Google Scholar
Batterman, Robert W. (2001a), The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction and Emergence. New York: Oxford University Press.CrossRefGoogle Scholar
Batterman, Robert W. (2001b), “Intertheory Relations in Physics”, The Stanford Encyclopedia of Philosophy (Spring), Edward N. Zalta (ed.), http://plato.stanford.edu/archives/spr2001/entries/physics-interrelate/.Google Scholar
Beatty, John (1984), “Chance and Natural Selection”, Chance and Natural Selection 51:183–211.Google Scholar
Brandon, Robert, and Carson, Scott (1996), “The Indeterministic Character of Evolutionary Theory: No ‘No Hidden Variable’ Proof, but No Room for Determinism Either”, The Indeterministic Character of Evolutionary Theory: No ‘No Hidden Variable’ Proof, but No Room for Determinism Either 63:315–337.Google Scholar
Callender, Craig (1999), “Reducing Thermodynamics to Statistical Mechanics: The Case of Entropy”, Reducing Thermodynamics to Statistical Mechanics: The Case of Entropy 96, 348–373.Google Scholar
Earman, John, and Rédei, M. (1996), “Why Ergodic Theory Does Not Explain the Success of Equilibrium Statistical Mechanics”, Why Ergodic Theory Does Not Explain the Success of Equilibrium Statistical Mechanics 47:63–78.Google Scholar
Gibbs, J. Willard ([1902] 1981), Elementary Principles in Statistical Mechanics. Woodbridge, CN: Ox Bow Press.Google Scholar
Gillespie, Daniel T. (1970), A Quantum Mechanics Primer: An Elementary Introduction to the Formal Theory of Nonrelativistic Quantum Mechanics. Scranton, PA: International Textbook Co.Google Scholar
Glymour, Bruce (2001), “Selection, Indeterminism and Evolutionary Theory”, Selection, Indeterminism and Evolutionary Theory 68:536–544.Google Scholar
Graves, Leslie, Horan, Barbara L., and Rosenberg, Alex (1999), “Is Indeterminism the Source of the Statistical Character of Evolutionary Theory?” Philosophy of Science 66:140–157.CrossRefGoogle Scholar
Horan, Barbara L. (1994), “The Statistical Character of Evolutionary Theory”, The Statistical Character of Evolutionary Theory 61:76–95.Google Scholar
Khinchin, Aleksandra (1949), Mathematical Foundations of Statistical Mechanics. Translated from the Russian by G. Gamov. Mineola, NY: Dover Publications.Google Scholar
Khinchin, Aleksandra (1960), Mathematical Foundations of Quantum Statistics. Mineola, NY: Dover Publications.Google Scholar
Mantegna, Rosario N., and Stanley, H. Eugene (2000), An Introduction to Econophysics. Cambridge: Cambridge University Press.Google Scholar
Messiah, Albert (1970), Quantum Mechanics, Vol. 1. Amsterdam: North-Holland.Google Scholar
Mills, Susan, and Beatty, John (1979), “The Propensity Interpretation of Fitness”, The Propensity Interpretation of Fitness 46:263–286.Google Scholar
Nagel, Ernst (1961), The Structure of Science. New York: Harcourt, Brace and World.CrossRefGoogle Scholar
Plerou, Vasiliki, Gopikrishnan, Parameswaran, and Stanley, H. Eugene (2003), “Two-Phase Behaviour of Financial Markets”, Two-Phase Behaviour of Financial Markets 421: 130.Google ScholarPubMed
Rieke, Fred, Warland, David, Steveninck, Rob van and Bialek, William (1997), Spikes: Exploring the Neural Code, Cambridge, MA: MIT Press.Google Scholar
Rosenberg, Alex (1985), “Is the Theory of Natural Selection a Statistical Theory?”, Canadian Journal of Philosophy (Supplement) 14:187–207.Google Scholar
Rosenberg, Alex (2001), “Discussion Note: Indeterminism, Probability, and Randomness in Evolutionary Theory”, Discussion Note: Indeterminism, Probability, and Randomness in Evolutionary Theory 68:536–544.Google Scholar
Schwabl, Franz (1993), Quantum Mechanics, 2d rev. ed. New York: Springer.Google Scholar
Sober, Elliott (1984), The Nature of Selection: Evolutionary Theory in Philosophical Focus. Cambridge, MA: MIT Press.Google Scholar
Waters, C. Kenneth (1990), “Why the Anti-Reductionist Consensus Won't Survive the Case of Classical Mendelian Genetics”, in Arthur Fine, M. Forbes, and L. Wessels (eds.) PSA 1990, Vol. 1:125–139.Google Scholar