## 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, access via your institution.

## Notes

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].

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

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

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.

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.

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’.

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

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?

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

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

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

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”.

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

## References

Barret, J.: Information processing in generalized probabilistic theories. Phys. Rev. A

**75**, 032304 (2007)Bell, J.S.: Against ‘measurement’. Phys. World

**8**, 33–35 (1990)Brukner, Č.: The Kreisgang between classical and quantum physics. arXiv:0905.3363 (2009)

Bub, J.: Why the quantum? Stud. Hist. Philos. Mod. Phys.

**35**, 241–266 (2004)Chiribella, G., D’Ariano, G.M., Perinotti, P.: Informational derivation of quantum theory. arXiv:1011.6451 (2011)

Clifton, R., Bub, J., Halvorson, H.: Characterizing quantum theory in terms of information-theoretic constraints. Found. Phys.

**33**, 1561–1591 (2003)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)

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

Dickson, M.: A view from nowhere: quantum reference frames and uncertainty. Stud. Hist. Philos. Sci. B

**35**, 195–220 (2004)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)

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)

Fuchs, C.: Quantum mechanics as quantum information, mostly. J. Mod. Opt.

**50**, 987–1023 (2003)Goyal, P.: An information-theoretic approach to quantum theory, I. The abstract quantum formalism. arXiv:quant-ph/0702124 (2007)

Goyal, P.: Information physics—towards a new conception of physical reality. Information

**3**, 567–594 (2012)Grinbaum, A.: Reconstruction of quantum theory. Br. J. Philos. Sci.

**58**, 387–408 (2007)Grinbaum, A.: Reconstructing instead of interpreting quantum theory. Philos. Sci.

**74**, 761–774 (2007)Hardy, L.: Quantum theory from five reasonable axioms. quant-ph/00101012 (2001)

Hilbert, D., von Neumann, J., Nordheim, L.: Über die grundlagen der quantenmechanik. Math. Ann.

**98**, 1–30 (1928)Ludwig, G.: An Axiomatic Basis for Quantum Mechanics. Springer, Berlin (1985)

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

Piron, C.: Axiomatique quantique. Helv. Phys. Acta

**37**, 439–468 (1964)Rovelli, C.: Relational quantum mechanics. Int. J. Theor. Phys.

**35**, 1637–1678 (1996)Spekkens, R.: In defense of the epistemic view of quantum states: a toy theory. quant-ph/0401052 (2004)

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

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

Wootters, W.: Communicating through probabilities: does quantum theory optimize the transfer of information? Entropy

**15**, 3130–3147 (2013)

## 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

### Corresponding author

## Rights and permissions

## About this article

### 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

Received:

Accepted:

Published:

Issue Date:

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

### Keywords

- Quantum theory
- Reconstruction
- Instrumentalism