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arXiv:quant-ph/0109153

Bell's Inequalities In 4-dimension Rieman's Space

T. F. Kamalov

Published Sep 28, 2001• 0 citations
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Abstract

It is shown that the nature of quantum statistics can study in assumption of existence of a background of random gravitational fields and waves, distributed isotropically in the space. This background is capable of correlating phases of oscillations of identical microobjects. If such a background of random gravitational fields and waves is considered as hidden variables. It is shown that the classic physical of Bells observable in the 4-dimensions Rieman's space gives the value matching the experimental data. The nature of the entanglement states we are study here.

DOI
10.48550/arxiv.quant-ph/0109153

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It is shown that the nature of quantum statistics can study in assumption of existence of a background of random gravitational fields and waves, distributed isotropically in the space. This background is capable of correlating phases of oscillations of identical microobjects. If such a background of random gravitational fields and waves is considered as hidden variables. It is shown that the classic physical of Bells observable in the 4-dimensions Rieman's space gives the value matching the experimental data. The nature of the entanglement states we are study here.
It is shown that the nature of quantum statistics can be clarified by assuming the existence of a background of random gravitational fields and waves, distributed isotropically in the space. This background is responsible for correlating phases of oscillations of identical microobjects. If such a background of random gravitational fields and waves is considered as hidden variables then taking it into account leads to the Bell-type inequalities that are fairly consistent with the experimental data.
Discussed in the study are gravitational noise and the nature of entanglement states. Their role in forming of entangled states. Nonlocal nature of entangled states can be brought about by Polarization Variables. Polarization Variables consists of sum a background of random classical gravitational fields and waves, random electromagnets fields and so on known or unknown, distributed average isotropically in the space. This background is capable of correlating phases the oscillations of microobjects. From this follow, that entanglement polarizations states is the functions of Polarization Variables in Vacuum.
Abstract It is shown that the Bell inequalities are closely related to the triangle inequalities involving distance functions amongst pairs of random variables with values { 0 , 1 } . A hidden variables model may be defined as a mapping between a set of quantum projection operators and a set of random variables. The model is noncontextual if there is a joint probability distribution. The Bell inequalities are necessary conditions for its existence. The inequalities are most relevant when measurements are performed at space-like separation, thus showing a conflict between quantum mechanics and local realism (Bell's theorem). The relations of the Bell inequalities with contextuality, the Kochen–Specker theorem, and quantum entanglement are briefly discussed.
Bell derived the given inequalities on the basis of one rather forceful assumption that was supposed to hold in the hidden variable theory. However, this assumption has been so strong that it has corresponded only to the classical physics; any dependence on spin orientations of individual objects (i.e., on quantum characteristics) having been practically excluded. And consequently, the hidden-variable theory has not been refused by corresponding experimental data. On the other side, Einstein's criticism of Copenhagen quantum mechanics based on ontological approach refusing nonlocality has been entitled as a much higher limit value corresponds to Bell's probability combination in such a case. And there is not any reason to believe in direct interaction between matter objects at greater distances as shown recently also by K. Hess on the basis of another approach.
INTRODUCTION Fine (1982) proved that Bell's (1964) inequalities are sufficient, as well as necessary, to guarantee the existence of a joint probability distribution of the random variables in question, e.g., those representing certain spin correlation experiments. Garg and Mermin (1982) gave an example of eight random variables satisfying Bell's inequalities but such that no joint distribution exists. The purpose of this paper is to extend Bell's inequalities to obtain some general necessary conditions for the existence of a joint probability distribution for any finite collection of Bell-type random variables. Our results show that, for N > 4, many new elementary inequalities beyond those of Bell must be satisfied by any hidden-variable theory. Since these additional inequalities are violated by quantum mechanical predictions for appropriate choice of measurement arrangements, they serve to increase the conceptual distance between what may be called Einstein locality, after the EPR paradox, and quantum mechanics. To give a concrete sense of the nature of our results, we exhibit one of the new inequalities violated by Garg and Mermin's example. For theoretical purposes it will suffice to introduce Bell-type random variables X 1 ,…, X N , N ≥ 4, having possible values ±1, with means E ( X i ) = 0 and with what we term Bell covariances E ( X i X j ) relative to the index i 0 , with 1 ≤ i ≤ i 0 , N , 2 ≤ i 0 N – 2. Notice that, when N = 4, we must, as is familiar, have i 0 = 2.
The Bell theorem and inequality were derived as consequences of seemingly reasonable physical and statistical hypotheses. Bell’s assumptions were used to deduce cross-correlations of three spin measurements on two entangled particles neglecting non-commutation. The assumed correlation functions, later confirmed for certain quantum measurements, violate the Bell inequality. The present paper reviews a more general derivation of the Bell inequality showing that it is identically satisfied by finite data sets whether deterministic or random, after assuming merely that they exist. It is thereafter concerned with the consequences of this result for interpretations of the inequality that result in its violation. A primary finding is that correlation functions have differing forms due to quantum commutation, non-commutation, and conditions of measurement, and result in satisfaction of the Bell inequality used consistently with its derivation. A stochastic process having the same correlation function for all variable pairs is shown to be inconsistent with experimentally reported data. The logic of the three and four variable inequalities is shown to be similar. Finally the inequalities in probabilities are shown to follow from those in correlations with quantum mechanical results satisfying either when properly implemented.