Einstein's 1935 Letters to Schrödinger and Popper and the Boundaries of the PBR $ψ$-Epistemic Framework

TL;DR

This paper reexamines Einstein’s 1935 critique of quantum mechanics by analyzing his letters to Schrödinger and Popper, arguing that his claim of incompleteness is fundamentally ontological rather than epistemic. It situates Einstein within the broader $ψ$-ontic/$ψ$-epistemic landscape, showing that his arguments do not instantiate the HS/PBR formalism, which requires an ontic state space $Λ$, preparation distributions $μ_ψ(λ)$, and overlap structures. It critically assesses Yemima Ben-Menahem’s reading that ties Einstein to an epistemic/ensemble lineage, showing that her categorization imports HS/PBR machinery not present in the German texts and that the direction of logical inference in PBR (from $ψ$ to $λ$) contrasts with Einstein’s $λ$ to $ψ$ reasoning. The analysis suggests that while retrospective readings can map Einstein onto modern frameworks, they do so only by importing structure absent from his writings, reinforcing the view that PBR remains a no-go for $ ext{psi}$-epistemic models in the HS sense. Overall, the paper clarifies the methodological boundaries between historical arguments about completeness and contemporary formal classifications of quantum states.

Abstract

Einstein's 1935 critique of quantum mechanics is often associated with the Einstein-Podolsky-Rosen (EPR) argument, yet his private correspondence from that year reveals a more exact conceptual structure guiding his claim that the $ψ$-function is incomplete. This paper reconstructs Einstein's reasoning in his letters to Schrödinger and Popper and examines how it engages, and fails to engage with contemporary $ψ$-ontic/$ψ$-epistemic distinctions. Recent scholarship, most notably by Ben-Menahem, has interpreted Einstein as an early representative of the modern $ψ$-epistemic tradition within the Harrigan-Spekkens ontological models framework and the Pusey-Barrett-Rudolph (PBR) theorem. I argue, however, that this retrospective classification is undermined by Ben-Menahem's own distinction between realist and radical epistemic interpretations: Einstein's 1935 view lacks the structural assumptions - defined ontic state space, preparation distributions, and overlap structure - required for membership in the HS/PBR class of $ψ$-epistemic models. Any such identification, therefore, requires importing formal machinery foreign to Einstein's original argument.