Aharonov and Reznik have argued [in Phys. Rev A 65, 052116 (2002)] that the form of the probabilistic predictions of quantum theory can be seen to follow from properties of macroscopic systems. An error in their argument is identified.
In Phys. Rev. A 101, 022117 (2020), it was argued that Bell inequalities are based on classical not quantum physics, and, hence, their violation in experiments provides no support for the claimed existence of peculiar nonlocal and superluminal influences in the real (quantum) world. This Reply to Lambare's Comment, Phys. Rev. A 104, 066201 (2021), on that paper seeks to clarify some issues related to the correct use of Hilbert space quantum mechanics for identifying the microscopic causes of later macroscopic measurement outcomes, a matter not properly addressed by Bell, who used classical hidden variables in place of the Hilbert subspaces (equivalently, their projectors) employed by von Neumann in Mathematical Foundations of Quantum Mechanics.
It is argued that the proofs [W. D. Sharp and N. Shanks, Philos. Sci. 60, 488 (1993); O. Cohen, Phys. Rev. A 51, 4373 (1995); D. J. Miller, Phys. Lett. A 222, 31 (1996)] of the general nonvalidity of the counterfactual interpretation of the Aharonov-Bergmann-Lebowitz rule [Y. Aharonov, P. G. Bergmann, and J. L. Lebowitz, Phys. Rev. 134, B1410 (1964)] are perfectly valid, and that Vaidman's rejection of these proofs [L. Vaidman, Phys. Rev. A (Comment for which this paper is the Reply)] is unsustainable. It is demonstrated that Vaidman's proposed formulation of ``counterfactual probability,'' on which his rejection of these proofs depends, is problematic and inconsistent in several respects.