Einstein, incompleteness, and the epistemic view of quantum states (0706.2661v1)

Abstract: Does the quantum state represent reality or our knowledge of reality? In making this distinction precise, we are led to a novel classification of hidden variable models of quantum theory. Indeed, representatives of each class can be found among existing constructions for two-dimensional Hilbert spaces. Our approach also provides a fruitful new perspective on arguments for the nonlocality and incompleteness of quantum theory. Specifically, we show that for models wherein the quantum state has the status of something real, the failure of locality can be established through an argument considerably more straightforward than Bell's theorem. The historical significance of this result becomes evident when one recognizes that the same reasoning is present in Einstein's preferred argument for incompleteness, which dates back to 1935. This fact suggests that Einstein was seeking not just any completion of quantum theory, but one wherein quantum states are solely representative of our knowledge. Our hypothesis is supported by an analysis of Einstein's attempts to clarify his views on quantum theory and the circumstance of his otherwise puzzling abandonment of an even simpler argument for incompleteness from 1927.

• The paper introduces a framework that distinguishes ψ-ontic models, where quantum states are real, from ψ-epistemic models, where they represent knowledge.
• It revisits Einstein’s critiques of quantum completeness and presents a nonlocality theorem that challenges local realism in ψ-ontic models.
• The authors encourage further exploration of ψ-epistemic models to address fundamental conceptual challenges in quantum mechanics.

Overview of "Einstein, incompleteness, and the epistemic view of quantum states"

The paper by Nicholas Harrigan and Robert W. Spekkens offers a comprehensive analysis of the interpretation of quantum states, exploring the epistemic versus ontic nature of these states within different hidden variable frameworks—particularly in the context of Einstein's views. The authors introduce a refined classification of ontological models by categorizing them as either $\psi$-ontic or $\psi$-epistemic, which interpret quantum states respectively as real physical states or as representations of knowledge about a system. This dichotomy sheds light on the foundational aspects of quantum theory, especially in relation to Einstein's arguments regarding its completeness and the nonlocality problem.

Core Findings and Arguments

Harrigan and Spekkens' exposition begins with a detailed framework for understanding hidden variable models, distinguishing them based on whether the quantum state $\psi$ is ontic or epistemic. They provide clear definitions: a $\psi$-ontic model implies that each ontic state corresponds to a unique quantum state, maintaining a one-to-one correspondence between the quantum description and reality, whereas a $\psi$-epistemic model suggests multiple quantum states overlapping across the same ontic state, thus treating quantum states as incomplete representations of reality.

The authors revisit Einstein's historical stance on the incompleteness of quantum mechanics, particularly through his preferred arguments against the $\psi$-complete view, most notably expressed during the Solvay Conferences and in correspondence with Schrödinger. Einstein pursued an interpretation where quantum mechanics might be rooted not just in a failure of completeness but in an inherent epistemic nature of quantum states. As Harrigan and Spekkens articulate, this aligns with Einstein's conviction that quantum states are better understood as cataloging information about systems rather than embodying reality itself.

Nonlocality and $\psi$-ontic Models

A substantive part of the paper is dedicated to highlighting a nonlocality theorem applicable to $\psi$-ontic models. The authors elucidate that for models where quantum states are assumed ontic, locality cannot be preserved, providing an argument more accessible than Bell’s theorem. They theorize that in Einstein's 1935 argument, he implicitly demonstrated the incompatibility of $\psi$-ontic models with locality, thus presaging results traditionally attributed to Bell’s later work.

Encouraging Progress in $\psi$-Epistemic Frameworks

Contrary to the challenges faced by $\psi$-ontic models, $\psi$-epistemic models warrant further examination as they allow for richer explanatory power without contravening locality to the same degree. The authors cite modern theoretical advances that showcase the utility of epistemic interpretations in explicating quantum phenomena—ranging from teleportation to classical limits of quantum mechanics—suggesting promising research directions.

Conclusion and Implications

Harrigan and Spekkens ultimately argue that exploring $\psi$-epistemic models presents an opportunity to further our understanding of quantum mechanics, advocating for re-evaluating the premises of hidden variable theories. While Bell's theorem precludes local-realism in traditional terms, their analysis shows that alternative approaches might still offer significant insights, holding implications for the theoretical framework of quantum mechanics and interpretations aligned with a knowledge-centric view of quantum states. The paper argues that emphasis should be placed on further developing and rigorously testing $\psi$-epistemic models to ascertain their viability and potential to resolve some of quantum theory's enduring conceptual challenges.