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Unsharp Quantum Reality

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Abstract

The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it an adequate concept of joint properties. A sharp or unsharp property manifests itself as an element of sharp or unsharp reality by its tendency to become actual or to actualize a specific measurement outcome. This actualization tendency—or potentiality—of a property is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way.

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References

  1. Heisenberg, W.: Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Z. Phys. 43, 172 (1927)

    Article  ADS  Google Scholar 

  2. Feynman, R.P.: The Character of Physical Law. MIT Press, Cambridge (1967)

    Google Scholar 

  3. Mermin, N.D.: Could Feynman have said this? Physics Today, May 2004, p. 10

  4. d’Espagnat, B.: On Physics and Philosophy, p. 225. Princeton University Press, Princeton (2006)

    Google Scholar 

  5. Birkhoff, G., von Neumann, J.: The logic of quantum mechanics. Ann. Math. 37, 823 (1936)

    Article  Google Scholar 

  6. Busch, P., Lahti, P., Mittelstaedt, P.: The Quantum Theory of Measurement, 2nd edn. Springer, Berlin (1996)

    MATH  Google Scholar 

  7. Mittelstaedt, P.: Philosophical Problems of Modern Physics. Reidel, Dordrecht (1975). English translation of Philosophische Probleme der Physik, 4th edn. 1972

    Google Scholar 

  8. Strohmeyer, I.: Tragweite und Grenze der Transzendentalphilosophie zur Grundlegung der Quantenphysik. Z. Allg. Wiss.theor. XVIII(1–2), 239 (1987)

    MathSciNet  Google Scholar 

  9. Mittelstaedt, P.: The constitution of objects in Kant’s philosophy and in modern physics. In: Parrini, P. (ed.) Kant and Contemporary Epistemology, p. 115. Kluwer Academic, Dordrecht (1994)

    Google Scholar 

  10. Bub, J.: Interpreting the Quantum World. Cambridge University Press, Cambridge (1997)

    MATH  Google Scholar 

  11. Krips, H.: The Metaphysics of Quantum Theory. Oxford University Press, Oxford (1987)

    Google Scholar 

  12. Heisenberg, W.: Physics and Philosophy. Harper and Row, New York (1958)

    Google Scholar 

  13. Heisenberg, W.: Die Planck’sche Entdeckung und die philosophischen Probleme der Atomphysik. Universitas 14, 135 (1959)

    MathSciNet  Google Scholar 

  14. Popper, K.R.: The propensity interpretation of the calculus of probability and the quantum theory. In: Körner, S. (ed.) Observation and Interpretation in the Philosophy of Physics. Butterworth, London (1957)

    Google Scholar 

  15. Popper, K.R.: Quantum theory and the schisms of physics. In: Bartley, W.W. III (ed.) Postscript III to the Logic of Scientific Discovery. Hutchinson, London (1982)

    Google Scholar 

  16. Mittelstaedt, P.: The Interpretation of Quantum Mechanics and the Measurement Process. Cambridge University Press, Cambridge (1998)

    MATH  Google Scholar 

  17. Busch, P.: Can quantum mechanical reality be considered sharp? In: Lahti, P., Mittelstaedt, P. (eds.) Symposium on the Foundations of Modern Physics 1985. World Scientific, Singapore (1985)

    Google Scholar 

  18. Busch, P.: Unsharp reality and joint measurements for spin observables. Phys. Rev. D 33, 2253 (1986)

    Article  MathSciNet  ADS  Google Scholar 

  19. Doplicher, S., Fredenhagen, K., Roberts, J.E.: The quantum structure of space-time at the Planck scale and quantum fields. Commun. Math. Phys. 172, 187 (1995)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  20. Bahns, D., Doplicher, S., Fredenhagen, K., Piacitelli, G.: Ultraviolet finite quantum field theory on quantum spacetime. Commun. Math. Phys. 237, 221 (2003)

    MATH  MathSciNet  ADS  Google Scholar 

  21. Misra, B.: A new concept of quantal state. In: Enz, C.P., Mehra, J. (eds.) Physical Reality and Mathematical Description. Reidel, Dordrecht (1974)

    Google Scholar 

  22. Bugajski, S.: Nonlinear quantum mechanics is a classical theory. Int. J. Theor. Phys. 30, 961 (1991)

    Article  Google Scholar 

  23. Bugajski, S.: Delinearization of quantum logic. Int. J. Theor. Phys. 32, 389 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  24. Bugajski, S.: Classical frames for a quantum theory—a bird’s-eye view. Int. J. Theor. Phys. 32, 969 (1993)

    Article  MathSciNet  Google Scholar 

  25. Bugajski, S.: Fundamentals of fuzzy probability theory. Int. J. Theor. Phys. 35, 2229 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  26. Stulpe, W., Busch, P.: The structure of classical extensions of quantum probability theory. J. Math. Phys. 49, 032104 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  27. Spekkens, R.: Contextuality for preparations, transformations, and unsharp measurements. Phys. Rev. A 71, 052108 (2005)

    Article  ADS  Google Scholar 

  28. Landsman, N.P.: Between classical and quantum. In: Butterfield, J., Earman, J. (eds.) Philosophy of Physics. Handbook of the Philosophy of Science, vol. 2, pp. 417–554. North-Holland, Amsterdam (2007)

    Chapter  Google Scholar 

  29. Busch, P., Grabowski, M., Lahti, P.: Operational Quantum Physics. Springer, Berlin (1995) (2nd printing 1997)

    MATH  Google Scholar 

  30. Busch, P., Shimony, A.: Insolubility of the quantum measurement problem for unsharp observables. Stud. Hist. Philos. Mod. Phys. 27, 397 (1996)

    Article  MathSciNet  Google Scholar 

  31. Busch, P.: Can ‘unsharp objectification’ solve the quantum measurement problem? Int. J. Theor. Phys. 37, 241 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  32. Pearle, P.: Reduction of the state vector by a nonlinear Schrödinger equation. Phys. Rev. B 13, 857 (1976)

    MathSciNet  ADS  Google Scholar 

  33. Ghirardi, G.-C., Rimini, A., Weber, T.: Unified dynamics for microscopic and macroscopic systems. Phys. Rev. D 34, 470 (1986)

    Article  MathSciNet  ADS  Google Scholar 

  34. Mittelstaedt, P.: Quantum logic versus alternative approaches. Phys. Philos. (2007). ISSN: 1863-7388, Article-ID: 009. http://hdl.handle.net/2003/24420

  35. Ghirardi, G.-C.: Collapse theories. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy, Fall edition (2008). http://plato.stanford.edu/archives/fall2008/entries/qm-collapse/

  36. Pearle, P.: How stands collapse I. J. Phys. A, Math. Theor. 40, 3189 (2007)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  37. Pearle, P.: How stands collapse II. In: Myrvold, W.C., Christian, J. (eds.) Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle, p. 257. Springer, New York (2009)

    Chapter  Google Scholar 

  38. Bell, J.S.: Speakable and Unspeakable in Quantum Mechanics, 2nd edn. Cambridge University Press, Cambridge (2004)

    Google Scholar 

  39. Shimony, A.: Search for a Naturalistic World View, vols. I and II. Cambridge University Press, Cambridge (1993)

    Book  Google Scholar 

  40. Esfeld, M.: Physics and causation. Found. Phys. (2009). doi:10.1007/s10701-009-9357-y

    Google Scholar 

  41. Busch, P., Heinonen, T., Lahti, P.: Heisenberg’s uncertainty principle. Phys. Rep. 452, 155 (2007)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of York, York, UK

    Paul Busch

  2. Quantum Communication and Measurement Laboratory, Department of Electrical and Computer Engineering and Division of Natural Science and Mathematics, Boston University, Boston, MA, USA

    Gregg Jaeger

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  1. Paul Busch
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  2. Gregg Jaeger
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Correspondence to Paul Busch.

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Busch, P., Jaeger, G. Unsharp Quantum Reality. Found Phys 40, 1341–1367 (2010). https://doi.org/10.1007/s10701-010-9497-0

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  • DOI: https://doi.org/10.1007/s10701-010-9497-0

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