Skip to main content
Log in

Reconstruction and Reinvention in Quantum Theory

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

I consider the fact that there are a number of interesting ways to ‘reconstruct’ quantum theory, and suggest that, very broadly speaking, a form of ‘instrumentalism’ makes good sense of the situation. This view runs against some common wisdom, which dismisses instrumentalism as ‘cheap’. In contrast, I consider how an instrumentalist might think about the reconstruction theorems, and, having made a distinction between ‘reconstructing’ quantum theory and ‘reinventing’ quantum theory, I suggest that there is an adequate (not ‘cheap’) instrumentalist approach to the theory (and to these theorems) that invokes both.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. My divisions are artificial, and set aside work that might be considered relevant. Bohmians, for example, might be taken as ‘reconstructing’ quantum theory from various assumptions about the nature of point particles, the forces they experience, and our capacities to interact with them. See, e.g., [11].

  2. Hardy’s axioms are not explicitly framed in terms of information, but they are explicitly connected with the probabilistic structure of the theory and how ‘tests’ can be designed to ascertain the values of observables. See, for example, [10, Sect. 2] and [15] for further discussion.

  3. Bub [4], for example, speaks of quantum information as “a new physical primitive”.

  4. Fuchs [12] is famous for giving something like this answer.

  5. I have left out of the discussion the ‘partial reconstructions’ identified by Grinbaum [15, 16], such as the ‘toy models’ of Spekkens [23]. In this work, researchers produce models that reconstruct a portion of quantum theory, intentionally leaving the rest out for the purpose of investigating some one (or few) principles independently of the rest of quantum theory. This activity is consonant with the instrumentalist view. In contrast, a traditional realist position appears to have more trouble making sense of the value of this theoretical activity, because of the ‘unreality’ of the assumptions that go into the construction of these ’intentionally incomplete’ models.

  6. The suggestion is not that these theorems ‘reinvent the wheel’ in a pejorative sense, but that they re-present quantum in a new light, potentially providing new understanding.

  7. I do not pretend to be the first to raise such questions, which are common in the history of the discussion of operationalism in physics. I merely apply them to recent work in axiomatics, not by way of objection to that work, but to suggest that there may be legitimate instrumentalist interest in what I will call ‘reconstruction’.

  8. No presumption is made here, by using the term ‘system’, that there are little yellow orbs, or anything of the kind, traveling from one apparatus to another. The presumption is simply that we have identified procedures that may, prima facie, be understood in the way described.

  9. I set aside, here, the interesting but thorny question of what counts as ‘success’ of a theory.

  10. These questions do not presuppose a realist standpoint, but only recognize that as a matter of fact, laboratory procedures are described in these terms. The question is: How are we to understand those descriptions?

  11. For the sake of keeping things relatively simple, I stick to non-relativistic quantum theory.

  12. I am leaving out some details. See [9] for a more careful discussion, and references to the original results.

  13. Again, I’m leaving out some mathematical details and assumptions. They do not affect the main point being made, here.

  14. This point perhaps echoes a similar point (arrived at from a somewhat different angle) made by Grinbaum [15]: “Philosophical and linguistic justification, and mathematical derivation, play here a game of mutual onslaught and retreat which, ultimately, leads to the advance of science”.

  15. I’m not convinced that anybody ever really thoughtfully believed in cheap instrumentalism.

References

  1. Barret, J.: Information processing in generalized probabilistic theories. Phys. Rev. A 75, 032304 (2007)

    Article  ADS  Google Scholar 

  2. Bell, J.S.: Against ‘measurement’. Phys. World 8, 33–35 (1990)

    Article  Google Scholar 

  3. Brukner, Č.: The Kreisgang between classical and quantum physics. arXiv:0905.3363 (2009)

  4. Bub, J.: Why the quantum? Stud. Hist. Philos. Mod. Phys. 35, 241–266 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. Chiribella, G., D’Ariano, G.M., Perinotti, P.: Informational derivation of quantum theory. arXiv:1011.6451 (2011)

  6. Clifton, R., Bub, J., Halvorson, H.: Characterizing quantum theory in terms of information-theoretic constraints. Found. Phys. 33, 1561–1591 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. D’Ariano, G.M.: Physics as information processing. In: Jaeger, G. (ed.) Advances in Quantum Theory, vol. 1327, pp. 7–18. American Institute of Physics, Melville (2011)

    Google Scholar 

  8. Deutsch, D.: The Fabric of Reality. Penguin Books, New York (1997)

    Google Scholar 

  9. Dickson, M.: A view from nowhere: quantum reference frames and uncertainty. Stud. Hist. Philos. Sci. B 35, 195–220 (2004)

    MATH  Google Scholar 

  10. Dickson, M.: Non-relativistic quantum mechanics. In: Butterfield, J., Earman, J. (eds.) Handbook for Philosophy of Physics, pp. 275–416. Kluwer Academic Press, Amsterdam (2007)

    Chapter  Google Scholar 

  11. Dürr, D., Goldstein, S., Zanghì, N.: Bohmian mechanics as the foundation of quantum mechanics. In: Cushing, J., Fine, A., Goldtein, S. (eds.) Bohmian Mechanics and Quantum Theory: An Appraisal, pp. 21–44. Springer, Dordrecht (1996)

    Chapter  Google Scholar 

  12. Fuchs, C.: Quantum mechanics as quantum information, mostly. J. Mod. Opt. 50, 987–1023 (2003)

    Article  MATH  ADS  Google Scholar 

  13. Goyal, P.: An information-theoretic approach to quantum theory, I. The abstract quantum formalism. arXiv:quant-ph/0702124 (2007)

  14. Goyal, P.: Information physics—towards a new conception of physical reality. Information 3, 567–594 (2012)

    Article  Google Scholar 

  15. Grinbaum, A.: Reconstruction of quantum theory. Br. J. Philos. Sci. 58, 387–408 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  16. Grinbaum, A.: Reconstructing instead of interpreting quantum theory. Philos. Sci. 74, 761–774 (2007)

    Article  MathSciNet  Google Scholar 

  17. Hardy, L.: Quantum theory from five reasonable axioms. quant-ph/00101012 (2001)

  18. Hilbert, D., von Neumann, J., Nordheim, L.: Über die grundlagen der quantenmechanik. Math. Ann. 98, 1–30 (1928)

    Article  MathSciNet  Google Scholar 

  19. Ludwig, G.: An Axiomatic Basis for Quantum Mechanics. Springer, Berlin (1985)

    Book  MATH  Google Scholar 

  20. Mackey, G.W.: Mathematical Foundations of Quantum Mechanics. W. A. Benjamin, New York (1963)

    MATH  Google Scholar 

  21. Piron, C.: Axiomatique quantique. Helv. Phys. Acta 37, 439–468 (1964)

    MATH  MathSciNet  Google Scholar 

  22. Rovelli, C.: Relational quantum mechanics. Int. J. Theor. Phys. 35, 1637–1678 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  23. Spekkens, R.: In defense of the epistemic view of quantum states: a toy theory. quant-ph/0401052 (2004)

  24. Van Fraassen, B.: Quantum Mechanics: An Empiricist View. Oxford University Press, New York (1991)

    Book  Google Scholar 

  25. Wootters, W.: The acquisition of information from quantum measurements, Ph.D. thesis, University of Texas at Austin (1980)

  26. Wootters, W.: Communicating through probabilities: does quantum theory optimize the transfer of information? Entropy 15, 3130–3147 (2013)

    Article  MathSciNet  ADS  Google Scholar 

Download references

Acknowledgments

Thanks to the organizers of the session on reconstruction theorems, to two anonymous referees, and to the participants for their helpful questions and comments.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michael Dickson.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dickson, M. Reconstruction and Reinvention in Quantum Theory. Found Phys 45, 1330–1340 (2015). https://doi.org/10.1007/s10701-015-9946-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-015-9946-x

Keywords

Navigation