Bell theorem involving all settings of measuring apparatus

Henry Krips

Koji Nagata, Santanu Kumar Patro, Shahrokh Heidari +4 more

Here, we consider the Bell experiment for a system described by multipartite states in the case where ndichotomic observables are measured per site.If n is two, we consider a two-setting Bell experiment.If n is infinite, we consider an infinite-setting Bell experiment.Two-setting model is an explicit local realistic model for the values of a correlation function, given in a two-setting Bell experiment.Infinite-setting model is an explicit local realistic model for the values of a correlation function, given in an infinite-setting Bell experiment.In the non-contextual scenario, there is not the essential difference between infinite-setting model and two-setting model.And we cannot classify local realistic theories in this case.This says that we can construct infinite-setting model from two-setting model.Surprisingly we can discuss incompleteness in the Bell theorem by using non-contextual models.On the other hand, in the contextual scenario, there is the essential difference between infinite-setting model and two-setting model.This says that we must distinguish infinite-setting model from two-setting model.And we can classify local realistic theories in this case.

Rakin Khan

While Bell’s theorem is traditionally seen as a total rejection of local classical models in quantum mechanics, this paper argues that such a conclusion relies on the narrow assumption of "joint definiteness." Bell’s derivation requires a single hidden state, λ, to account for all possible measurement outcomes simultaneously, which implies that the measurement apparatus remains microscopically unchanged regardless of its settings. However, because physical instruments are composed of matter, their internal microstates necessarily vary with the chosen settings, meaning the relevant hidden variables are setting-dependent. This physical reality prevents the formation of a global joint probability distribution, placing these types of models outside the mathematical constraints of Bell’s and Fine’s theorems. Consequently, the authors conclude that while Bell’s theorem remains mathematically sound, it only excludes hidden-variable models that ignore the setting-dependent nature of the measuring apparatus, leaving the door open for classical descriptions of physical reality.

James Owen Weatherall

Koji Nagata, Renata Wong, Santanu Kumar Patro +2 more

Richard David Gill, Gregor Weihs, Anton Zeilinger +1 more

Hess and Philipp recently claimed [(2001) Proc. Natl. Acad. Sci. USA 98, 14224-14227 and 14228-14233] that proofs of Bell's theorem have overlooked the possibility of time dependence in local hidden variables, hence the theorem has not been proven true. Moreover they present what is claimed to be a local realistic model of the EPR correlations. If this is true then Bell's theorem is not just unproven, but false. We refute both claims. First, we explain why time is not an issue in Bell's theorem, and second, we show that their hidden variables model violates Einstein separability. Hess and Philipp have overlooked the freedom of the experimenter to choose settings of a measurement apparatus at will: any setting could be in force during the same time period.