Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0108071

Quantum mechanics and the continuum problem (with referee reports)

Yaremchuk, O.

Published Aug 15, 2001• 0 citations
arXivHTMLPDF

Abstract

It is shown that Feynman's formulation of quantum mechanics can be reproduced as a description of the set of intermediate cardinality. Properties of the set follow directly from the independence of the continuum hypothesis. Six referee reports of Physical Review Letters, Europhysics Letters, and Journal of Physics A are enclosed.
DOI
10.48550/arxiv.quant-ph/0108071

Related papers

Quantum phenomenology and the Continuum Problem

Yaremchuk, O.

A new approach to quantum mechanics based on independence of the Continuum Hypothesis is proposed. In one-dimensional case, it is shown that the properties of the set of intermediate cardinality coincide with quantum phenomenology.

arXiv:quant-ph/9902060•Feb 17, 1999•0 citations

Real continuum

Olga Yaremchuk

Some physical consequences of the negation of the continuum hypothesis are considered. It is shown that quantum and classical mechanics are component parts of the multicomponent description of the set of variable infinite cardinality. Existence and properties of the set follow directly from the independence of the continuum hypothesis. Particular emphasis is laid on set-theoretic aspect.

arXiv:quant-ph/0110024•Oct 4, 2001•0 citations

Quantum mechanics without interpretation

Yaremchuk, O.

It is shown that the independence of the continuum hypothesis points to the unique definite status of the set of intermediate cardinality: the intermediate set exists only as a subset of continuum. This latent status is a consequence of duality of the members of the set. Due to the structural inhomogeneity of the intermediate set, its complete description falls into several "sections" (theories) with their special main laws, dimensions, and directions, i.e., the complete description of the one-dimensional intermediate set is multidimensional. Quantum mechanics is one of these theories.

arXiv:quant-ph/0007075•Jul 20, 2000•0 citations

Quantum mechanics and the continuum problem(II)

Yaremchuk, O.

In one-dimensional case, it is shown that the basic principles of quantum mechanics are properties of the set of intermediate cardinality.

arXiv:quant-ph/0001097•Jan 27, 2000•0 citations

Resource Letter GPP-1: Geometric Phases in Physics

J. Anandan, Christian, J, Wanelik, K

This Resource Letter provides a guide to the literature on the geometric angles and phases in classical and quantum physics. Journal articles and books are cited for the following topics: anticipations of the geometric phase, foundational derivations and formulations, books and review articles on the subject, and theoretical and experimental elaborations and applications.

•Jan 1, 1997•67 citations

Quantum Mechanics

Sara McMurry, Alex Van Someren

From the Publisher: This book provides an introduction to the theoretical foundations of quantum mechanics for students of experimental physics. It is intended as an intermediate text for those who have already completed an introductory course in quantum physics.

•Nov 1, 1993•19 citations
It is shown that the independence of the continuum hypothesis points to the unique definite status of the set of intermediate cardinality: the intermediate set exists only as a subset of continuum. This latent status is a consequence of duality of the members of the set. Due to the structural inhomogeneity of the intermediate set, its complete description falls into several "sections" (theories) with their special main laws, dimensions, and directions, i.e., the complete description of the one-dimensional intermediate set is multidimensional. Quantum mechanics is one of these theories.