Contextual Incompleteness and Observation

Bernard d’Espagnat

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.

Rob Clifton

What if Einstein, Podolsky, and Rosen were right that quantum mechanics is incomplete, and there do exist ‘‘elements-of-reality’’ corresponding to all observables whether or not they are compatible? The implications are surprising. Not only must the values of these elements-of-reality depend upon what measurements are actually performed on the system, but also upon measurements performed at spacelike separation from it! The former dependence has been dubbed ‘‘contextualism,’’ and the latter ‘‘nonlocality.’’ It is important for students to understand the necessity of these two features, if only to reinforce the point that a straightforward classical recasting of quantum theory in terms of pre-existing measurement independent elements-of-reality is not feasible. Unfortunately the argument for contextualism, in particular, is daunting due to its reliance on an elaborate geometrical argument. I aim here to minimize the geometry needed to argue for contextualism by using some ideas inspired by the original arguments of Bell and of Kochen and Specker. Using similar methods, I simplify the closely related geometrical argument for nonlocality due to Heywood and Redhead and to Stairs.

Michael L. G. Redhead

George Jaroszkiewicz

IntroductionClassical mechanics (CM) is conventionally formulated according to partially contextually complete Block Universe principles: an exophysical observer sitting in some frame of reference looks in on a system under observation (SUO) and assigns truth values to propositions about states of that SUO, but the details of how these truth values are obtained are not given.There is a curious aspect to this scenario: the contextual incompleteness of CM is itself contextual.By this we mean that there are two scenarios, with different general propositional classifications (GPCs). The Experimentalist's PerspectiveFrom a classical experimentalist's perspective, generalized propositions (GPs) in CM take the form P(P , ∅|∅, F ).(6.1)Here P is some proposition of scientific interest, such as "The orbit of Jupiter is an ellipse," and F is relative external context describing the frame of reference used to describe states of the SUO relative to the wider Universe external to that SUO.This form of GP has a GPC of 2 according to the algorithm discussed in Chapter 2.Remark 6.1 Suppose an astronomer used a telescope T to test proposition P .That would not upgrade the GP to one of the form P(P , T |∅, F ) with a GPC of 3. The reason is that the use of a telescope is not essential in this context.Historically, Kepler did not use a telescope to state his laws of planetary motion: he used the data obtained by Tycho using naked eye observations.On the other hand, the observation of the Hubble red shift using telescopes fitted with spectrum analyzers would qualify for such an upgrade.

Jeffrey Bub