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.
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Notes
- 1.
Frede and Patzig (1988).
- 2.
Cf. Wieland (1973).
- 3.
Cf., e.g., Johannes Philoponos. De opificio miindi, 1.10 ff., Herder, Freiburg, (1977).
- 4.
English translation by Fathers of the English Domenican Province. Westininstei (Maryland), 1981.
- 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.
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.
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.
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.
…he is in one place, in such a manner that he is not in another.
- 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.
G.W. Leibniz, Discourse de Metaphysique, 9. (GP IV, p. 433).
- 12.
More details about this point can be found in E. Castellani and P. Mittelstaedt (1998).
- 13.
G. W. Leibniz, Nouveaux Essais sur l’entendement humain, Chap. XXVII, § 3. (GP V, p. 214).
- 14.
I. Kant, Critique of Pure Reason, A 272.
- 15.
I. Kant, Critique of Pure Reason, B 600.
- 16.
Kant, Critique of Pure Reason, A 272.
- 17.
Weyl (1966).
- 18.
- 19.
Hegerfeld and Ruijsenaars (1980).
- 20.
Schlieder (1968).
- 21.
Schlieder (1968).
- 22.
Schlieder (1968).
- 23.
Piron (1976).
- 24.
Heisenberg (1930).
- 25.
- 26.
Aharanov and Albert (1984).
- 27.
- 28.
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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
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