Advertisement

Quantum Identity and Indistinguishability

  • Holger Lyre
Chapter

Abstract

This chapter stands conceptually between Chaps.  1 and  6. In Chap.  1, we introduced single-particle quantum mechanics in a Hilbert space \(\mathcal{H}\), while the present chapter treats n particles in a many-particle Hilbert space \(\mathcal{H}_n\); and Chap.  6 deals with variable particle numbers using creation and annihilation operators in a Fock space \(\mathcal{H}_F=\oplus \mathcal{H}_n\). The present chapter consists of two parts, of which Sect. 3.1 is more physical, while Sect. 3.2 has a stronger philosophical orientation.

References

  1. Adams, Robert M. 1979. Primitive thisness and primitive identity. Journal of Philosophy 76: 5–26.CrossRefGoogle Scholar
  2. Black, Max. 1952. The identity of indiscernibles. Mind 61: 153–64.CrossRefGoogle Scholar
  3. Born, Max. 1927. Quantenmechanik und Statistik. Naturwissenschaften 15: 238–242.ADSCrossRefGoogle Scholar
  4. Brown, Harvey, Erik Sjöqvist, and Guido Bacciagaluppi. 1999. Remarks on identical particles in de Broglie-Bohm theory. Physics Letters A 251: 229–235.ADSMathSciNetCrossRefGoogle Scholar
  5. Butterfield, Jeremy. 1993. Interpretation and identity in quantum theory. Studies in History and Philosophy of Science 24: 443–476.CrossRefGoogle Scholar
  6. Cassirer, Ernst. 1956. Determinism and Indeterminism in Modern Physics. New Haven: Yale University Press.Google Scholar
  7. Castellani, Elena (ed.). 1998. Interpreting Bodies: Classical and Quantum Objects in Modern Physics. Princeton: Princeton University Press.Google Scholar
  8. Castellani, Elena, and Peter Mittelstaedt. 2000. Leibniz’s principle, physics, and the language of physics. Foundations of Physics 30 (10): 1587–1604.MathSciNetCrossRefGoogle Scholar
  9. Caulton, Adam, and Jeremy Butterfield. 2012. Symmetries and paraparticles as a motivation for structuralism. British Journal for the Philosophy of Science 63 (2): 233–285.MathSciNetCrossRefGoogle Scholar
  10. Cortes, Alberto. 1976. Leibniz’s Principle of the identity of indiscernibles: A false principle. Philosophy of Science 43 (4): 491–505.MathSciNetCrossRefGoogle Scholar
  11. Dainton, Barry. 2001. Time and Space. Chesham: Acumen.Google Scholar
  12. Darrigol, Oliver. 1991. Statistics and combinatorics in early quantum theory II: Early symptoms of indistinguishability and holism. Historical Studies in the Physical Sciences 21: 237–98.MathSciNetCrossRefGoogle Scholar
  13. Della Rocca, Michael. 2005. Two spheres, twenty spheres, and the identity of indiscernibles. Pacific Philosophical Quarterly 86: 480–492.CrossRefGoogle Scholar
  14. Dieks, Dennis, and Marijn A.M. Versteegh. 2008. Identical quantum particles and weak discernibility. Foundations of Physics 38: 923–934.ADSMathSciNetCrossRefGoogle Scholar
  15. Dorato, Mauro, and Matteo Morganti. 2013. Grades of individuality. A pluralistic view of identity in quantum mechanics and in the sciences. Philosophical Studies 163 (3): 591–610.MathSciNetCrossRefGoogle Scholar
  16. Feynman, Richard P., Robert B. Leighton, and Matthew Sands. 1964. The Feynman Lectures on Physics, vol. 3. Reading: Addison-Wesley. http://www.feynmanlectures.caltech.edu/.
  17. French, Steven. 2011. Identity and individuality in quantum theory. The Stanford Encyclopedia of Philosophy (Summer 2011 Edition). http://plato.stanford.edu.
  18. French, Steven. 1975. Hacking away at the identity of indiscernibles: Possible worlds and Einstein’s principle of equivalence. Journal of Philosophy 92 (9): 455–466.MathSciNetCrossRefGoogle Scholar
  19. French, Steven. 1989. Identity and individuality in classical and quantum physics. Australasian Journal of Philosophy 67: 432–446.CrossRefGoogle Scholar
  20. French, Steven. 2014. The Structure of the World. Oxford: Oxford University Press.Google Scholar
  21. French, Steven, and Decio Krause (eds.). 2006. Identity and Individuality in Modern Physics. Oxford: Oxford University Press.Google Scholar
  22. French, Steven, and James Ladyman. 2003. Remodelling structural realism: Quantum physics and the metaphysics of structure. Synthese 136 (1): 31–56.MathSciNetCrossRefGoogle Scholar
  23. French, Steven, and James Ladyman. 2011. In defence of ontic structural realism. In Scientific Structuralism, ed. P. Bokulich, and A. Bokulich. New York: Springer.Google Scholar
  24. French, Steven, and Michael Redhead. 1988. Quantum physics and the identity of indiscernibles. British Journal for the Philosophy of Science 39: 233–246.MathSciNetCrossRefGoogle Scholar
  25. Friebe, Cord. 2014. Individuality, distinguishability, and (non-)entanglement: A defense of Leibniz’s principle. Studies in History and Philosophy of Modern Physics 48: 89–98.ADSMathSciNetCrossRefGoogle Scholar
  26. Ghirardi, GianCarlo, Luca Marinatto, and Tullio Weber. 2002. Entanglement and properties of composite quantum systems: A conceptual and mathematical analysis. Journal of Statistical Physics 108: 49–122.MathSciNetCrossRefGoogle Scholar
  27. Hacking, Ian. 1975. The identity of indiscernibles. Journal of Philosophy 72 (9): 249–256.CrossRefGoogle Scholar
  28. Hawley, Katherine. 2009. Identity and indiscernibility. Mind 118 (1): 101–119.CrossRefGoogle Scholar
  29. Hesse, Mary B. 1966. Models and Analogies in Science. Notre Dame: University of Notre Dame Press.Google Scholar
  30. Huggett, Nick, and Josh Norton. 2014. Weak discernibility for quanta, the right way. British Journal for the Philosophy of Science 65 (1): 39–58.MathSciNetCrossRefGoogle Scholar
  31. Ladyman, James, and Tomasz Bigaj. 2010. The principle of the identity of indiscernibles and quantum mechanics. Philosophy of Science 77 (1): 117–136.MathSciNetCrossRefGoogle Scholar
  32. Landau, L.D., and E.M. Lifschitz. 1965. Quantum Mechanics. Non-relativistic Theory, vol. 3, 2nd ed., Course of Theoretical Physics Oxford: Pergamon Press.Google Scholar
  33. Leitgeb, Hannes, and James Ladyman. 2008. Criteria of identity and structuralist ontology. Philosophia Mathematica (III) 16: 388–396.MathSciNetCrossRefGoogle Scholar
  34. Lewis, David K. 1986. On the Plurality of Worlds. Oxford: Blackwell.Google Scholar
  35. Loux, Michael J. 1998, \(^3\)2006. Metaphysics: A Contemporary Introduction. London: Routledge.Google Scholar
  36. Lyre, Holger. 2010. Humean perspectives on structural realism. In The Present Situation in the Philosophy of Science, ed. F. Stadler. Dordrecht: Springer.CrossRefGoogle Scholar
  37. Margenau, Henry. 1944. The exclusion principle and its philosophical importance. Philosophy of Science 11 (4): 187–208.CrossRefGoogle Scholar
  38. Messiah, Albert. 1979. Quantenmechanik, Band 2. Berlin: W. de Gruyter (French original: Mécanique quantique, Paris, 1959).Google Scholar
  39. Messiah, Albert, and Oscar Greenberg. 1964. Symmetrization postulate and its experimental foundation. Physical Review 136 (1B): 248–267.ADSMathSciNetCrossRefGoogle Scholar
  40. Meyenn, Karl von. 1987. Pauli’s belief in exact symmetries. In Symmetries in Physics (1600–1980), ed. M. Doncel, 329–358. Barcelona: Universitat Autònoma de Barcelona.Google Scholar
  41. Muller, Fred A, and Simon Saunders. 2008. Discerning fermions. British Journal for the Philosophy of Science 59: 499–548.MathSciNetCrossRefGoogle Scholar
  42. Muller, Fred A, and Michiel P. Seevinck. 2009. Discerning elementary particles. Philosophy of Science 76: 179–200.MathSciNetCrossRefGoogle Scholar
  43. Post, Heinz. 1963. Individuality and physics. The. Listener 70: 534–537.Google Scholar
  44. Quine, Willard van Orman. 1969. Ontological Relativity and Other Essays. New York: Columbia University Press.Google Scholar
  45. Quine, Willard van Orman. 1976. Grades of discriminability. Journal of Philosophy 73 (5): 113–116.CrossRefGoogle Scholar
  46. Saunders, Simon. 2003. Physics and Leibniz’s principles. In Symmetries in Physics: Philosophical Reflections, ed. K. Brading, and E. Castellani. Cambridge: Cambridge University Press.Google Scholar
  47. Saunders, Simon. 2006. Are quantum particles objects? Analysis 66: 52–63.CrossRefGoogle Scholar
  48. Stachel, John. 2002. ‘The relations between things’ versus ‘the things between relations’: The deeper meaning of the hole argument. In Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics, ed. D.B. Malament, 231–266. La Salle, IL: Open Court.Google Scholar
  49. Teller, Paul. 1983. Quantum physics, the identity of indiscernibles and some unanswered questions. Philosophy of Science 50 (2): 309–319.MathSciNetCrossRefGoogle Scholar
  50. Weyl, Hermann. 1950. The Theory of Groups and Quantum Mechanics. Dover edition, Courier Corporation.Google Scholar
  51. Weyl, Hermann. 1949. Philosophy of Mathematics and Natural Science. Princeton: Princeton University Press.zbMATHGoogle Scholar
  52. Weyl, Hermann. 1952. Symmetry. Princeton: Princeton University Press.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Chair of Theoretical PhilosophyUniversity of MagdeburgMagdeburgGermany

Personalised recommendations