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How Classical Particles Emerge From the Quantum World

Abstract

The symmetrization postulates of quantum mechanics (symmetry for bosons, antisymmetry for fermions) are usually taken to entail that quantum particles of the same kind (e.g., electrons) are all in exactly the same state and therefore indistinguishable in the strongest possible sense. These symmetrization postulates possess a general validity that survives the classical limit, and the conclusion seems therefore unavoidable that even classical particles of the same kind must all be in the same state—in clear conflict with what we know about classical particles. In this article we analyze the origin of this paradox. We shall argue that in the classical limit classical particles emerge, as new entities that do not correspond to the “particle indices” defined in quantum mechanics. Put differently, we show that the quantum mechanical symmetrization postulates do not pertain to particles, as we know them from classical physics, but rather to indices that have a merely formal significance. This conclusion raises the question of whether many discussions in the literature about the status of identical quantum particles have not been misguided.

References

  1. 1.

    Black, M.: The identity of indiscernibles. Mind 61, 153–164 (1952)

    Article  Google Scholar 

  2. 2.

    Dieks, D.: Quantum statistics, identical particles and correlations. Synthese 82, 127–155 (1990)

    MathSciNet  Article  Google Scholar 

  3. 3.

    Dieks, D., Versteegh, M.A.M.: Identical particles and weak discernibility. Found. Phys. 38, 923–934 (2008)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  4. 4.

    Dieks, D.: Are ‘identical quantum particles’ weakly discernible objects. In: Suarez, M., Dorato, M., Redei, M. (eds.) EPSA Philosophical Issues in the Sciences: Launch of the European Philosophy of Science Association, vol. 2, pp. 21–31. Springer, Berlin (2010)

    Google Scholar 

  5. 5.

    French, S., Krause, D.: Identity in Physics: A Historical, Philosophical, and Formal Analysis. Oxford University Press, London (2006)

    Google Scholar 

  6. 6.

    Lubberdink, A.: De individualiseerbaarheid van identieke deeltjes. Master Thesis, Utrecht University (1998). http://gradthesis.andrealubberdink.nl

  7. 7.

    Lubberdink, A.: Identical particles in quantum mechanics. arXiv:0910.4642

  8. 8.

    Mullin, W.J., Blaylock, G.: Quantum statistics: is there an effective fermion repulsion or boson attraction? Am. J. Phys. 71, 1223–1231 (2003)

    ADS  Article  Google Scholar 

  9. 9.

    Muller, F.A., Saunders, S.: Discerning fermions. Br. J. Philos. Sci. 59, 499–548 (2008)

    MathSciNet  MATH  Article  Google Scholar 

  10. 10.

    Muller, F.A., Seevinck, M.: Discerning elementary particles. Philos. Sci. 76, 179–200 (2009)

    MathSciNet  Article  Google Scholar 

  11. 11.

    Quine, W.V.: Grades of discriminability. J. Philos. 73, 113–116 (1976). Reprinted in Quine, W.V.: Theories and Things. Harvard University Press (1981)

    Article  Google Scholar 

  12. 12.

    Saunders, S.: Physics and Leibniz’s principles. In: Brading, K., Castellani, E. (eds.) Symmetries in Physics: Philosophical Reflections, pp. 289–307. Cambridge University Press, Cambridge (2003)

    Chapter  Google Scholar 

  13. 13.

    Saunders, S.: Are quantum particles objects? Analysis 66, 52–63 (2006)

    MATH  Article  Google Scholar 

  14. 14.

    Teller, P.: Quantum mechanics and haecceities. In: Castellani, E. (ed.) Interpreting Bodies: Classical and Quantum Objects in Modern Physics, pp. 114–141. Princeton University Press, Princeton (1998)

    Google Scholar 

  15. 15.

    van Fraassen, B.: Quantum Mechanics: An Empiricist View. Oxford University Press, London (1991)

    Google Scholar 

  16. 16.

    von Neumann, J.: Mathematische Grundlagen der Quantenmechanik. Springer, Berlin (1932) and (1996)

    MATH  Google Scholar 

  17. 17.

    Zurek, W.H.: Decoherence and the transition from quantum to classical—revisited. In: Duplantier, B., Raimond, J.-M., Rivasseau, M. (eds.) Quantum Decoherence, Poincaré Seminar 2005. Progress in Mathematical Physics, vol. 48, pp. 1–31. Birkhäuser, Basel (2007)

    Google Scholar 

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Correspondence to Dennis Dieks.

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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Dieks, D., Lubberdink, A. How Classical Particles Emerge From the Quantum World. Found Phys 41, 1051–1064 (2011). https://doi.org/10.1007/s10701-010-9515-2

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  • DOI: https://doi.org/10.1007/s10701-010-9515-2

Keywords

  • Identical particles
  • Indistinguishability
  • Emergence
  • Classical limit of quantum mechanics