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arXiv:2511.23125

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

Galina Weinstein

Published Jan 1, 2026• 1 citation
arXivHTMLPDF
DOI
10.2139/ssrn.5866982

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The Pusey–Barrett–Rudolph (PBR) theorem is widely regarded as one of the most important results in the foundations of quantum mechanics. It shows that, under broad and physically reasonable assumptions, the quantum wave function cannot be interpreted as a purely epistemic object. This conclusion has traditionally been taken to force a binary choice: either accept the wave function as ontic, or reject one of the theorem’s assumptions. This work presents a third option. Triadic Mesh Dynamics (TMD) provides an ontological framework in which the wave function ψ is not a fundamental physical entity, but an emergent statistical quantity summarizing the behaviour of a deeper, deterministic, and local triadic dynamics. In TMD, the ontic objects are the orientations of triads and their local flip dynamics, while ψ arises as a macroscopic description of orientational statistics, analogous to temperature in thermodynamics. Within this framework, distinct wave functions correspond to distinct statistical configurations of the triadic network, and TMD therefore automatically satisfies the empirical conclusion of the PBR theorem—without requiring ψ to be ontic. The result is a consistent third path: ψ is neither ontic nor epistemic, but emergent. This paper outlines the formal mapping between triadic orientation statistics and the emergent amplitude ψ, shows how the Schrödinger equation arises as the continuous limit of flip‑field dynamics, and argues that the PBR theorem naturally supports—rather than excludes—emergent ontologies such as TMD.
Formalizing an old desire of Einstein, “ψ-epistemic theories” try to reproduce the predictions of quantum mechanics, while viewing quantum states as ordinary probability distributions over underlying objects called “ontic states.” Regardless of one's philosophical views about such theories, the question arises of whether one can cleanly rule them out by proving no-go theorems analogous to the Bell inequality. In the 1960s, Kochen and Specker (who first studied these theories) constructed an elegant ψ-epistemic theory for Hilbert space dimension d = 2, but also showed that any deterministic ψ-epistemic theory must be “measurement contextual” in dimensions 3 and higher. Last year, the topic attracted renewed attention, when Pusey, Barrett, and Rudolph (PBR) showed that any ψ-epistemic theory must “behave badly under tensor product.” In this paper, we prove that even without the Kochen-Specker or PBR assumptions, there are no ψ-epistemic theories in dimensions d ≥ 3 that satisfy two reasonable conditions: (1) symmetry under unitary transformations and (2) “maximum nontriviality” (meaning that the probability distributions corresponding to any two nonorthogonal states overlap). This no-go theorem holds if the ontic space is either the set of quantum states or the set of unitaries. The proof of this result, in the general case, uses some measure theory and differential geometry. On the other hand, we also show the surprising result that without the symmetry restriction, one can construct maximally nontrivial ψ-epistemic theories in every finite dimension d.
The quantum Pusey–Barrett–Rudolph (PBR) theorem addresses the question of whether the quantum state corresponds to a ψ-ontic model (system’s physical state) or to a ψ-epistemic model (observer’s knowledge about the system). We reformulate the PBR theorem as a Monty Hall game and show that winning probabilities, for switching doors in the game, depend on whether it is a ψ-ontic or ψ-epistemic game. For certain cases of the latter, switching doors provides no advantage. We also apply the concepts involved in quantum teleportation, in particular for improving reliability.