Abstract
In this paper we list some minimal requirements for a physically natural, straightforwardly realist interpretation of non-relativistic quantum mechanics. The goal is to characterize what one might call a ‘simple realism’ of quantum systems, and of the observables associated with them.
Simple realism as developed here is a generalized interpretation-scheme, one that abstracts important shared features of ‘Einsteinian naive realism,’ the so-called ‘modal’ interpretations, and the orthodox interpretation itself. Some such schemes run afoul of the classic ‘no-go’ theorems, while others do not. The role of non-commuting observables plays a major role in this success or failure. In particular, we show that if a simple-realist interpretation attributes simultaneously definite values to canonically conjugate observables, then it necessarily falls prey to Kochen-Specker contradictions.
This exercise provides some insight into ‘why modal interpretations work,’ while more generally placing limits on the scope of simple realism itself. In particular, we find that within the framework of simple realism, the only consistent interpretation of the uncertainty relations is the orthodox one. What's more, we point out that similar conclusions are bound to hold for many other non-commuting observables as well.
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References
A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of reality be considered complete?” Phys. Rev. 47, 777–780 (1935); reprinted in J. Wheeler and W. Zurek, eds., Quantum Theory and Measurement (Princeton University Press, Princeton, 1983), pp. 138–141.
D. Bohm, “A suggested interpretation of the quantum theory in terms of ‘hidden variables,’ part II,” Phys. Rev. 85, 180–193 (1952); reprinted in J. Wheeler and W. Zurek, eds., Quantum Theory and Measurement (Princeton University Press, Princeton, 1983), pp. 383–396; see p. 385.
E. Wigner, “Interpretation of quantum mechanics,” lecture notes dating from 1976, published for the first time in J. Wheeler and W. Zurek, eds., Quantum Theory and Measurement (Princeton University Press, Princeton, 1983), pp. 260–314. See p. 267.
J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, 1983), translation by Robert T. Beyer of J. von Neumann, Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932).
J. Bell, “On the problem of hidden-variables in quantum mechanics,” Rev. Mod. Phys. 38, 447–452 (1966).
S. Kochen and E. Specker, “The problem of hidden variables in quantum mechanics,” J. Math. Mech. 17(59) (1967).
J. von Neumann, op. cit.; see Chap. IV.
J. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987), see p. ix.
H. Brown, “Bell’s other theorem and its connection with nonlocality, part IBell’s other theorem and its connection with nonlocality, part I,” in A. van der Merwe, F. Selleri, and G. Tarozzi, eds., Bell’s Theorem and the Foundations of Modern Physics (World Scientific, Singapore, 1992).
S. Kochen, “A new interpretation of quantum mechanics,” in P. Lahti and P. Mittelstaedt, eds., Symposium on the Foundations of Modern Physics 1985 (World Scientific, Singapore, 1985).
D. Dieks, “Quantum mechanics without the projection postulate and its realistic interpretation,” Found. Phys. 19, 1395–1423 (1989).
E. Wigner, “The problem of measurement,” Am. J. Phys. 31, 6–15 (1963). Reprinted in J. Wheeler and W. Zurek, eds., Quantum Theory and Measurement (Princeton University Press, Princeton, 1983), pp. 324–341.
J. Bub, Interpreting the Quantum World (Cambridge University Press, Cambridge, 1997).
G. Bacciagaluppi, Topics in the Modal Interpretation of Quantum Mechanics, University of Cambridge D. Phil. Thesis, 1996; see Chap. 3.
I. Segal, “Postulates for general quantum mechanics,” Ann. Math. 48, 930–940 (1947).
R. Clifton, “Beables in algebraic quantum mechanics,” to appear in Festschrift volume in tribute to Michael Redhead (Cambridge University Press, Cambridge, 19981998).
N. Bohr, “Can quantum-mechanical description of reality be considered complete?” Phys. Rev. 48, 696–702 (1935); reprinted in J. Wheeler and W. Zurek, eds., Quantum Theory and Measurement (Princeton University Press, Princeton, 1983), pp. 145–151.
D. Bohm, op. cit. See p. 390 of J. Wheeler and W. Zurek, eds., Quantum Theory and Measurement (Princeton University Press, Princeton, 1983).
J. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987); see p. 175.
A. Gleason, “Measures on the closed subspaces of a Hilbert space,” J. Math. Mech. 6, 885 (1957).
J. Zimba, “Irreducibility, uncertainty, and quantum realism,” forthcoming.
D. Albert and B. Loewer, “Non-ideal measurements,” Found. Phys. Lett. 6, 297–305 (1993).
R. Healey, “‘Modal’ interpretations, decoherence, and the quantum measurement problem,” 1993 preprint.
M. Redhead, From Physics to Metaphysics (Cambridge University Press, Cambridge, 1995).
R. Clifton, “Independently motivating the Kochen-Dieks modal interpretation of quantum mechanics”, British J. Phil. Sci. 46, 33–57 (1995).
J. Zimba and R. Clifton, “Valuations on functionally closed sets of quantum mechanical observables and von Neumann’s ‘no-hiddenvariables’ theorem,” in P. Vermaas and D. Dieks, eds., The Modal Interpretation of Quantum Mechanics (Kluwer Academic, Dordrecht, 1998).
A. R. Swift and R. Wright, “Generalized Stern-Gerlach experiments and the observability of arbitrary spin operators,” J. Math. Phys. 21, 77 (1980).
J. Bub and R. Clifton, “A uniqueness theorem for ‘no-collapse’ interpretations of quantum mechanics,” Stud. Hist. Phil. Mod. Phys. 27, 181–219 (1996).
J. L. Bell and R. Clifton, “Quasi-Boolean algebras and simultaneously definite properties in quantum mechanics,” Int. J. Theor. Phys. 34, 2409–2421 (1995).
M. Redhead, Incompleteness, Nonlocality, and Realism (Clarendon Press, Oxford, 1987).
R. Jost, “Measures on the finite dimensional subspaces of a Hilbert space: remarks on a theorem by A. M. Gleason”, in E. H. Lieb, B. Simon, and S. Wightman, eds., Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann (Princeton University Press, Princeton, 1976), pp. 209–228.
J. L. Bell, “Logical reflections on the Kochen-Specker Theorem,” in R. Clifton, ed., Perspectives on Quantum Reality: Non-Relativistic, Relativistic, and Field-Theoretic (Volume 57, University of Western Ontario Series in Philosophy of Science) (Kluwer Academic, Dordrecht, 1996).
T. Kato, Perturbation Theory for Linear Operators (Springer, Berlin, 1980).
K. Yosida, Functional Analysis (Springer, Berlin, 1980). See p. 198.
M. Reed and B. Simon, Analysis of Operators, Volume 4 of the series Methods of Modern Mathematical Physics (Academic, San Diego, 1980).
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Zimba, J. Simple Realism and Canonically Conjugate Observables in Non-Relativistic Quantum Mechanics. Found Phys Lett 11, 503–533 (1998). https://doi.org/10.1023/A:1022176607848
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DOI: https://doi.org/10.1023/A:1022176607848