{"title":"Wiener Interpretation of Quantum Mechanics, the Skyrme–Faddeev Chiral Model, and Neutrino Oscillations","authors":"Yu. P. Rybakov","doi":"10.1134/S0202289325700318","DOIUrl":null,"url":null,"abstract":"<p>We consider the essence of the well-known discussion between Bohr and Einstein (1935), which concerned the completeness of quantum mechanics. If one followed Bohr, then the wave function would give the probability description of an individual particle. However, Einstein considered the wave function as an instrument for describing the statistical ensemble of identical particles—solitons. On the other hand, Wiener found the special <span>\\(\\alpha\\)</span>-representation of quantum mechanics, for which the wave function appeared to be an element of the random Hilbert space with normal dispersion. This fact proves the equivalence of Bohr’s and Einstein’s positions, the central limiting theorem being taken into account. Also the dark matter hypothesis and new possibilities of the Brioschi 16-spinor realization of the Skyrme–Faddeev chiral model are discussed, including the neutrino oscillation problem.</p>","PeriodicalId":583,"journal":{"name":"Gravitation and Cosmology","volume":"31 4","pages":"447 - 453"},"PeriodicalIF":2.1000,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Gravitation and Cosmology","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S0202289325700318","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the essence of the well-known discussion between Bohr and Einstein (1935), which concerned the completeness of quantum mechanics. If one followed Bohr, then the wave function would give the probability description of an individual particle. However, Einstein considered the wave function as an instrument for describing the statistical ensemble of identical particles—solitons. On the other hand, Wiener found the special \(\alpha\)-representation of quantum mechanics, for which the wave function appeared to be an element of the random Hilbert space with normal dispersion. This fact proves the equivalence of Bohr’s and Einstein’s positions, the central limiting theorem being taken into account. Also the dark matter hypothesis and new possibilities of the Brioschi 16-spinor realization of the Skyrme–Faddeev chiral model are discussed, including the neutrino oscillation problem.
期刊介绍：
Gravitation and Cosmology is a peer-reviewed periodical, dealing with the full range of topics of gravitational physics and relativistic cosmology and published under the auspices of the Russian Gravitation Society and Peoples’ Friendship University of Russia. The journal publishes research papers, review articles and brief communications on the following fields: theoretical (classical and quantum) gravitation; relativistic astrophysics and cosmology, exact solutions and modern mathematical methods in gravitation and cosmology, including Lie groups, geometry and topology; unification theories including gravitation; fundamental physical constants and their possible variations; fundamental gravity experiments on Earth and in space; related topics. It also publishes selected old papers which have not lost their topicality but were previously published only in Russian and were not available to the worldwide research community
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