Bell (1981, C2-57):

“… it may be that it is not permissible to regard the experimental settings a and b in the analyzers as independent variables, as we did. We supposed them in particular to be independent of the supplementary [a.k.a. hidden] variables ฮป, in that a and b could be changed without changing the probability distribution ฯ(ฮป). Now even if we have arranged that a and b are generated by apparently random radioactive devices, housed in separate boxes and thickly shielded, or by Swiss national lottery machines, or by elaborate computer programmes, or by apparently free willed experimental physicists, or by some combination of all of these, we cannot be sure that a and b are not significantly influenced by the same factors ฮป that influence A and B [measurement outcomes]. But this way of arranging quantum mechanical correlations would be even more mind boggling that one in which causal chains go faster than light. Apparently separate parts of the world would be deeply and conspiratorially entangled, and our apparent free will would be entangled with them.”

Hance and Hossenfelder (2022, p. 1382) on the assumption of statistical independence of supplementary/hidden variables and experimental settings:

“Types of hidden variables theories which violate statistical independence include those which are superdeterministic, retrocausal, and supermeasured. Some have dismissed them on metaphysical grounds, by associating a violation of statistical independence with the existence of ‘free will’ or ‘free choice’ and then arguing that these are not assumptions we should give up.

“It is, in hindsight, difficult to understand how this association came about. We believe it originated in the idea that a correlation between the hidden variables and the measurement setting would somehow prevent the experimentalist from choosing the setting to their liking. However, this is mistaking a correlation with a causation. And any serious philosophical discussion of free will acknowledges that human agency is of course constrained by the laws of nature anyway.”


Bell, J. S. (1981). Bertlmannโ€™s socks and the nature of reality.ย Le Journal de Physique Colloques,ย 42(C2), C2-41-C2-62. Reprinted in Bell (2004).

Bell, J. S. (2004). Speakable and unspeakable in quantum mechanics: Collected papers on quantum philosophyย (2nd ed.). Cambridge University Press.

Hance, J. R., & Hossenfelder, S. (2022). Bellโ€™s theorem allows local theories of quantum mechanics. Nature Physics, 18(12), 1382.ย  [Preprint]