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Physics of Atomic Nuclei

Hidden Variables in Angular Correlations of Fission Products

F. F. Karpeshin

Published Dec 1, 2022• 0 citations
Publisher

Abstract

A comparative analysis of experiments devoted to studying, in the fission process, ( $$n,f$$ ) angular correlations, on one hand, and ( $$n,n$$ ) and ( $$n,nf$$ ) angular correlations, on the other hand, is performed on the basis of the model proposed earlier for describing muon conversion in fragments originating from the prompt fission of $${}^{238}$$ U nuclei that is induced by negatively charged muons. It is shown that each of these experiments may provide information that does not depend on the results of the other experiments and which is complementary to them. Historically, the situation resembles the Einstein–Podolsky–Rosen (EPR) paradox. An experimental verification of the theoretical relation between the alignment and polarization of fragment spins in the CORA experiment is of crucial importance.

DOI
10.1134/s1063778823010258

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A comparative analysis of experiments devoted to studying, in the fission process, ( n,fn,fn,f ) angular correlations, on one hand, and ( n,nn,nn,n ) and ( n,nfn,nfn,nf ) angular correlations, on the other hand, is performed on the basis of the model proposed earlier for describing muon conversion in fragments originating from the prompt fission of 238{}^{238}238 U nuclei that is induced by negatively charged muons. It is shown that each of these experiments may provide information that does not depend on the results of the other experiments and which is complementary to them. Historically, the situation resembles the Einstein–Podolsky–Rosen (EPR) paradox. An experimental verification of the theoretical relation between the alignment and polarization of fragment spins in the CORA experiment is of crucial importance.
A comparative analysis of experiments on studying the (n, f), on one hand, and (n, n), on the other hand, angular correlations in fission is carried out, based on the model proposed by muonic conversion in fragments of prompt fission of 238U with negative muons. Their fundamental difference is shown in the sense of the information that can be inferred from them. Historically, the situation resembles the EPR paradox. An experimental check of the empirical relation between the alignment and polarization parameters, the former is twice as small as the latter one.
The orbital angular momentum [OAM] of light and its applications in quantum telecommunication and cryptography has recently attracted scientific attention. In this context also entanglement and the implications of the Einstein‐Podolsky‐Rosen [EPR] experiment have experienced a renewed interest. In an attempt to find an experimentally feasible criterion for the demonstration of an EPR paradox for the conjugate variables of OAM and the azimuthal position, we study quantum correlations in these variables of down converted photons. We include a model for the uncertainties inherent to the measurement and discuss the effects of these uncertainties on the proposed criterion.
The EPR-Bohm experiment is studied in a classical model with hidden variables. The main hypothesis of Bell about this experiment must be modified in a non-trivial way to allow for the fact that our model is non-linear and so non fully deterministic. With our classical model, we then arrive at the same angular behaviour than the one that is predicted by Quantum Mechanics for the correlated measurement of spin projections on the polarizer axis. If the spin-spin interaction predicted by our particle model, or more precisely in the present case, the spin-polarizer field axis interaction, is not able to align the spin axis with the polarizer axis, then our classical result differs by a factor 3 from the quantum mechanical result. It is surprising to find that the angular behaviour is easier to reproduce by a classical model than the amount of probability. Naively, one would have expected the reverse.
Bohm's spin polarization modification of the paradox of Einstein, Podolsky, and Rosen has served as the basis for numerous analyses of the roles of hidden variables and Einstein locality in quantum mechanics. The present note points out how corresponding analyses can be carried out on the original formulation of Einstein, Podolsky, and Rosen (EPR) in terms of observations of position and momentum. Concrete conceptual experiments are proposed to furnish tangible illustrations of EPR tests of reality, and a position-momentum variant of Bell's inequality is formulated. Implications regarding joint measurements of position and momentum, delayed choice experiments, and superluminal communication are discussed briefly.
The generation of angular momentum (intrinsic spin) in fission fragments has recently attracted renewed attention. While several microscopic approaches reproduce the spin distribution qualitatively using projection techniques, the physical origin of the fragments' angular momentum in density functional theory remains unclear. In this work, we investigate the mechanisms responsible for the spin distribution of fission fragments within a microscopic TDDFT framework. We compare spin distributions obtained from projection operators with those predicted by a simple expression derived from the uncertainty relation between angle and angular momentum, where angular fluctuations are estimated using a Monte Carlo sampling of nucleon positions. We find that a large portion of the spin distribution obtained from projection methods can be explained by the uncertainty principle. Our results thus show that, within microscopic approaches, the spin of fission fragments originates primarily from quantum uncertainty associated with their orientation angle with respect to the fission axis, mainly due to quadrupole deformation and, to a lesser extent, octupole deformation.
Abstract Einstein's severe critique of quantum mechanics took its ultimate form in the so‐called Einstein Podolsky Rosen (EPR) paradox. The latter remained a subject of mere dispute, until a remarkable progress was initiated in 1964 by Bell who showed that quantum mechanical correlations specific for an EPR type experiment cannot be reproduced in any local hidden—variables theory. Afterwards, realistic versions of EPR experiments have been conceived and, in fact, carried out. The objective of the present paper is to give a review of this recent exciting development, both theoretical and experimental, which reveals one of the most striking features of quantum theory, the “quantum interconnectedness of distant systems”.