Skip to main content
SpringerLink
Log in

Can Pragmatist Quantum Realism Explain Protective Measurements?

Foundations of Physics Aims and scope Submit manuscript

Cite this article

Abstract

According to Healey’s pragmatist quantum realism, the only physical properties of quantum systems are those to which the Born rule assigns probabilities. In this paper, I argue that this approach to quantum theory fails to explain the results of protective measurements.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Notes

  1. Note that the protection requires that some information about the measured system should be known before a PM, and thus PM cannot measure an arbitrary unknown state.

  2. A PM is a protected interaction between a measured system and a measuring device, and it can be understood by using the standard von Neumann procedure. The initial wave function of the pointer of a measuring device is usually supposed to be a Gaussian wavepacket of very small width centered in an initial position. After a PM, the final state of the pointer is a Gaussian wavepacket with the same width but shifted by the expectation value of the measured observable. This means that a PM of an observable yields a definite result, being the expectation value of the observable. For a more detailed introduction to PM, see [11]. Note that the principle of PM is independent of the reality of the wave function, and it only needs to assume that a pointer being in a definite position is assigned to a wavepacket of very small width centered in this position. Moreover, no matter how to understand PM, it has been realized in experiments for the polarisation of a single photon [12].

  3. The following analysis can be regarded as a further development of my objections to QBism [14].

  4. The conditions for making such an adiabatic-type PM are: (1) the measuring time of the electron is long enough compared to \(\hbar /\Delta E\), where \(\Delta E\) is the smallest of the energy differences between the ground state and other energy eigenstates, and (2) at all times the potential energy of interaction between the electron and the system is small enough compared to \(\Delta E\) [10].

  5. Since the state of the system \(\psi (x)\) is degenerate with its orthogonal state \(\psi ^{\perp }(x)=b^*\psi _1(x)-a^*\psi _2(x)\), we need a protection procedure to remove the degeneracy, e.g. joining the two boxes with a long tube whose diameter is small compared to the size of the box. By this protection \(\psi (x)\) will be a nondegenerate energy eigenstate. Then we can make an adiabatic-type PM of the charge of the system in box 1 as in the first example.

  6. If the distance between the two boxes is long enough and the charge Q does not move faster than the speed of light, then the time interval during which there is no charge distribution in box 1 can be even longer than the measuring time of the PM. In this case, it is more obvious that the continuous motion of the charge cannot explain the results of PMs.

  7. It can be further argued that at a deeper level the wave function density represents an instantaneous propensity property which determines the discontinuous jumps of the charge to form the right effective charge distribution \(|a|^2Q\) in box 1 [15].

  8. The analysis given above can be used to demonstrate the reality of the wave function (see also [16]).

References

  1. Healey, R.: Quantum theory: a pragmatist approach. Br. J. Philos. Sci. 63(4), 729–771 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  2. Healey, R.: Quantum states as objective informational bridges. Found. Phys. 47(2), 161–173 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Healey, R.: The Quantum Revolution in Philosophy. Oxford University Press, Oxford (2017)

    Book  MATH  Google Scholar 

  4. Healey, R.: Pragmatist quantum realism. In: French, Steven, Saatsi, Juha (eds.) Scientific Realism and the Quantum, pp. 123–146. Oxford University Press, Oxford (2020)

    Chapter  Google Scholar 

  5. Healey, R.: Securing the objectivity of relative facts in the quantum world. Found. Phys. 52, 88 (2022)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Jansson, L.: Can pragmatism about quantum theory handle objectivity about explanations? In: French, Steven, Saatsi, Juha (eds.) Scientific Realism and the Quantum, pp. 147–67. Oxford University Press, Oxford (2020)

    Chapter  Google Scholar 

  7. Lewis, P.J.: Quantum mechanics and its (dis)contents. In: French, Steven, Saatsi, Juha (eds.) Scientific Realism and the Quantum, pp. 168–82. Oxford University Press, Oxford (2020)

    Chapter  Google Scholar 

  8. Wallace, D.: The quantum revolution in philosophy. Analysis 80(2), 381–388 (2020)

    Article  Google Scholar 

  9. Aharonov, Y., Anandan, J., Vaidman, L.: Meaning of the wave function. Phys. Rev. A 47, 4616 (1993)

    Article  ADS  Google Scholar 

  10. Aharonov, Y., Vaidman, L.: Measurement of the Schrödinger wave of a single particle. Phys. Lett. A 178, 38 (1993)

    Article  ADS  Google Scholar 

  11. Gao, S. (ed.): Protective Measurement and Quantum Reality: Toward a New Understanding of Quantum Mechanics. Cambridge University Press, Cambridge (2015)

    Google Scholar 

  12. Piacentini, F., et al.: Determining the quantum expectation value by measuring a single photon. Nat. Phys. 13, 1191 (2017)

    Article  Google Scholar 

  13. Vaidman, L.: Protective measurements. In: Greenberger, D., Hentschel, K., Weinert, F. (eds.) Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy, pp. 505–507. Springer, Berlin (2009)

    Chapter  Google Scholar 

  14. Gao, S.: A no-go result for QBism. Found. Phys. 51, 103 (2021)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Gao, S.: The Meaning of the Wave Function: In Search of the Ontology of Quantum Mechanics. Cambridge University Press, Cambridge (2017)

  16. Gao, S.: Protective measurements and the reality of the wave function. Br. J. Philos. Sci. 73(3), 777–794 (2022)

    Article  MathSciNet  Google Scholar 

  17. Fuchs, C. A.: Notwithstanding Bohr, the Reasons for QBism. (2018). arxiv:1705.03483

  18. Schack, R.: QBism and normative probability in quantum mechanics. Talk given at the Symposium “Concepts of Probability in the Sciences”, Erwin Schrödinger International Institute for Mathematics and Physics, University of Vienna (2018)

  19. Myrvold, W.: On the status of quantum state realism. In: French, Steven, Saatsi, Juha (eds.) Scientific Realism and the Quantum, pp. 229–51. Oxford University Press, Oxford (2020)

    Chapter  Google Scholar 

  20. Myrvold, W.: Subjectivists about quantum probabilities should be realists about quantum states. In: Hemmo, M., Shenker, O. (eds.) Quantum, Probability, Logic, pp. 449–465. Springer, New York (2020)

    Chapter  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Center for Philosophy of Science and Technology, Shanxi University, Taiyuan, 030006, People’s Republic of China

    Shan Gao

Authors
  1. Shan Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shan Gao.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gao, S. Can Pragmatist Quantum Realism Explain Protective Measurements?. Found Phys 53, 11 (2023). https://doi.org/10.1007/s10701-022-00654-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10701-022-00654-x

Keywords

search

Navigation