Strong constraints on models that explain the violation of Bell inequalities with hidden superluminal influences (1304.0532v1)

Abstract: We discuss models that attempt to provide an explanation for the violation of Bell inequalities at a distance in terms of hidden influences. These models reproduce the quantum correlations in most situations, but are restricted to produce local correlations in some configurations. The argument presented in [Bancal et al. Nature Physics 8, 867 (2012)] applies to all of these models, which can thus be proved to allow for faster-than-light communication. In other words, the signalling character of these models cannot remain hidden.

• The paper shows that hidden superluminal influence models cannot reproduce quantum correlations without leading to faster-than-light signalling.
• It analyzes finite-distance and multisimultaneity frameworks and reveals that specific spacetime configurations violate the no-signalling principle.
• The work underscores that reconciling these models with relativity is untenable, urging the search for alternative explanations of quantum nonlocality.

Constraints on Models Explaining Bell Inequality Violations with Hidden Influences

This paper interrogates models proposing explanations for the violation of Bell inequalities using hidden superluminal influences. These models, aiming to reproduce quantum correlations, invariably encounter challenging constraints and lead to the possibility of faster-than-light communication, defying the principles of relativity.

Overview of the Models

The paper considers alternative models striving to explain nonlocal quantum correlations by means of hidden influences that propagate through a specific reference frame. Two primary models are the focus:

1. Finite-Distance Model: This model allows for instantaneous interactions but only between parties separated by a distance not exceeding a predefined critical value.
2. Multisimultaneity Model: Within this framework, the particle's rest frame designates the frame in which influences propagate instantly. Two variants of this model are analyzed: one based on influences proceeding backward in time (before-before configuration) and the other forward in time (after-after configuration).

Implications and Evaluation

Both models share common properties:

• They reproduce quantum predictions accurately in most spacetime configurations.
• In certain configurations, these models predict that nonlocal correlations vanish where quantum theory anticipates Bell inequality violations.

The authors expound on the implications of these models regarding faster-than-light communication. This potential arises due to the intrinsic signalling character of the models becoming evident in specific spacetime arrangements. For instance, by employing the hidden influence inequality $S\leq 7$ introduced by Bancal et al. (2012), the paper demonstrates scenarios where these models necessarily permit superluminal signalling.

Critical Findings

Key outcomes include:

• Constrained Models: The hidden influence framework inherently contradicts relativity when applied to explain quantum correlations, as demonstrated by hidden influence inequalities. Specifically, achieving nonlocal correlations via finite-speed or finite-distance hidden influences is untenable without conflicting with relativity.
• Incompatibility with Relativity: By leveraging multipartite configurations and examining different sequences of measurements across spatially separated systems, the analysis concludes that both finite-distance and multisimultaneity models facilitate communication exceeding light speed.

Speculation on Theoretical Advancement

Given the results presented, future explorations in quantum foundational research may hinge on:

• Investigating the extent to which no-signalling models can be reconciled (or definitively refuted) with quantum theory constraints.
• Exploring alternative explanations for Bell inequality violations that conform to relativistic principles without invoking hidden variables or superluminal influences.

Conclusion

By constraining models attempting to inject hidden influences into quantum mechanics, this work underscores the discordance such models have with relativity. In providing strong evidence against the viability of finite-speed and multisimultaneity models, the paper hints at the necessity for other, potentially more orthodox, resolutions to the quantum nonlocality conundrum. Researchers are thus encouraged to scrutinize and perhaps ultimately deconstruct such alternative models, forging novel paths consistent with observed quantum phenomena and the tenets of special relativity.