Foundations of Quantum Mechanics

A special issue of Universe (ISSN 2218-1997). This special issue belongs to the section "Foundations of Quantum Mechanics and Quantum Gravity".

Deadline for manuscript submissions: closed (30 April 2021) | Viewed by 8438

Special Issue Editor

St. Petersburg B. P. Konstantinov Nuclear Physics Institute, NRC Kurchatov Institute, Leningrad District, Gatchina 188300, Russia
Interests: quantum mechanics; superfluidity; Bose-Einstein condensate; quantum ether; quaternion algebra of physical fields; edge of chaos; neurodynamics; consciousness
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Special Issue Information

Dear Colleagues,

Just over 100 years have passed since Max Planck proposed a formula that correctly describes the process of black body radiation. The essence of the formula is that it clearly shows that the radiation occurs by quantum portions. The year 1900 is that of the formulation of the quantum hypothesis proclaiming that the energy states of a physical system can be discrete. Since then, a whole galaxy of scientists has made a significant contribution to the development of quantum mechanics, the success of which was confirmed at a series of Solvay congresses.

It would seem that the triumph of quantum mechanics is impeccable—its results are incredibly prolific. However, some dark spots still remain. For that reason, the Nobel laureate Richard Feynman once said that no one really understands quantum mechanics. Now, it seems that physicists have come to terms with the fact that the most important theory remains a mystery.

The unexpected turn in understanding quantum mechanics came from a direction which no one expected. It is the amazing article of Couder and Fort, entitled "Single-Particle Diffraction and Interference at a Macroscopic Scale", from 2006. It describes an oil droplet moving along silicon oil that is subjected to shaking of frequencies and amplitudes slightly below the supercritical bifurcation, leading to the emergence of Faraday waves. Surprisingly, the droplet bouncing in the beat with the frequency of the Faraday waves moves through a two-slit obstacle, similar to a quantum particle controlled by a guiding wave passing through the two-slit grating. This work provided a new perspective on da Broglie's double solution theory.

We invite academia and industry researchers to submit original and unpublished manuscripts to this Special Issue that develops research works related to this topic.

The goal of the Special Issue is to publish the most recent research results with foundations in quantum mechanics:

  • Interpretations of quantum mechanics, their commonality and differences;
  • Nonequilibrium thermodynamics as a basic of quantum mechanics;
  • Hydrodynamical analogues of quantum phenomena;
  • Nonrelativistic limit, Schrodinger equation;
  • Relativistic limit, Dirac equation;
  • Bohmian quantum mechanics;
  • Principle of nonlocality and Bell theorem;
  • Superconductivity and superfluidity;

Dr. Valeriy Sbitnev
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Universe is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Nonequilibrium thermodynamics
  • Schrodinger equation
  • Havier–Stokes equation
  • Bohmian mechanics
  • quantum nonlocality
  • quantum potential
  • wavefunction
  • vortex

Published Papers (3 papers)

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15 pages, 765 KiB  
Article
On the Stochastic Mechanics Foundation of Quantum Mechanics
by Michael Beyer and Wolfgang Paul
Universe 2021, 7(6), 166; https://0-doi-org.brum.beds.ac.uk/10.3390/universe7060166 - 27 May 2021
Cited by 6 | Viewed by 2884
Abstract
Among the famous formulations of quantum mechanics, the stochastic picture developed since the middle of the last century remains one of the less known ones. It is possible to describe quantum mechanical systems with kinetic equations of motion in configuration space based on [...] Read more.
Among the famous formulations of quantum mechanics, the stochastic picture developed since the middle of the last century remains one of the less known ones. It is possible to describe quantum mechanical systems with kinetic equations of motion in configuration space based on conservative diffusion processes. This leads to the representation of physical observables through stochastic processes instead of self-adjoint operators. The mathematical foundations of this approach were laid by Edward Nelson in 1966. It allows a different perspective on quantum phenomena without necessarily using the wave-function. This article recaps the development of stochastic mechanics with a focus on variational and extremal principles. Furthermore, based on recent developments of optimal control theory, the derivation of generalized canonical equations of motion for quantum systems within the stochastic picture are discussed. These so-called quantum Hamilton equations add another layer to the different formalisms from classical mechanics that find their counterpart in quantum mechanics. Full article
(This article belongs to the Special Issue Foundations of Quantum Mechanics)
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6 pages, 694 KiB  
Article
Testing Quantum Mechanics with an Ultra-Cold Particle Trap
by Peter J. Riggs
Universe 2021, 7(4), 77; https://0-doi-org.brum.beds.ac.uk/10.3390/universe7040077 - 24 Mar 2021
Viewed by 1777
Abstract
It is possible to empirically discriminate between the predictions of orthodox (i.e., Copenhagen) quantum theory and the de Broglie−Bohm theory of quantum mechanics. A practical experiment is proposed in which a single, laser-cooled ion inside an ultra-cold particle trap is either found to [...] Read more.
It is possible to empirically discriminate between the predictions of orthodox (i.e., Copenhagen) quantum theory and the de Broglie−Bohm theory of quantum mechanics. A practical experiment is proposed in which a single, laser-cooled ion inside an ultra-cold particle trap is either found to be near the trap’s walls or not. Detections of the former kind would support the prediction of orthodox quantum theory and of the latter kind would support the de Broglie−Bohm theory. The outcome of this experiment would show which theory gives the more correct description and, consequently, would have far-reaching implications for our understanding of quantum mechanics. Full article
(This article belongs to the Special Issue Foundations of Quantum Mechanics)
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40 pages, 1715 KiB  
Article
Quaternion Algebra on 4D Superfluid Quantum Space-Time: Can Dark Matter Be a Manifestation of the Superfluid Ether?
by Valeriy Sbitnev
Universe 2021, 7(2), 32; https://0-doi-org.brum.beds.ac.uk/10.3390/universe7020032 - 31 Jan 2021
Cited by 4 | Viewed by 3046
Abstract
Quaternions are a natural framework of 4D space-time, where the unit element relates to time, and three others relate to 3D space. We define a quaternion set of differential torsion operators (shifts with rotations) that act to the energy-momentum tensor written on the [...] Read more.
Quaternions are a natural framework of 4D space-time, where the unit element relates to time, and three others relate to 3D space. We define a quaternion set of differential torsion operators (shifts with rotations) that act to the energy-momentum tensor written on the same quaternion basis. It results in the equations of gravity-torsion (gravitomagnetic) fields that are similar to Maxwell’s equations. These equations are parent equations, generating the following equations: (a) equations of the transverse gravity-torsion waves; (b) the vorticity equation describing vortices orbital speed of which grows monotonically in the vortex core but far from it, it goes to a permanent level; (c) the modified Navier–Stokes equation leading to the Schrödinger equation in the nonrelativistic limit and to the Dirac equation in the relativistic limit. The Ginsburg–Landau theory of superfluidity resulting from the Schrödinger equation shows the emergence of coupled proton-antiproton pairs forming the Bose–Einstein condensate. In the final part of the article, we describe Samokhvalov’s experiment with rotating nonelectric, nonferromagnetic massive disks in a vacuum. It demonstrates an unknown force transferring the rotational moment from the driving disk to a driven one. It can be a manifestation of the dark matter. For studying this phenomenon, we propose a neutron interference experiment that is like the Aharonov–Bohm one. Full article
(This article belongs to the Special Issue Foundations of Quantum Mechanics)
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