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/0608138

The certainty principle (review)

D. A. Arbatsky

Published Aug 17, 2006• 0 citations
arXivHTMLPDF

Abstract

The certainty principle (2005) allowed to conceptualize from the more fundamental grounds both the Heisenberg uncertainty principle (1927) and the Mandelshtam-Tamm relation (1945). In this review I give detailed explanation and discussion of the certainty principle, oriented to all physicists, both theorists and experimenters.
DOI
10.48550/arxiv.quant-ph/0608138

Related papers

The certainty principle II: Proof of the uncertainty principle

D. A. Arbatsky

A more detailed derivation of the Heisenberg uncertainty principle from the certainty principle is given.

arXiv:quant-ph/0603155•Mar 17, 2006•1 citation

More certainty about the uncertainty principle

Jan Hilgevoord, Jos Uffink

The uncertainty principle of position and momentum is a mathematically more involved relation than is usually realised. The well-known Heisenberg uncertainty relation between standard deviations is much too weak to express the uncertainty principle. By employing other notions of width, relations are given which do express the uncertainty principle.

European Journal of Physics•Jul 1, 1985•21 citations

A brief review on uncertainty principle and its variants

Manas Protim Saikia

In this paper, using two different formulations, we attempted to first provide an overview of mathematical interpretations of Heisenberg's uncertainty principle. This was done in order to emphasise the mathematical justification for the uncertainty principle's existence. First, we went over in detail the matrix formulation found in Schrodinger's original paper on uncertainty. Next, we reviewed the mathematical proof of the uncertainty principle in a Fourier series formulation and examined the results. We attempted to provide a comprehensive overview of the modified forms of the uncertainty relation in the Quantum Gravitational, Relativistic, and Entropic domains along with other variants after realizing that the most well-known uncertainty relation is not universal. All of these concepts also demonstrate a great deal of potential for use in the emerging new technologies. Our goal was to gather all of these dispersed variations of the uncertainty principle in one location. The current state of these theories, as well as their applications and limitations, are thoroughly discussed.

Journal of Advanced Education and Sciences•Jan 1, 2026•0 citations

Certezas e incertezas sobre as relações de Heisenberg (Certainties and uncertainties about the Heisenberg relations)

Silvio Seno Chibeni

Recebido em 4/10/2004; Aceito em 21/11/2004O objetivo deste artigo ´e apresentar e discutir as famosas rela¸c˜oes de Heisenberg, usualmente denominadasde “princ´ipio da incerteza”. A abordagem adotada ´e primordialmente conceitual, embora referˆencias hist´oricassejam feitas para auxiliar a exposi¸c˜ao. Distinguem-se trˆes interpreta¸c˜oes principais das rela¸c˜oes, cada umaderivando de bases inteiramente distintas e conduzindo a conseq¨uˆencias f´isicas e filos´oficas igualmente diferentes.Palavras-chave: rela¸c˜oes de Heisenberg, princ´ipio de incerteza, indetermina¸c˜ao quˆantica, Heisenberg, Bohr,Einstein, Popper.This article offers a conceptual analysis of the famous Heisenberg relations, usually referred to as “the un-certainty principle”. After a brief historical introduction, it is pointed out that the relations can be interpretedin three entirely different ways. It is shown in some detail how each interpretation derives from a distinct basis,and leads to distinct physical and philosophical consequences.Keywords: Heisenberg relations, uncertainty principle, quantum indeterminacy, Heisenberg, Bohr, Einstein,Popper.

•Jan 1, 2005•0 citations

The certainty principle

D. A. Arbatsky

The notion of the quantum angle is introduced. The quantum angle turns out to be a metric on the set of physical states of a quantum system. Its kinematics and dynamics is studied. The certainty principle for quantum systems is formulated and proved. It turns out that the certainty principle is closely connected with the Heisenberg uncertainty principle (it presents, in some sense, an opposite point of view). But at the same time the certainty principle allows to give rigorous formulations for wider class of problems (it allows to rigorously interpret and ground the analogous inequalities for the pairs of quantities like time - energy, angle - angular momentum etc.)

arXiv:quant-ph/0506165•Jun 20, 2005•3 citations

The Improvement of the Heisenberg Uncertainty Principle

L. M. Arévalo Aguilar, C. P. Garcia Quijas, Carlos Robledo-

One of the fundamental cornerstone of quantum mechanics is the Heisenberg uncertainty principle. This principle is so fundamental to quantum theory that it is believed that if a single phenomenon that could violate it is found then the whole building of quantum mechanics will fall apart. However, since the formulation of the uncertainty principle until today there is not clear and universal agreement in its formulation or interpretation. Even Heisenberg was not clear about the exact meaning of p1 and x1 in their first formulation of the uncertainty relations [1]:

InTech eBooks•Apr 3, 2013•1 citation
In this paper, using two different formulations, we attempted to first provide an overview of mathematical interpretations of Heisenberg's uncertainty principle. This was done in order to emphasise the mathematical justification for the uncertainty principle's existence. First, we went over in detail the matrix formulation found in Schrodinger's original paper on uncertainty. Next, we reviewed the mathematical proof of the uncertainty principle in a Fourier series formulation and examined the results. We attempted to provide a comprehensive overview of the modified forms of the uncertainty relation in the Quantum Gravitational, Relativistic, and Entropic domains along with other variants after realizing that the most well-known uncertainty relation is not universal. All of these concepts also demonstrate a great deal of potential for use in the emerging new technologies. Our goal was to gather all of these dispersed variations of the uncertainty principle in one location. The current state of these theories, as well as their applications and limitations, are thoroughly discussed.
Recebido em 4/10/2004; Aceito em 21/11/2004O objetivo deste artigo ´e apresentar e discutir as famosas rela¸c˜oes de Heisenberg, usualmente denominadasde “princ´ipio da incerteza”. A abordagem adotada ´e primordialmente conceitual, embora referˆencias hist´oricassejam feitas para auxiliar a exposi¸c˜ao. Distinguem-se trˆes interpreta¸c˜oes principais das rela¸c˜oes, cada umaderivando de bases inteiramente distintas e conduzindo a conseq¨uˆencias f´isicas e filos´oficas igualmente diferentes.Palavras-chave: rela¸c˜oes de Heisenberg, princ´ipio de incerteza, indetermina¸c˜ao quˆantica, Heisenberg, Bohr,Einstein, Popper.This article offers a conceptual analysis of the famous Heisenberg relations, usually referred to as “the un-certainty principle”. After a brief historical introduction, it is pointed out that the relations can be interpretedin three entirely different ways. It is shown in some detail how each interpretation derives from a distinct basis,and leads to distinct physical and philosophical consequences.Keywords: Heisenberg relations, uncertainty principle, quantum indeterminacy, Heisenberg, Bohr, Einstein,Popper.
The notion of the quantum angle is introduced. The quantum angle turns out to be a metric on the set of physical states of a quantum system. Its kinematics and dynamics is studied. The certainty principle for quantum systems is formulated and proved. It turns out that the certainty principle is closely connected with the Heisenberg uncertainty principle (it presents, in some sense, an opposite point of view). But at the same time the certainty principle allows to give rigorous formulations for wider class of problems (it allows to rigorously interpret and ground the analogous inequalities for the pairs of quantities like time - energy, angle - angular momentum etc.)
One of the fundamental cornerstone of quantum mechanics is the Heisenberg uncertainty principle. This principle is so fundamental to quantum theory that it is believed that if a single phenomenon that could violate it is found then the whole building of quantum mechanics will fall apart. However, since the formulation of the uncertainty principle until today there is not clear and universal agreement in its formulation or interpretation. Even Heisenberg was not clear about the exact meaning of p1 and x1 in their first formulation of the uncertainty relations [1]: