Bell's Two Theorems?

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For the last thirty years there has been a great deal of controversy among philosophers of science over what exactly John Bell said about nonlocality, determinism, hidden variables, and the idea of a common_cause producing perfectly correlated outcomes in widely separated experiments.

In general, the papers have minimal discussion of the quantum physics, especially Erwin Schrödinger's two-particle wave function Ψ₁₂ and his prediction of perfect measurement correlations for widely separated entangled particles.

Instead the arguments are stated in verbal terms, with a few space-time diagrams and a famous "contraption" imagined by David Mermin. Dozens of new terms are defined and some older terms are given conflicting definitions. We provide a glossary of the terms, individual web pages on the philosophers, and downloadable PDFs of their critical articles.

John Bell's work begins with the problem of hidden variables as suggested by the 1935 Einstein-Podolsky Paradox paper, but we trace its origins back as early as Einstein's 1905 photoelectric effect paper and Schrödinger's formulation of wave mechanics in 1926.

We date the beginning of vigorous philosophical discussions to 1984 at Harvard University, when Abner Shimony invited philosopher of science Jon Jarrett to discuss his 1983 thesis Jarrett_Thesis.pdf">Bell's Theorem, Quantum Mechanics, and Local Realism

Shimony, author of the landmark Stanford Encyclopedia of Philosophy page on Bell's Theorem, inspired by Jarrett's thesis, began the creation of new terminology with his "parameter independence" and "outcome independence."

Parameter independence states that the probability of a measurement outcome for one observer (e.g., Alice) does not depend on the choice of measurement setting made by a distant observer (e.g., Bob) in a spacelike separated region.
[1] (https://link.aps.org/doi/10.1103/PhysRevA.104.032205),
[2] (https://www.bu.edu/cphs/about/abner-shimony/)

Alongside Parameter Independence (PI), Outcome Independence (OI) decomposes John Bell’s "local causality" condition into two distinct logical requirements to explain the nonlocality of quantum mechanics.
[1] (https://arxiv.org/html/1010.3969v1),
[2] (https://plato.stanford.edu/archives/fall2025/entries/bell-theorem/),
[3] (https://www.bu.edu/philo/2015/08/11/professor-abner-shimony-1928-2015/)

By breaking Bell's theorem down into these two types of independence, Shimony provided the mathematical and logical framework for why quantum mechanics can violate Bell inequalities without violating Albert Einstein's special relativity—a state Shimony famously termed "peaceful coexistence" - a term borrowed from Cold War politics and famously reapplied by Shimony to describe a non-contradictory relationship between quantum mechanics and special relativity.

But of course there remains a conflict between special relativity, which prohibits instantaneous interactions between spacelike separated events (Einstein's "spooky action-at-a-distance) and the perfectly correlated outcomes in widely separated experiments performed at the same time. "Saying cannot make it so!"

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