[Paper Review] Shedding (red and green) light on "time related hidden parameters"

N. David Mermin|ArXiv.org|Jun 18, 2002

Neural Networks and Reservoir Computing4 citations

TL;DR

This paper refutes Hess and Philipp's critique of Bell's theorem by demonstrating that their proposed 'time-related hidden parameters'—in the form of detector microsettings correlated across time—do not invalidate Mermin's simple, instructive version of Bell's theorem. The argument shows that even with such time-dependent parameters, local hidden-variable models still cannot reproduce the quantum correlation statistics, as they inevitably lead to same-color flashes in at least 5/9 of identical-setting runs, contradicting the observed 50% frequency of same-color outcomes. The core contribution is proving the robustness of Bell's theorem against this specific classical loophole.

ABSTRACT

I explain in elementary terms why the critique of Hess and Philipp in Section 3.2 of quant-ph/0103028 fails to invalidate the nontechnical version of Bell's theorem I gave twenty years ago, involving two detectors with 3-pole switches and red and green lights.

Motivation & Objective

• To counter Hess and Philipp's claim that time-dependent detector microsettings invalidate Bell's theorem in a simplified EPR scenario.
• To demonstrate that even with correlated microsettings across time, local hidden-variable models cannot reproduce the observed quantum statistics.
• To show that the core argument of Mermin's 1985 EPR thought experiment remains valid despite attempts to introduce time-dependent hidden parameters.
• To establish that the 5/9 lower bound on same-color flashes under local realism is inescapable, regardless of microsetting correlations.
• To clarify that quantum mechanics' prediction of 50% same-color flashes contradicts any local hidden-variable model, even with complex time-dependent parameters.

Proposed method

• Reformulate Mermin's original 1985 EPR thought experiment using three detector settings (1, 2, 3) and red/green flash outcomes.
• Introduce the concept of detector microsettings—hidden variables underlying each setting—that may vary from run to run and be correlated across time.
• Extend the standard instruction set (e.g., GGR) to include type-I and type-II microsettings, where the output depends on which type is active at detection.
• Analyze the effective flash outcomes by considering all nine possible pairs of detector settings and the resulting color correlations under different microsetting configurations.
• Show that for any such extended instruction set, the probability of same-color flashes on identical settings remains at least 5/9, regardless of microsetting correlations.
• Argue that since quantum mechanics predicts only 50% same-color flashes, no such local model can reproduce the data, even with time-dependent microsettings.

Experimental results

Research questions

• RQ1 Can Hess and Philipp's time-related hidden parameters invalidate Mermin's 1985 EPR thought experiment?
• RQ2 Does the introduction of correlated detector microsettings across time allow local hidden-variable models to reproduce the quantum correlation statistics?
• RQ3 Is the 5/9 lower bound on same-color flashes under local realism still valid when microsettings are time-dependent and correlated?
• RQ4 Can a local hidden-variable model be constructed that reproduces the 50% same-color flash rate observed in quantum mechanics?
• RQ5 Does the requirement for synchronized clock times at detectors imply that microsetting information could be predetermined at the source, undermining the need for time-dependent parameters?

Key findings

• The requirement that identical settings always produce the same flash color forces particles to carry identical instruction sets for all three settings, which is incompatible with the observed 50% same-color flash rate.
• Even when extended to include time-dependent microsettings, any local hidden-variable model must still predict same-color flashes in at least 5/9 of identical-setting runs.
• The observed 50% same-color flash rate in quantum mechanics violates this 5/9 lower bound, proving that no local hidden-variable model can account for the data.
• The microsetting correlations proposed by Hess and Philipp do not escape the 5/9 bound because the effective output depends on the type (I or II) of microsetting active at detection, which still leads to the same statistical constraint.
• The model's time dependence does not resolve the contradiction, as the same 5/9 bound holds regardless of whether microsettings are chosen at the source or at detection.
• The argument remains valid even if microsettings are determined at detection, because the same statistical constraint applies to the effective instruction sets derived from them.