Reply to "Comment on 'Nonlocality claims are inconsistent with Hilbert-space quantum mechanics' '"

TL;DR

This paper defends the view that Bell inequalities are rooted in classical assumptions and clarifies the correct use of Hilbert space quantum mechanics in analyzing measurement outcomes, countering claims of nonlocal influences.

Contribution

It clarifies the proper application of Hilbert space quantum mechanics in understanding measurement outcomes, contrasting it with classical hidden variable approaches used in Bell's analysis.

Findings

Bell inequalities are based on classical assumptions.

Hilbert space quantum mechanics provides a different framework.

Proper use of Hilbert space clarifies measurement causes.

Abstract

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 his \it{Mathematical Foundations of Quantum Mechanics}.