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 ultimate loophole in Bell’s theorem: The inequality is identically satisfied by data sets composed of ±1′sassuming merely that they exist

“…Thus, no inconsistency between quantum mechanics and the analysis presented above occurs. In Example 2, hidden variables using nonlocal information are employed to simulate quantum probabilities for computation of correlations between measurements, and between measurements and a counterfactual [5]. This is the case that Bell considered, but when the correlation is explicitly computed, rather than assumed, the Bell inequality must be satisfied in spite of the use of nonlocal information.…”

“…These correlations are mathematical creations. However, when quantum mechanical probabilities are used to compute correlations of predicted values with experimentally realizable variables [5], the resulting sets of correlations satisfy the Bell inequality -as they must, since all the corresponding data under consideration consists of ±1 ′ s.…”

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

“…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

“…A measurement of 1 A that reveals individual spins would collapse Equation (13) to one of these terms. Suppose it is the first for which all spins are positive.…”

“…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.…”