European Journal for Philosophy of Science

, Volume 3, Issue 1, pp 87–100 | Cite as

Insolubility Theorems and EPR Argument

  • Guido Bacciagaluppi
Original paper in Philosophy of Physics


I present a very general and simple argument—based on the no-signalling theorem—showing that within the framework of the unitary Schrödinger equation it is impossible to reproduce the phenomenological description of quantum mechanical measurements (in particular the collapse of the state of the measured system) by assuming a suitable mixed initial state of the apparatus. The thrust of the argument is thus similar to that of the ‘insolubility theorems’ for the measurement problem of quantum mechanics (which, however, focus on the impossibility of reproducing the macroscopic measurement results). Although I believe this form of the argument is new, I argue it is essentially a variant of Einstein’s reasoning in the context of the EPR paradox—which is thereby illuminated from a new angle.


Quantum mechanics Measurement problem Insolubility theorems EPR argument 



I wish to thank in particular Arthur Fine for very perceptive comments on a previous draft of this paper. Many thanks also to Theo Nieuwenhuizen for inspiration, to Max Schlosshauer for correspondence, to two anonymous referees for shrewd observations, and to audiences at Aberdeen, Cagliari and Oxford (in particular to Harvey Brown, Elise Crull, Simon Saunders, Chris Timpson and David Wallace) for stimulating questions. This paper was written during my tenure of a Leverhulme Grant on ‘The Einstein Paradox’: The Debate on Nonlocality and Incompleteness in 1935 (Project Grant nr. F/00 152/AN), and it was revised for publication during my tenure of a Visiting Professorship in the Doctoral School of Philosophy and Epistemology, University of Cagliari (Contract nr. 268/21647).


  1. Allahverdyan, A. E., Balian, R., & Nieuwenhuizen, T. M. (2011). Understanding quantum measurement from the solution of dynamical models. arXiv:1107.2138v1.
  2. Bacciagaluppi, G. (2012). Non-equilibrium in Nelsonian Mechanics. Journal of Physics: Conference Series, 361, 012017/1–12.CrossRefGoogle Scholar
  3. Bacciagaluppi, G., & Crull, E. M. (in preparation). ‘The Einstein Paradox’: The debate on nonlocality and incompleteness in 1935. Cambridge: Cambridge University Press, expected publication 2014 or 2015.Google Scholar
  4. Bassi, A., & Ghirardi, G.C. (2000). A general argument against the universal validity of the superposition principle. Physics Letters, A 275, 373–381.CrossRefGoogle Scholar
  5. Bell, J. S. (1964). On the Einstein-Podolsky-Rosen paradox. Physics, 1, 195–200 (Reprinted in Bell, J. S. (1987). Speakable and unspeakable in quantum mechanics (pp. 14–21). Cambridge: Cambridge University Press).Google Scholar
  6. Brown, H. R. (1986). The insolubility proof of the quantum measurement problem. Foundations of Physics, 16, 857–870.CrossRefGoogle Scholar
  7. Busch, P., Grabowski, M., & Lahti, P. (1995). Operational quantum physics (Vol. m31). Lecture Notes in Physics. Berlin: Springer; second, corrected printing, 1997.Google Scholar
  8. Busch, P., & Shimony, A. (1996). Insolubility of the quantum measurement problem for unsharp observables. Studies in History and Philosophy of Modern Physics, 27 B, 397–404.CrossRefGoogle Scholar
  9. Daneri, A., Loinger, A., & Prosperi, G. M. (1962). Quantum theory of measurement and ergodicity conditions. Nuclear Physics, 33, 297–319.CrossRefGoogle Scholar
  10. Doebner, H.-D., & Goldin, G. A. (1996). Introducing nonlinear gauge transformations in a family of nonlinear Schrödinger equations. Physical Review, A 54, 3764–3771.CrossRefGoogle Scholar
  11. Earman, J., & Shimony, A. (1968). A note on measurement. Il Nuovo Cimento, B 54, 332–334.CrossRefGoogle Scholar
  12. Einstein, A., Podolsky, B., & Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete? Physical Review, 47, 777–780.CrossRefGoogle Scholar
  13. d’Espagnat, B. (1966). Two remarks on the theory of measurement. Supplemento al Nuovo Cimento, 4, 828–838.Google Scholar
  14. d’Espagnat, B. (1971). Conceptual foundations of quantum mechanics. Reading, Mass.: W. A. Benjamin.Google Scholar
  15. Fehrs, M. H., & Shimony, A. (1974). Approximate measurement in quantum mechanics, I’. Physical Review, D 9, 2317–2320.CrossRefGoogle Scholar
  16. Fine, A. (1970). Insolubility of the quantum measurement problem. Physical Review, D 2, 2783–2787.CrossRefGoogle Scholar
  17. Fine, A. (1981). Einstein’s critique of quantum theory: The roots and significance of EPR. In P. Barker, & C. G. Shugart (Eds.), After Einstein: Proceedings of the Einstein centennial celebration at Memphis State University, 14–16 March 1979 (pp. 147–158). Memphis: Memphis State University Press (Reprinted in Fine, A. (1986). The shaky game: Einstein, realism and the quantum theory (pp. 26–39). Chicago: University of Chicago Press).Google Scholar
  18. Gisin, N. (1989). Stochastic quantum dynamics and relativity. Helvetica Physica Acta, 62(4), 363–371.Google Scholar
  19. Gisin, N. (1990). Weinberg’s non-linear quantum mechanics and supraluminal communications. Physics Letters, A 143, 1–2.CrossRefGoogle Scholar
  20. Ghirardi, G.C., Rimini, A., & Weber, T. (1980). A general argument against superluminal transmission through the quantum mechanical measurement process. Lettere al Nuovo Cimento, 27(10), 293–298.CrossRefGoogle Scholar
  21. Howard, D. (1985). Einstein on locality and separability. Studies in History and Philosophy of Science, 16, 171–201.CrossRefGoogle Scholar
  22. Howard, D. (1990). ‘Nicht sein kann was nicht sein darf’, or the Prehistory of EPR, 1909–1935: Einstein’s early worries about the quantum mechanics of composite systems. In A. I. Miller (Ed.), Sixty-two years of uncertainty (pp. 61–111). New York: Plenum Press.CrossRefGoogle Scholar
  23. Price, H. (1996). Time’s arrow and Archimedes’ point: New directions for the physics of time. New York: Oxford University Press.Google Scholar
  24. Shimony, A. (1974). Approximate measurement in quantum mechanics, II. Physical Review, D 9, 2321–2323.CrossRefGoogle Scholar
  25. Stein, H. (1997). Maximal extension of an impossibility theorem concerning quantum measurement. In R. S. Cohen, M. Horne, & J. Stachel (Eds.), Potentiality, entanglement and passion-at-a-distance: Quantum mechanical studies for Abner Shimony, Vol. 2 (Vol. 194, pp. 231–243). Boston Studies in the Philosophy of Science, Dordrecht: Kluwer.Google Scholar
  26. von Meyenn, K. (Ed.) (2011). Eine Entdeckung von ganz außerordentlicher Tragweite: Schrödingers Briefwechsel zur Wellenmechanik und zum Katzenparadoxon, 2 vols. Berlin and Heidelberg: Springer.Google Scholar
  27. von Neumann, J. (1932). Mathematische Grundlagen der Quantenmechanik. Berlin: Springer 2nd ed. 1996. (Transl. by R. T. Beyer (1955). Mathematical foundations of quantum mechanics. Princeton: Princeton University Press).Google Scholar
  28. Wigner, E. P. (1963). The problem of measurement. American Journal of Physics, 31, 6–15.CrossRefGoogle Scholar

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© Springer Science + Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of AberdeenAberdeenUK
  2. 2.Institut d’Histoire et de Philosophie des Sciences et des Techniques(CNRS, Paris 1, ENS)ParisFrance

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