## 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.

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## Notes

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.

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].

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

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].

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.

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.

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].

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

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

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