Bell's inequality violation due to misidentification of spatially non-stationary random processes

Abstract

Correlations for the Bell gedankenexperiment are constructed using probabilities given by quantum mechanics, and nonlocal information. They satisfy Bell's inequality and exhibit spatial non stationarity in angle. Correlations for three successive local spin measurements on one particle are computed as well. These correlations also exhibit non stationarity, and satisfy the Bell inequality. In both cases, the mistaken assumption that the underlying process is wide-sense-stationary in angle results in violation of Bell's inequality. These results directly challenge the wide-spread belief that violation of Bell's inequality is a decisive test for nonlocality. PACS number 03.65.Bz

The Bell Inequality Is Satisfied by Quantum Correlations Computed Consistently with Quantum Non-Commutation

“…This eliminates the need for nonlocal information. The same correlations are produced as in the conventional Bell case [8] except for a minus sign that does not effect Inequality (2.4). The relevant conditional probabilities in this situation are [16]…”

“…This is the situation considered by Bell in the construction of his theorem. It has been treated in [8], but a variation is considered here in which one and two alternate counterfactual measurements are carried out on one particle. This eliminates the need for nonlocal information.…”

“…No nonlocal information is used by the algorithm to determine B and B' since only a single particle is considered whereas if the correlations are predicted for measurements on two particles on opposite sides of a Bell apparatus as in [8], the sign of AB and AB' are reversed, and the algorithm requires that B and B' know A's outcome and setting angle, θ A . The point of this example is that, in the present case, the same sets of Bell cosine correlations (up to a minus sign that does not effect validity of (2.4)) are associated with the use of local information as are associated with nonlocal information in the case given previously in [8]. However, it is the use of incorrect assumptions regarding the form of the correlations for the non-commuting counterfactuals that causes violation of the Bell inequality.…”

“…Unfortunately, Bell did not explicitly compute values of these counterfactuals using quantum mechanics, but assumed that if they could be accounted for by a random process underlying quantum mechanics, it must be a second order stationary (SOS) process [7]. A number of authors have voiced objections to aspects of Bell's logic in the construction of his theorem (of which a sampling is given in [8]- [11]). However, the physics community overall has accepted it.…”

Logical Difficulty from Combining Counterfactuals in the GHZ-Bell Theorems

“…One would use an additional apparatus in tandem on either side of the usual Bell experiment operating in a retrodictive mode [10]. The second would use separate experiments from which correlations conditional on the usual outcomes could be computed [12,13]. Either of these would yield a third correlation that is functionally different from those obtained in standard Bell experiments such that the three would satisfy the Bell inequality as required by basic mathematics.…”