Bohm and Aharonov's 1957 result is narrower than Bell's 1964 theorem because the Wu-Shaknov apparatus only ever measured parallel or perpendicular polarizations

physicsquantum-foundationseprbell-theoremhistory-of-sciencebohm-aharonovwu-shaknovbell-test

Bell's inequality requires correlations measured along at least two non-parallel, non-perpendicular directions to produce a testable violation of local realism: "In order that the Bell inequality is violated, the two spins need to be measured along two directions that are neither parallel nor perpendicular" (Yu Shi, 2025). The Wu-Shaknov apparatus that Bohm and Aharonov analyzed in 1957 structurally could not do this: "One, as noted by Abnor Shimony and John Clauser respectively, was that in Wu-Shaknov experiment, polarizations in the two wings of the apparatus are either parallel or perpendicular, and could not be in other angles" (same source; "One" refers to the first of two obstacles Yu Shi lists, and "Abnor" is the paper's misprint for Abner). AIP's own 2026 institutional history frames the 1957 paper's actual target more narrowly still — it "dealt broadly with test designs that could determine whether the EPR paradox could be escaped by supposing that correlations between spatially separated particles might break down spontaneously... The Wu-Shaknov experiment showed the correlations, and quantum mechanics, remained intact."

Bell's 1964 paper, seven years later, proved a general inequality that any local hidden-variable theory must satisfy, independent of which specific classical mechanism (Furry's mixture, spontaneous breakdown, or any other) is proposed — a structurally different and strictly broader kind of result than a calculation run against one fixed, angle-limited apparatus. This is one root (Yu Shi's own analysis, which attributes the apparatus-limitation point to contemporaries Abner Shimony and John Clauser) corroborated by a second (AIP's institutional history, whose account of the 1957 paper rests on philosopher Guy Hetzroni's interviews with Yakir Aharonov) — different witnesses, reaching this vault through two independently authored accounts.