Skip to main content
SpringerLink
Log in
Book cover

Philosophers Look at Quantum Mechanics pp 181–197Cite as

The Problem of Individualism from Greek Thought to Quantum Physics

  • Chapter
  • First Online:

  • 497 Accesses

Part of the book series: Synthese Library ((SYLI,volume 406))

Abstract

Individuals in the strict sense do not exist in quantum physics. This paper argues that unsharp observables, almost repeatable and weakly disturbing measurements allow for the definition of unsharp individuals which is sufficient for all practical purposes. Many quantum physical experiments and the obvious existence of individuals in the classical world can be explained in this way. On the other hand, if quantum mechanics is considered as universally valid then there is no classical world in the strict sense. The paper includes a Divertimento on an analogy between the motion of individual quantum systems and the motion of angels according to the treatment of Thomas Aquinas in his Summa Theologica.

Peter Mittlestatedt (deceased, 2014) was Professor of Physics at the University of Cologne, Germany.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    Frede and Patzig (1988).

  2. 2.

    Cf. Wieland (1973).

  3. 3.

    Cf., e.g., Johannes Philoponos. De opificio miindi, 1.10 ff., Herder, Freiburg, (1977).

  4. 4.

    English translation by Fathers of the English Domenican Province. Westininstei (Maryland), 1981.

  5. 5.

    But an angel is not in a place as commensurate and contained, but rather as containing it. Neither then is the local movement of an angel commensurate with place: ...; in fact it may he either continuous or not.

  6. 6.

    But if an angel’s movement is not continuous, it is possible for him to pass from one extreme to another without going through the middle.

  7. 7.

    So an angel can be in one place (x) in one instant (t), and in another place (x′, x′ ≠ x) in the next instant (t’) without any time intervening (t – t′ = +0). (Formulas are added by the author).

  8. 8.

    In order to avoid that the angel is omnipresent, in Questio 53.3 “nullo tempore” must be understood such that t – t’ = +0, i. e., the time difference is arbitrary small but positive.

  9. 9.

    …he is in one place, in such a manner that he is not in another.

  10. 10.

    The movement of an angel in a place is nothing else than the various contacts of various places successively but not at once.

  11. 11.

    G.W. Leibniz, Discourse de Metaphysique, 9. (GP IV, p. 433).

  12. 12.

    More details about this point can be found in E. Castellani and P. Mittelstaedt (1998).

  13. 13.

    G. W. Leibniz, Nouveaux Essais sur l’entendement humain, Chap. XXVII, § 3. (GP V, p. 214).

  14. 14.

    I. Kant, Critique of Pure Reason, A 272.

  15. 15.

    I. Kant, Critique of Pure Reason, B 600.

  16. 16.

    Kant, Critique of Pure Reason, A 272.

  17. 17.

    Weyl (1966).

  18. 18.

    Cf. Mittlestaedt (1994), Strohmeyer (1995).

  19. 19.

    Hegerfeld and Ruijsenaars (1980).

  20. 20.

    Schlieder (1968).

  21. 21.

    Schlieder (1968).

  22. 22.

    Schlieder (1968).

  23. 23.

    Piron (1976).

  24. 24.

    Heisenberg (1930).

  25. 25.

    Cf. Mittelstaedt (1984, 1995), Busch et al. (1995), Giuntini (1995), Dalla Chiara (1995).

  26. 26.

    Aharanov and Albert (1984).

  27. 27.

    Cf., e.g., Stachow (1985), Mittelstaedt (1983), Islam (1994).

  28. 28.

    Cf. Bunch et al. (1995, 1996).

References

  • Aharonov, Y., & Albert, D. (1984). Is the usual notion of time evolution adequate for quantum mechanical systems I. Physics Review D, 29, 223–227.

    Article  Google Scholar 

  • Bunch, P., Grabowski, M., & Lahti, P. (1995). Operational quantum physics. Heidelberg: Springer.

    Google Scholar 

  • Bunch, P., Lahti, P., & Mittelstaedt, P. (1996). The quantum theory of measurement (2nd. ed.). Heidelberg: Springer.

    Google Scholar 

  • Castellani, E., & Mittelstaedt, P. (1998). Leibniz’ principle, physics, and the language of physics. Foundations of Physics, 30, 1587–1604.

    Article  Google Scholar 

  • Dally Chiara, M. L. (1995). Unsharp quantum logics. International Journal of Theoretical Physics, 34, 1331–1336.

    Article  Google Scholar 

  • Frede, M., & Patzig, G. (1988). Aristoteles “Metaphysik Z” (2 Vol.) C.H. Beck, Miinchen.

    Google Scholar 

  • Giuntini, R. (1995). Quasilinear QMV algebras. International Journal of Theoretical Physics, 34, 1397–1407.

    Article  Google Scholar 

  • Hegerfeld, G. C., & Ruijsenaars, S. N. M. (1980). Remarks on causality, localization and speeding of wave packets. Physics Review D, 22, 377–384.

    Article  Google Scholar 

  • Heisenberg, W. (1930). Die physikalischen Prinzipien der Quantentheorie. Leipzig: S. Hirzel.

    Google Scholar 

  • Islam, C. J. (1994). Quantum logic and the history approach to quantum theory. Journal of Mathematical Physics, 35, 2157–2185.

    Article  Google Scholar 

  • Mittelstaedt, P. (1983). Relativistic quantum logic. International Journal of Theoretical Physics, 22, 293–313.

    Article  Google Scholar 

  • Mittelstaedt, R. (1984). Constituting, naming, and identity in quantum logic. In Recent developments in quantum logic (pp. 215–234). Mannheim: B.I. Wissenschaftsvedag.

    Google Scholar 

  • Mittelstaedt, P. (1994). The constitution of objects in Kant’s philosophy and in modern physics. In P. Parrini (Ed.), Kant and contemporary epistemology (pp. 115–129). Dordrecht: Kluwer.

    Chapter  Google Scholar 

  • Mittelstaedt, P. (1995). Constitution of objects in classical mechanics and in quantum mechanics. International Journal of Theoretical Physics, 34, 1615–1626.

    Article  Google Scholar 

  • Piron, C. (1976). Foundations of quantum physics (p. 93 ff, 77–90). Reading: Benjamin.

    Google Scholar 

  • Schlieder, S. (1968). Einige Bemerkungen zu Zustandsanderungen von relativistischen quanten-mechanischen Systemen durch Messung and zur Lukalitatsforderung. Communications in Mathematical Physics, 7, 303–331.

    Article  Google Scholar 

  • Stachow, E.-W. (1985). Structures of quantum language for individual systems. In Recent developments in quantum logic (pp. 129–145). Mannheim: B.I. Wissenschaftsverlag.

    Google Scholar 

  • Strohmeyer, I. (1995). Quantentheorie und Transzendentalphilosophie. Heidelberg: Spektrum.

    Google Scholar 

  • Weyl, H. (1966). Philosophie der Mathematik und der Naturwissenschaften, Oldenburg.

    Google Scholar 

  • Wieland, W. (1973). Kontinuum and Engelszeit bei Thomas von Aquino. In: E. Scheibe u. G. Siiflmann (Eds.), Einheit und Vielheit. Gottingen: Vandenhoeck and Rupprecht.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of Cologne, Cologne, Germany

    Peter Mittlestatedt

Authors
  1. Peter Mittlestatedt
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. CUNY Graduate Center & Queens College CUNY, The City University of New York, New York City, NY, USA

    Alberto Cordero

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Mittlestatedt, P. (2019). The Problem of Individualism from Greek Thought to Quantum Physics. In: Cordero, A. (eds) Philosophers Look at Quantum Mechanics. Synthese Library, vol 406. Springer, Cham. https://doi.org/10.1007/978-3-030-15659-6_12

Download citation

Publish with us

Policies and ethics

Search

Navigation