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Universal Journal of Physics and Application

Contradiction of the DENSITY MATRIX Notion in Quantum Mechanics

V. K. Ignatovich

Published Sep 1, 2013• 2 citations
Publisher

Abstract

It is shown for the first time that description of an unpolarized neutron beam by density matrix can be contradictory. Density matrix is invariant with respect to choice of a quantization axis, while experimental devices can discriminate between different quantization axes. An experiment is proposed to discriminate a direction of a quantization axis of a specially prepared nonpolarized beam. The discrimination can be seen by observation of oscillations in statistical uncertainties. The success of the experiment will mean that an entanglement, following from the EPR paradox permits communication with a superluminal speed. A criticism of the EPR paradox and of some experiments on proof of Bell’s inequalities violation is presented.

DOI
10.13189/ujpa.2013.010218

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It is shown for the first time that description of an unpolarized neutron beam by density matrix can be contradictory. Density matrix is invariant with respect to choice of a quantization axis, while experimental devices can discriminate between different quantization axes. An experiment is proposed to discriminate a direction of a quantization axis of a specially prepared nonpolarized beam. The discrimination can be seen by observation of oscillations in statistical uncertainties. The success of the experiment will mean that an entanglement, following from the EPR paradox permits communication with a superluminal speed. A criticism of the EPR paradox and of some experiments on proof of Bell’s inequalities violation is presented.
This article shows that the there is no paradox. Violation of Bell's inequalities should not be identified with a proof of non locality in quantum mechanics. A number of past experiments is reviewed, and it is concluded that the experimental results should be re-evaluated. The results of the experiments with atomic cascade are shown not to contradict the local realism. The article points out flaws in the experiments with down-converted photons. The experiments with neutron interferometer on measuring the "contextuality" and Bell-like inequalities are analyzed, and it is shown that the experimental results can be explained without such notions. Alternative experiment is proposed to prove the validity of local realism.
We show that paradoxical consequences of violations of Bell's inequality are induced by the use of an unsuitable probabilistic description for the EPR-Bohm-Bell experiment. The conventional description (due to Bell) is based on a combination of statistical data collected for different settings of polarization beam splitters (PBSs). In fact, such data consists of some conditional probabilities which only partially define a probability space. Ignoring this conditioning leads to apparent contradictions in the classical probabilistic model (due to Kolmogorov). We show how to make a completely consistent probabilistic model by taking into account the probabilities of selecting the settings of the PBSs. Our model matches both the experimental data and is consistent with classical probability theory.
EPR paper contains an error. Its correction leads to a conclusion that position and momentum of a particle can be defined precisely simultaneously, EPR paradox does not exist and uncertainty relations have nothing to do with quantum mechanics. Logic of the EPR paper shows that entangled states of separated particles do not exist and therefore there are no nonlocality in quantum mechanics. Bell's inequalities are never violated, and results of experiments, proving their violation, are shown to be false. Experiments to prove absence of nonlocality are proposed where Bell's inequalities are replaced by precise prediction. Interpretation of quantum mechanics in terms of classical field theory is suggested. Censorship against this paper is demonstrated.
The EPR paradox is known as an interpretive problem, as well as a technical discovery in quantum mechanics. It defined the basic features of two-quantum entanglement, as needed to study the relationships between two non-commuting variables. In contrast, four variables are observed in a typical Bell experiment. This is no longer the same problem. The full complexity of this process can only be captured by the analysis of four-quantum entanglement. Indeed, a new paradox emerges in this context, with straightforward consequences. Quantum mechanics cannot violate CHSH-type inequalities, in the same sense in which local realism cannot do it. The solution is to assume that quantum correlations do not work at the level of full populations, when violations occur, but only apply to incompatible slices of input beams.
In spite of the fact that statistical predictions of quantum theory (QT) can only be tested if large amount of data is available a claim has been made that QT provides the most complete description of an individual physical system. Einstein’s opposition to this claim and the paradox he presented in the article written together with Podolsky and Rosen in 1935 inspired generations of physicists in their quest for better understanding of QT. Seventy years after EPR article it is clear that without deep understanding of the character and limitations of QT one may not hope to find a meaningful unified theory of all physical interactions, manipulate qubits or construct a quantum computer.. In this paper we present shortly the EPR paper, the discussion, which followed it and Bell inequalities (BI). To avoid various paradoxes we advocate purely statistical contextual interpretation (PSC) of QT. According to PSC a state vector is not an attribute of a single electron, photon, trapped ion or quantum dot. A value of an observable assigned to a physical system has only a meaning in a context of a particular physical experiment PSC does not provide any mental space‐time picture of sub phenomena. The EPR paradox is avoided because the reduction of the state vector in the measurement process is a passage from a description of the whole ensemble of the experimental results to a particular sub‐ensemble of these results. We show that the violation of BI is neither a proof of the completeness of QT nor of its non‐locality. Therefore we rephrase the EPR question and ask whether QT is “predictably “complete or in other words does it provide the complete description of experimental data. To test the “predictable completeness” it is not necessary to perform additional experiments it is sufficient to analyze more in detail the existing experimental data by using various non‐parametric purity tests and other specific statistical tools invented to study the fine structure the time‐series.