Abstract
In QBism the wave function does not represent an element of physical reality external to the agent, but represent an agent’s personal probability assignments, reflecting his subjective degrees of belief about the future content of his experience. In this paper, I argue that this view of the wave function is not consistent with protective measurements. The argument does not rely on the realist assumption of the ψ-ontology theorems, namely the existence of the underlying ontic state of a quantum system.
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Notes
There are two known schemes of protection. The first one is to introduce a protective potential, and the second one is via the quantum Zeno effect. It should be pointed out that the protection requires that some information about the measured system should be known before a PM, and PMs cannot measure an arbitrary unknown wave function. In some cases, the information may be very little. For example, we only need to know that a quantum system such as an electron is in the ground state of an external potential before we make PMs on the system to find its wave function, no matter what form the external potential has.
Note that PMs are different from quantum non-demolition measurements. In a quantum non-demolition measurement, the measured observable is required to commute with the total Hamiltonian so that it is a constant of the motion. This implies that the measurement is repeatable, but it does not imply that the wave function of the measured system is unchanged during the measurement. By comparison, a PM does not require that the measured observable must commute with the total Hamiltonian, and the wave function of the measured system does not change during the measurement.
An example of how to measure B is given by [14, p. 4622]. In the gedanken experiment, a charged particle Q is in a thin circular tube enclosing a magnetic but with the magnetic field vanishing inside the tube. A protective measurement of each eigenstate can be made by shooting electrons near the tube and observing their trajectories; from the accelerations of the electrons the charge density \(Q\rho\) and the current density Qj can be determined.
In most cases the measured wave function can be reconstructed only in principle. For a spatial wave function like \(\psi (x)\), since one needs to measure the observables A and B in infinitely many points in space, this is an impossible task in practice.
References
Caves, C.M., Fuchs, C.A., Schack, R.: Quantum probabilities as Bayesian probabilities. Phys. Rev. A 65, 022305 (2002)
Caves, C.M., Fuchs, C.A., Schack, R.: Subjective probability and quantum certainty. Stud. Hist. Philos. Mod. Phys. 38, 255 (2007)
Fuchs, C.A., Mermin, N.D., Schack, R.: An introduction to QBism with an application to the locality of quantum mechanics. Am. J. Phys. 82, 749–754 (2013). arXiv:1311.5253
Fuchs, C.A., Stacey, B.C.|: QBism: Quantum Theory as a Hero’s Handbook. Proceedings of the International School of Physics Enrico Fermi: Course 197, Foundations of Quantum Theory (2016). arXiv:1612.07308
Mermin, N.D.: QBism puts the scientist back into science. Nature 507, 421–423 (2014)
Colbeck, R., Renner, R.: Is a systems wave function in one-to-one correspondence with its elements of reality? Phys. Rev. Lett. 108, 150402 (2012)
Hardy, L.: Are quantum states real? Int. J. Mod. Phys. B 27, 1345012 (2013)
Pusey, M., Barrett, J., Rudolph, T.: On the reality of the quantum state. Nat. Phys. 8, 475–478 (2012)
Bacciagaluppi, G.: A critic looks at QBism. In: Galavotti, M.C., Dieks, D., Gonzalez, W.J., Hartmann, S., Uebel, T., Weber, M. (eds.). New Directions in the Philosophy of Science, pp. 403–416. Springer, Cham (2014)
Earman, J.: Quantum Bayesianism assessed. Monist 102, 403–423 (2019)
McQueen, K. J. (2017). Is QBism the future of quantum physics? arXiv:1707.02030
Norsen, T.: Quantum solipsism and non-locality. In: Bell, M., Gao, S. (eds.) Quantum Nonlocality and Reality: 50 Years of Bells Theorem, pp. 204–237. Cambridge University Press, Cambridge (2016)
Timpson, C.G.: Quantum Bayesianism: A study. Stud. Hist. Philos. Mod. Phys. 39, 579–609 (2008)
Aharonov, Y., Anandan, J., Vaidman, L.: Meaning of the wave function. Phys. Rev. A 47, 4616 (1993)
Aharonov, Y., Vaidman, L.: Measurement of the Schrödinger wave of a single particle. Phys. Lett. A 178, 38 (1993)
Gao, S. (ed.): Protective Measurement and Quantum Reality: Toward a New Understanding of Quantum Mechanics. Cambridge University Press, Cambridge (2015)
Piacentini, F., et al.: Determining the quantum expectation value by measuring a single photon. Nat. Phys. 13, 1191 (2017)
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)
Combes, J., Ferrie, C., Leifer, M., Pusey, M.: Why protective measurement does not establish the reality of the quantum state. Quantum Stud. Math. Found. 5, 189–211 (2018)
Gao, S.: Protective measurements and the reality of the wave function. Brit. J. Philos. Sci. (2020). https://doi.org/10.1093/bjps/axaa004
Gao, S.: The Meaning of the Wave Function. In Search of the Ontology of Quantum Mechanics. Cambridge University Press, Cambridge (2017)
Healey, R.: Quantum-Bayesian and pragmatist views of quantum theory. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy, Spring 2017 edn. Metaphysics Research Laboratory, Stanford University, Stanford (2017)
Timpson, C.G.: QBism, Ontology, and Explanation. Talk given at the Mini-Workshop on QBism and the Interpretation of Quantum Theory (May 25, 2021)
Acknowledgements
I am grateful to the editors and reviewers of this journal for their useful comments and suggestions. This work is supported by the National Social Science Foundation of China (Grant No. 16BZX021).
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Gao, S. A No-Go Result for QBism. Found Phys 51, 103 (2021). https://doi.org/10.1007/s10701-021-00505-1
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DOI: https://doi.org/10.1007/s10701-021-00505-1