In 1960, he moved to work for the European Organization for Nuclear Research (CERN, Conseil Européen pour la Recherche Nucléaire), in Geneva, Switzerland.

[13] There he worked almost exclusively on theoretical particle physics and on accelerator design, but found time to pursue a major avocation, investigating the foundations of quantum theory.

The wave functions would prove to be a provisional or incomplete description of the quantum-mechanical part, of which an objective account would become possible.

Here are some words which, however legitimate and necessary in application, have no place in a formulation with any pretension to physical precision: system, apparatus, environment, microscopic, macroscopic, reversible, irreversible, observable, information, measurement.

[18]: 215 To thoroughly explore the viability of Bohm's theory, Bell needed to answer the challenge of the so-called impossibility proofs against hidden variables.

[10]: 144 ) He showed that John von Neumann's no hidden variables proof[20] does not prove the impossibility of hidden variables, as was widely claimed, due to its reliance on a physical assumption that is not valid for quantum mechanics—namely, that the probability-weighted average of the sum of observable quantities equals the sum of the average values of each of the separate observable quantities.

[10]: 141  This flaw in von Neumann's proof had been previously discovered by Grete Hermann in 1935, but did not become common knowledge until after it was rediscovered by Bell.

"[22]: 88  In this same work, Bell showed that a stronger effort at such a proof (based upon Gleason's theorem) also fails to eliminate the hidden-variables program.

However, in 2010, Jeffrey Bub published an argument that Bell (and, implicitly, Hermann) had misconstrued von Neumann's proof, saying that it does not attempt to prove the absolute impossibility of hidden variables, and is actually not flawed, after all.

[26] In this work, he showed that carrying forward EPR's analysis[27] permits one to derive the famous Bell's theorem.

[28] The resultant inequality, derived from basic assumptions that apply to all classical situations, is violated by quantum theory.

Bell regretted that results of the tests did not agree with the concept of local hidden variables: For me, it is so reasonable to assume that the photons in those experiments carry with them programs, which have been correlated in advance, telling them how to behave.

"[30]: 84 Bell seemed to have become resigned to the notion that future experiments would continue to agree with quantum mechanics and violate his inequality.

Most mainstream physicists are highly skeptical about all these "loopholes", admitting their existence but continuing to believe that Bell's inequalities must fail.

This situation and the background of Bell's position is described in detail by his collaborator Johann Rafelski in the textbook "Relativity Matters" (2017).