Abstract
A source of much difficulty and confusion in the interpretation of quantum mechanics is a “naive realism about operators.” By this we refer to various ways of taking too seriously the notion of operator-as-observable, and in particular to the all too casual talk about “measuring operators” that occurs when the subject is quantum mechanics. Without a specification of what should be meant by “measuring” a quantum observable, such an expression can have no clear meaning. A definite specification is provided by Bohmian mechanics, a theory that emerges from Schrödinger’s equation for a system of particles when we merely insist that “particles” means particles. Bohmian mechanics clarifies the status and the role of operators as observables in quantum mechanics by providing the operational details absent from standard quantum mechanics. It thereby allows us to readily dismiss all the radical claims traditionally enveloping the transition from the classical to the quantum realm- for example, that we must abandon classical logic or classical probability. The moral is rather simple: Beware naive realism, especially about operators!
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Albert, D. Z.: 1992, Quantum Mechanics and Experience, Harvard University Press, Cambridge, MA.
Bell, J. S.: 1964, ‘Onthe Einstein-Podolski-Rosen Paradox’, Physics 1, 195–200. Reprinted in Bell 1987.
Bell, J. S.: 1966, ‘On the problem of hidden variables in quantum mechanics’, Review of Modern Physics 38, 447–452. Reprinted in Bell 1987.
Bell, J. S.: 1981, ‘Quantum mechanics for cosmologists’, in Quantum Gravity 2, C. Isham, R. Penrose, and D. Sciama (eds.), Oxford University Press, New York, pp. 611–637. Reprinted in Bell 1987.
Bell, J. S.: 1982, ‘On the impossible pilot wave’, Foundations of Physics 12, 989–999. Reprinted in Bell, 1987.
Bell, J. S.: 1987, Speakable and unspeakable in quantum mechanics, Cambridge University Press, Cambridge.
Bell, J. S.: 1990, ‘Against “measurement”’, Physics World 3, 33–40. [Also appears in’ sixty-two Years of Uncertainty: Historical, Philosophical, and Physical Inquiries into the Foundations of Quantum Mechanics’, Plenum Press, New York, pp. 17–31.]
Beltramerti, E. G. and Cassinelli, G.: 1981, The Logic of Quantum Mechanics, Reading, Mass.
Berndl, K., Dürr, D., Goldstein, S., and Zanghi, N.: 1996, ‘EPR-Bell Nonlocality, Lorentz Invariance, and Bohmian Quantum Theory’, quant-ph/9510027, preprint. (To appear in Physical Review A, April 1996.)
Berndl, K., Dürr, D., Goldstein, S., Peruzzi G., and Zanghi, N.: 1995, ‘On the Global Existence of Bohmian Mechanics’, Communications in Mathematical Physics 173, 647–673.
Birkhoff, G. and von Neumann, J.: 1936, ‘The logic of Quantum Mechanics’, Ann. Math. 37.
Böhm, D.: 1952, ‘A Suggested Interpretation of the Quantum Theory in Terms of ‘Hidden’ Variables, I and II,’ Physical Review 85, 166–193. Reprinted in Wheeler and Zurek 1983, pp. 369–396.
Bohm, D. and Hiley, B. J.: 1993, The Undivided Universe: An Ontological Interpretation of Quantum Theory, Routledge & Kegan Paul, London.
Daumer, M., Dürr, D., Goldstein, S., and Zanghì, N.: 1996, ‘On the role of operators in quantum theory’, in preparation.
Davies, E. B.: 1976, Quantum Theory of Open Systems, Academic Press, London.
De Witt, B. S. and Graham, N. (eds.): 1973, The Many-Worlds interpretation of Quantum Mechanics, Princeton, N.J..
Dieks, D.: 1991, ‘On some alleged difficulties in interpretation of quantum mechanics’, Synthese 86, 77–86.
Dürr, D., Goldstein, S., and Zanghì, N.: 1992, ‘Quantum Equilibrium and the Origin of Absolute Uncertainty’, Journal of Statistical Physics 67, 843–907; “Quantum Mechanics, Randomness, and Deterministic Reality,” Physics Letters A 172, 6–12.
Dürr, D., Goldstein, S., and Zanghì, N.: 1996, ‘Bohmian Mechanics as the Foundation of Quantum Mechanics’, in Bohmian Mechanics and Quantum Theory: An Appraisal, J. Cushing, A. Fine and S. Goldstein (eds.), Kluwer Academic Press.
Everett, H.: 1957, ‘Relative state formulation of quantum mechanics’, Review of Modern Physics 29, 454–462. Reprinted in De Witt et al. 1973, and Wheeler et al. 1983.
Gell-Mann, M. and Hartle, J. B.: 1993, ‘Classical Equations for Quantum Systems’, Physical Review D 47, 3345–3382.
Ghirardi, G. C., Rimini, A., and Weber, T.: 1986, ‘Unified Dynamics for Microscopic and Macroscopic Systems’, Physical Review D 34, 470–491.
Ghirardi, G. C., Pearle, P., and Rimini, A.: 1990, ‘Markov Processes in Hilbert Space and Continuous Spontaneous Localization of Systems of Identical Particles’, Physical Review A 42, 78–89.
Ghirardi, G. C., Grassi, R., and Benatti, F.: 1995, ‘Describing the Macroscopic World: Closing the Circle within the Dynamical Reduction Program’, Foundations of Physics 23, 341–364.
Gleason, A. M: 1957, ‘Measures on the Closed Subspaces of a Hilbert Space’, Journal of Mathematics and Mechanics 6, 885–893.
Griffiths, R. B: 1984, ‘Consistent Histories and the Interpretation of Quantum Mechanics’ Journal of Statistical Physics 36, 219–272.
Goldstein, S.: 1987, ‘Stochastic Mechanics and Quantum Theory’, Journal of Statistical Physics 47, 645–667.
Jauch, J. M. and Piron, C.: 1963, ‘Can Hidden Variables be Excluded in Quantum Mechanics?’, Helvetica Phisica Acta 36, 827–837.
Jauch, J. M.: 1968, Foundations of Quantum Mechanics, Addison-Wesley, Reading, Mass.
Holland, P. R.: 1993, The Quantum Theory of Motion, Cambridge University Press, Cambridge.
Kochen, S. and Specker, E. P.: 1967, ‘The Problem of Hidden Variables in Quantum Mechanics’, Journal of Mathematics and Mechanics 17, 59–87.
Kochen, S.: ‘A New Interpretation of Quantum Mechanics’, in P. Lathi and P. Mittelstaedt (eds.), Symposium on the Foundations of Modern Physics, World Scientific, Singapore.
Mott, N. F: 1929, Proceedings of the Royal Society A 124, 440.
Nelson, E.: 1966 ‘Derivation of the Schrödinger Equation from Newtonian Mechanics’, Physical Review 150, 1079–1085.
Nelson, E.: 1985 Quantum Fluctuations, Princeton University Press, Princeton.
Omnès, R.: 1988, ‘Logical Reformulation of Quantum Mechanics I’, Journal of Statistical Physics 53, 893–932.
von Neumann, J.: 1932, Mathematische Grundlagen der Quantenmechanik Springer Verlag, Berlin. English translation: 955, Princeton University Press, Princeton.
Schrödinger, E.: 1935, ‘Die gegenwärtige Situation in der Quantenmechanik,’ Die Naturwissenschaften 23, 807–812, 824–828, 844–849. [Also appears in translation as “The Present Situation in Quantum Mechanics,” in Wheeler and Zurek 1983, pp. 152–167.]
van Fraassen, B.: 1991, Quantum Mechanics, an Empiricist View, Oxford University Press, Oxford.
Wheeler, J. A. and Zurek, W. H. (eds.): 1983, Quantum Theory and Measurement, Princeton University Press, Princeton.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Daumer, M., Dürr, D., Goldstein, S., Zanghì, N. (1997). Naive Realism about Operators. In: Costantini, D., Galavotti, M.C. (eds) Probability, Dynamics and Causality. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5712-4_15
Download citation
DOI: https://doi.org/10.1007/978-94-011-5712-4_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6409-5
Online ISBN: 978-94-011-5712-4
eBook Packages: Springer Book Archive