The Problem of Individualism from Greek Thought to Quantum Physics

  • Peter Mittlestatedt
Part of the Synthese Library book series (SYLI, volume 406)


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.


  1. Aharonov, Y., & Albert, D. (1984). Is the usual notion of time evolution adequate for quantum mechanical systems I. Physics Review D, 29, 223–227.CrossRefGoogle Scholar
  2. Bunch, P., Grabowski, M., & Lahti, P. (1995). Operational quantum physics. Heidelberg: Springer.Google Scholar
  3. Bunch, P., Lahti, P., & Mittelstaedt, P. (1996). The quantum theory of measurement (2nd. ed.). Heidelberg: Springer.Google Scholar
  4. Castellani, E., & Mittelstaedt, P. (1998). Leibniz’ principle, physics, and the language of physics. Foundations of Physics, 30, 1587–1604.CrossRefGoogle Scholar
  5. Dally Chiara, M. L. (1995). Unsharp quantum logics. International Journal of Theoretical Physics, 34, 1331–1336.CrossRefGoogle Scholar
  6. Frede, M., & Patzig, G. (1988). Aristoteles “Metaphysik Z” (2 Vol.) C.H. Beck, Miinchen.Google Scholar
  7. Giuntini, R. (1995). Quasilinear QMV algebras. International Journal of Theoretical Physics, 34, 1397–1407.CrossRefGoogle Scholar
  8. Hegerfeld, G. C., & Ruijsenaars, S. N. M. (1980). Remarks on causality, localization and speeding of wave packets. Physics Review D, 22, 377–384.CrossRefGoogle Scholar
  9. Heisenberg, W. (1930). Die physikalischen Prinzipien der Quantentheorie. Leipzig: S. Hirzel.Google Scholar
  10. Islam, C. J. (1994). Quantum logic and the history approach to quantum theory. Journal of Mathematical Physics, 35, 2157–2185.CrossRefGoogle Scholar
  11. Mittelstaedt, P. (1983). Relativistic quantum logic. International Journal of Theoretical Physics, 22, 293–313.CrossRefGoogle Scholar
  12. 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
  13. 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.CrossRefGoogle Scholar
  14. Mittelstaedt, P. (1995). Constitution of objects in classical mechanics and in quantum mechanics. International Journal of Theoretical Physics, 34, 1615–1626.CrossRefGoogle Scholar
  15. Piron, C. (1976). Foundations of quantum physics (p. 93 ff, 77–90). Reading: Benjamin.Google Scholar
  16. Schlieder, S. (1968). Einige Bemerkungen zu Zustandsanderungen von relativistischen quanten-mechanischen Systemen durch Messung and zur Lukalitatsforderung. Communications in Mathematical Physics, 7, 303–331.CrossRefGoogle Scholar
  17. 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
  18. Strohmeyer, I. (1995). Quantentheorie und Transzendentalphilosophie. Heidelberg: Spektrum.Google Scholar
  19. Weyl, H. (1966). Philosophie der Mathematik und der Naturwissenschaften, Oldenburg. Google Scholar
  20. 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

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Peter Mittlestatedt
    • 1
  1. 1.Department of PhysicsUniversity of CologneCologneGermany

Personalised recommendations