Arguments for and Against Hidden Variables

Emilio Santos

Abner Shimony

The study of hidden-variable interpretations of quantum mechanics was transformed by two papers of Bell. In his 1966 paper in Reviews of Modern Physics [1] he analysed the argument of von Neumann [2] and the more powerful arguments of Jauch and Piron [3] and of Gleason [4], all leading to similar conclusions about the nonassignability of simultaneous values to all the observables of a nontrivial quantum system; and he showed that these arguments do not exclude what may be called “contextualistic” hidden-variable theories, in which the value of an observable O is allowed to depend not only upon the hidden state λ, but also upon the set C of compatible observables measured along with O . In Bell's 1964 paper in Physics [5] (written later than the other, in spite of the earlier publication date) he gave a new kind of argument against a hidden-variable interpretation of quantum mechanics, by showing that no hidden-variables theory which satisfies a certain condition of locality can agree with all the statistical predictions of quantum mechanics. The main purpose of this lecture is to discuss an experiment, designed by Clauser, Horne, Holt and myself [6], which is based on Bell's proof of the incompatibility of quantum mechanics and local hidden-variable theories. Before doing this, however, I wish to make several comments.

Miklós Rédei

Rob Clifton, Adrian Kent

No physical measurement can be performed with infinite precision. This leaves a loophole in the standard no–go arguments against non–contextual hidden variables. All such arguments rely on choosing special sets of quantum–mechanical observables with measurement outcomes that cannot be simulated non–contextually. As a consequence, these arguments do not exclude the hypothesis that the class of physical measurements in fact corresponds to a dense subset of all theoretically possible measurements with outcomes and quantum probabilities that can be recovered from a non–contextual hidden–variable model. We show here by explicit construction that there are indeed such non–contextual hidden–variable models, both for projection–valued and positive–operator–valued measurements.

J. M. Jauch, C. Piron

Indrajit Sen

In a recent article (arXiv:2108.08144), Hance, Hossenfelder and Palmer have advanced arguments claiming to show that the analysis of Invariant-set theory in a hidden-variable setting (arXiv:2107.04761) is wrong. We explain here why these arguments are incorrect, and involve misunderstandings of the hidden-variable model in question and Bell's notion of local causality.