What is Orthodox Quantum Mechanics?

  • David WallaceEmail author
Part of the Synthese Library book series (SYLI, volume 406)


What is called “orthodox” quantum mechanics, as presented in standard foundational discussions, relies on two substantive assumptions—the projection postulate and the eigenvalue-eigenvector link—that do not in fact play any part in practical applications of quantum mechanics. I argue for this conclusion on a number of grounds, but primarily on the grounds that the projection postulate fails correctly to account for repeated, continuous and unsharp measurements (all of which are standard in contemporary physics) and that the eigenvalue-eigenvector link implies that virtually all interesting properties are maximally indefinite pretty much always. I present an alternative way of conceptualising quantum mechanics that does a better job of representing quantum mechanics as it is actually used, and in particular that eliminates use of either the projection postulate or the eigenvalue-eigenvector link, and I reformulate the measurement problem within this new presentation of orthodoxy.



This paper has benefitted greatly from conversations with Simon Saunders and Chris Timpson, and from feedback when it was presented at the 2016 Michigan Foundations of Modern Physics workshop, especially from Jeff Barrett, Gordon Belot, and Antony Leggett.


  1. Albert, D. Z. (1992). Quantum mechanics and experience. Cambridge, MA: Harvard University Press.Google Scholar
  2. Albert, D. Z., & Loewer, B. (1996). Tails of Schrödinger’s Cat. In R. Clifton (Ed.), Perspectives on quantum reality (pp. 81–92). Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar
  3. Barrett, J. A. (1999). The quantum mechanics of minds and worlds. Oxford: Oxford University Press.Google Scholar
  4. Bell, J. S. (1966). On the problem of hidden variables in quantum mechanics. Reviews of Modern Physics, 38, 447–452. Reprinted in Bell ( 1987), pp. 1–13.CrossRefGoogle Scholar
  5. Bell, J. S. (1987). Speakable and unspeakable in quantum mechanics. Cambridge: Cambridge University Press.Google Scholar
  6. Belot, G., Earman, J., & Ruetsche, L. (1999). The Hawking information loss paradox: the anatomy of a controversy. British Journal for the Philosophy of Science, 50, 189–229.CrossRefGoogle Scholar
  7. Bokulich, A. (2014). Metaphysical indeterminacy, properties, and quantum theory. Res Philosophica, 91, 449–475.CrossRefGoogle Scholar
  8. Bub, J. (1997). Interpreting the quantum world. Cambridge: Cambridge University Press.Google Scholar
  9. Bub, J., & Clifton, R. (1996). A uniqueness theorem for “no collapse” interpretations of quantum mechanics. Studies in the History and Philosophy of Modern Physics, 27, 181–219.CrossRefGoogle Scholar
  10. Bub, J., Clifton, R., & Goldstein, S. (2000). Revised proof of the uniqueness theorem for ‘no collapse’ interpretations of quantum mechanics. Studies in the History and Philosophy of Modern Physics, 31, 95.CrossRefGoogle Scholar
  11. Busch, P., Lahti, P. J., & Mittelstaedt, P. (1996). The quantum theory of measurement (2nd revised ed.). Berlin: Springer.Google Scholar
  12. Caves, C., Fuchs, C., Manne, K., & Renes, J. (2004). Gleason-type derivations of the quantum probability rule for generalized measurements. Foundations of Physics, 34, 193.CrossRefGoogle Scholar
  13. Cushing, J. T. (1994). Quantum mechanics: Historical contingency and the Copenhagen hegemony. Chicago: University of Chicago Press.Google Scholar
  14. Darby, G. (2010). Quantum mechanics and metaphysical indeterminacy. Australasian Journal of Philosophy, 88, 227–245.CrossRefGoogle Scholar
  15. DeWitt, B., & Graham, N. (Eds.) (1973). The many-worlds interpretation of quantum mechanics. Princeton: Princeton University Press.Google Scholar
  16. Dirac, Paul (1930): The principles of quantum mechanics. Oxford: Oxford University Press.Google Scholar
  17. Einstein, A., Podolsky, B., & Rosen, N. (1935). Can quantum-mechanical description of reality be considered complete? Physical Review, 47, 777–780.CrossRefGoogle Scholar
  18. Elitzur, A. C., & Vaidman, L. (1993). Quantum mechanical interaction-free measurements. Foundations of Physics, 23, 987–997.CrossRefGoogle Scholar
  19. Everett, H. I. (1957). Relative state formulation of quantum mechanics. Review of Modern Physics, 29, 454–462. Reprinted in DeWitt and Graham ( 1973).
  20. Fuchs, C. (2002). Quantum mechanics as quantum information (and only a little more). Available online at Scholar
  21. Fuchs, C., & Peres, A. (2000). Quantum theory needs no “interpretation”. Physics Today, 53(3), 70–71.CrossRefGoogle Scholar
  22. Fuchs, C. A., Mermin, N. D., & Schack, R. (2014). An introduction to QBism with an application to the locality of quantum mechanics. American Journal of Physics, 82, 749–754.CrossRefGoogle Scholar
  23. Fuchs, C. A., & Schack, R. (2015). QBism and the Greeks: Why a quantum state does not represent an element of physical reality. Physica Scripta, 90, 015104.CrossRefGoogle Scholar
  24. Gell-Mann, M., & Hartle, J. B. (1993). Classical equations for quantum systems. Physical Review D, 47, 3345–3382.CrossRefGoogle Scholar
  25. Gleason, A. (1957). Measures on the closed subspaces of a Hilbert space. Journal of Mathematics and Mechanics, 6, 885–893.Google Scholar
  26. Griffiths, R. (1993). Consistent interpretation of quantum mechanics using quantum trajectories. Physical Review Letters, 70, 2201–2204.CrossRefGoogle Scholar
  27. Griffiths, R. B. (1984). Consistent histories and the interpretation of quantum mechanics. Journal of Statistical Physics, 36, 219–272.CrossRefGoogle Scholar
  28. Griffiths, R. B. (1996). Consistent histories and quantum reasoning. Physical Review A, 54, 2759–2773.CrossRefGoogle Scholar
  29. Halvorson, H., & Clifton, R. (2002). No place for particles in relativistic quantum theories? Philosophy of Science, 69, 1–28.CrossRefGoogle Scholar
  30. Hawking, S. W. (1976). Black holes and thermodynamics. Physical Review D, 13, 191–197.CrossRefGoogle Scholar
  31. Hegerfeldt, G. A. (1998a). Causality, particle localization and positivity of the energy. In A. Böhm (Ed.), Irreversibility and causality (pp. 238–245). New York: Springer.Google Scholar
  32. Hegerfeldt, G. A. (1998b). Instantaneous spreading and Einstein causality. Annalen der Physik, 7, 716–725.CrossRefGoogle Scholar
  33. Home, D., & Whitaker, M. A. B. (1997). A conceptual analysis of quantum Zeno: Paradox, measurement and experiment. Annals of Physics, 258, 237–285.CrossRefGoogle Scholar
  34. Joos, E., & Zeh, H. (1985). The emergence of classical particles through interaction with the environment. Zeitschrift fur Physik, B59, 223–243.CrossRefGoogle Scholar
  35. Kochen, S., & Specker, E. (1967). The problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics, 17, 59–87.Google Scholar
  36. Leifer, M. (2014). Is the quantum state real? An extended review of ψ-ontology theorems. Quanta, 3, 67–155.CrossRefGoogle Scholar
  37. Maroney, O. (2012). How statistical are quantum states? Available online at Scholar
  38. Mermin, N. D. (1993). Hidden variables and the two theorems of John Bell. Reviews of Modern Physics, 65, 803–815.CrossRefGoogle Scholar
  39. Mermin, N. D. (2004). Could Feynman have said this? Physics Today, 57, 10.Google Scholar
  40. Misra, B., & Sudarshan, E. C. G. (1977). The Zeno’s paradox in quantum theory. Journal of Mathematical Physics, 18, 756.CrossRefGoogle Scholar
  41. Omnes, R. (1988). Logical reformulation of quantum mechanics. I. Foundations. Journal of Statistical Physics, 53, 893–932.CrossRefGoogle Scholar
  42. Omnes, R. (1992). Consistent interpretations of quantum mechanics. Reviews of Modern Physics, 64, 339–382.CrossRefGoogle Scholar
  43. Omnes, R. (1994). The interpretation of quantum mechanics. Princeton: Princeton University Press.CrossRefGoogle Scholar
  44. Page, D. (1994). Black hole information. In R. Mann & R. McLenaghan (Eds.), Proceedings of the 5th Canadian conference on general relativity and relativistic astrophysics (pp. 1–41). Singapore: World Scientific.Google Scholar
  45. Penrose, R. (1989). The Emperor’s new mind: Concerning computers, brains and the laws of physics. Oxford: Oxford University Press.Google Scholar
  46. Peres, A. (1993). Quantum theory: Concepts and methods. Dordrecht: Kluwer Academic Publishers.Google Scholar
  47. Pusey, M. F., Barrett, J., & Rudolph, T. (2011). On the reality of the quantum state. Nature Physics, 8, 476. arXiv:1111.3328v2.Google Scholar
  48. Quine, W. V. O. (1951). Two dogmas of empiricism. Philosophical Review, 60, 20–43.CrossRefGoogle Scholar
  49. Redhead, M. (1987). Incompleteness, nonlocality and realism: A prolegomenon to the philosophy of quantum mechanics. Oxford: Oxford University Press.Google Scholar
  50. Rudin, W. (1991). Functional analysis (2nd ed.). New York: McGraw-Hill.Google Scholar
  51. Ruetsche, L. (2011). Interpreting quantum theories. Oxford: Oxford University Press.CrossRefGoogle Scholar
  52. Saunders, S. (2005). Complementarity and scientific rationality. Foundations of Physics, 35, 347–372.CrossRefGoogle Scholar
  53. Skow, B. (2010). Deep metaphysical indeterminacy. Philosophical Quarterly, 58, 851–858.CrossRefGoogle Scholar
  54. Spekkens, R. W. (2007). In defense of the epistemic view of quantum states: A toy theory. Physical Review A, 75, 032110.CrossRefGoogle Scholar
  55. Timpson, C. (2010). Quantum information theory and the foundations of quantum mechanics. Oxford: Oxford University Press.Google Scholar
  56. von Neumann, J. (1955). Mathematical foundations of quantum mechanics. Princeton: Princeton University Press.Google Scholar
  57. Wallace, D. (2012). The emergent multiverse: Quantum theory according to the Everett interpretation. Oxford University Press.CrossRefGoogle Scholar
  58. Wallace, D. (2013). Inferential vs. dynamical conceptions of physics. Available online at
  59. Wallace, D. (2016, forthcoming). Interpreting the quantum mechanics of cosmology. In A. Ijjas & B. Loewer (Eds.), Introduction to the philosophy of cosmology. Oxford University Press.Google Scholar
  60. Weinberg, S. (2008). Cosmology. Oxford: Oxford University Press.Google Scholar
  61. Wilson, J. (2016). Quantum metaphysical indeterminacy. Talk to the Jowett Society, Oxford, 26 Feb 2016.Google Scholar
  62. Wolff, J. (2015). Spin as a determinable. Topoi, 34, 379–386.CrossRefGoogle Scholar
  63. Zeh, H. D. (1993). There are no quantum jumps, nor are there particles! Physics Letters, A172, 189.CrossRefGoogle Scholar
  64. Zurek, W. H. (1991). Decoherence and the transition from quantum to classical. Physics Today, 43, 36–44. Revised version available online at Scholar
  65. Zurek, W. H. (1998). Decoherence, einselection, and the quantum origins of the classical: The rough guide. Philosophical Transactions of the Royal Society of London, A356, 1793–1820. Available online at

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of Southern CaliforniaLos AngelesUSA

Personalised recommendations