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/0506165

The certainty principle

D. A. Arbatsky

Published Jun 20, 2005• 3 citations
arXivHTMLPDF

Abstract

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.)

DOI
10.48550/arxiv.quant-ph/0506165

Related papers

Quantum certainty mechanics

Muhammad Yasin

Quantum certainty mechanics is a theory for measuring the position and momentum of a particle. Mathematically proven certainty principle from uncertainty principle, which is basically one of the most important formulas of quantum certainty mechanics theory. The principle of uncertainty can be proved by the principle of certainty and why uncertainty comes can also be proved. The principle of certainty can be proved from the theory of relativity And in the uncertainty principle equation, the principle of certainty can be proved by fulfilling the conditions of the principle of certainty by multiplying the uncertain constant with the certain values of momentum-position and energy-time. The principle of certainty proves that the calculation of θ π/2 between the particle and the wave involved in the particle leads to uncertainty. But calculating with θ=0 does not bring uncertainty. Quantum certainty mechanics has been established by combining Newtonian mechanics, relativity theory and quantum mechanics. Quantum entanglement can be explained by protecting the principle of conservation of energy.

International Journal of Sciences: Basic and Applied Research•Jan 10, 2021•0 citations

Quantum certainty mechanics

Muhammad Yasin

Quantum certainty mechanics is a theory for measuring the position and momentum of a particle. Mathematically proven certainty principle from uncertainty principle, which is basically one of the most important formulas of quantum certainty mechanics theory. The principle of uncertainty can be proved by the principle of certainty and why uncertainty comes can also be proved. The principle of certainty can be proved from the theory of relativity and in the uncertainty principle equation, the principle of certainty can be proved by fulfilling the conditions of the principle of uncertainty by multiplying the uncertain constant with the certain values of momentum-position and energy-time. The principle of certainty proves that the calculation of θ ≥π/2 between the particle and the wave involved in the particle leads to uncertainty. But calculating with θ=0 does not bring uncertainty. Again, if the total energy E of the particle is measured accurately in the laboratory, the momentum and position can be measured with certainty. Quantum certainty mechanics has been established by combining Newtonian mechanics, relativity theory and quantum mechanics. Quantum entanglement can be explained by protecting the conservation law of energy.

International Journal of Sciences: Basic and Applied Research•Jan 7, 2021•3 citations

The Logic of Quantum Mechanics

Garrett Birkhoff, John von Neumann

One of the aspects of quantum theory which has attracted the most general attention, is the novelty of the logical notions which it presupposes. It asserts that even a complete mathematical description of a physical system S does not in general enable one to predict with certainty the result of an experiment on S, and that in particular one can never predict with certainty both the position and the momentum of S, (Heisenberg’s Uncertainty Principle). It further asserts that most pairs of observations are incompatible, and cannot be made on S, simultaneously (Principle of Non-commutativity of Observations).

Annals of Mathematics•Oct 1, 1936•2,849 citations

Uncertainty principle for angular position and angular momentum

Sonja Franke‐Arnold, Stephen Mark Barnett, Eric Yao +3 more

The uncertainty principle places fundamental limits on the accuracy with which we are able to measure the values of different physical quantities (Heisenberg 1949 The Physical Principles of the Quantum Theory (New York: Dover); Robertson 1929 Phys. Rev. 34 127). This has profound effects not only on the microscopic but also on the macroscopic level of physical systems. The most familiar form of the uncertainty principle relates the uncertainties in position and linear momentum. Other manifestations include those relating uncertainty in energy to uncertainty in time duration, phase of an electromagnetic field to photon number and angular position to angular momentum (Vaccaro and Pegg 1990 J. Mod. Opt. 37 17; Barnett and Pegg 1990 Phys. Rev. A 41 3427). In this paper, we report the first observation of the last of these uncertainty relations and derive the associated states that satisfy the equality in the uncertainty relation. We confirm the form of these states by detailed measurement of the angular momentum of a light beam after passage through an appropriate angular aperture. The angular uncertainty principle applies to all physical systems and is particularly important for systems with cylindrical symmetry.

New Journal of Physics•Aug 9, 2004•265 citations

Incertidumbre de Heisenberg: en la significación críticas e ontológica

Ramiro Délio Borges de Meneses

Heisenberg's uncertainty principle, which he announced in 1927, grow out of his attempts to explain some of the quantum mechanics peculiarities. This principle holds that it is impossible to determine simultaneously, with any certainty, the position, and the particle's momentum, the more accurately the investigator determines one, the less accurate by he can know the other, according to the metric expression: Δx·Δp x ≥ h. On this article I aim the philosophical certainty of Quantum Mechanics, because one effect of Heisenberg's research was to transform some physical laws into probability's statements.

Filosofia oggi•Jan 1, 2010•0 citations

Quantum Mechanics

Hitoshi Kitada

I consider in this book a formulation of Quantum Mechanics. Usually QM is formulated based on the notion of time and space, both of which are thought a priori given quantities or notions. However, when we try to define the notion of velocity or momentum, we encounter a difficulty as we will see in chapter 1. The problem is that if the notion of time is given a priori, the velocity is definitely determined when given a position, which contradicts the uncertainty principle of Heisenberg. We then set the basis of QM on the notion of position and momentum operators as in chapter 2. Time of a local system then is defined approximately as a ratio $|x|/|v|$ between the space coordinate $x$ and the velocity $v$. In this formulation of QM, we can keep the uncertainty principle, and time is a quantity that does not have precise values unlike the usually supposed notion of time has. The feature of local time is that it is a time proper to each local system, which is defined as a finite set of quantum mechanical particles. We now have an infinite number of local times that are unique and proper to each local system. Based on the notion of local time, the motion inside a local system is described by the usual Schrodinger equation. We investigate such motion in a given local system in part II. This is a usual quantum mechanics. After some excursion of the investigation of local motion, we consider in part III the relative relation or motion between plural local systems. In the final part IV, we will prove that there is at least one Universe wave function $\phi$ in which all local systems have local motions and thus local times. This concludes our formulation of Quantum Mechanics.

•Oct 8, 2004•2 citations
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.)
Quantum certainty mechanics is a theory for measuring the position and momentum of a particle. Mathematically proven certainty principle from uncertainty principle, which is basically one of the most important formulas of quantum certainty mechanics theory. The principle of uncertainty can be proved by the principle of certainty and why uncertainty comes can also be proved. The principle of certainty can be proved from the theory of relativity And in the uncertainty principle equation, the principle of certainty can be proved by fulfilling the conditions of the principle of certainty by multiplying the uncertain constant with the certain values of momentum-position and energy-time. The principle of certainty proves that the calculation of θ π/2 between the particle and the wave involved in the particle leads to uncertainty. But calculating with θ=0 does not bring uncertainty. Quantum certainty mechanics has been established by combining Newtonian mechanics, relativity theory and quantum mechanics. Quantum entanglement can be explained by protecting the principle of conservation of energy.
Quantum certainty mechanics is a theory for measuring the position and momentum of a particle. Mathematically proven certainty principle from uncertainty principle, which is basically one of the most important formulas of quantum certainty mechanics theory. The principle of uncertainty can be proved by the principle of certainty and why uncertainty comes can also be proved. The principle of certainty can be proved from the theory of relativity and in the uncertainty principle equation, the principle of certainty can be proved by fulfilling the conditions of the principle of uncertainty by multiplying the uncertain constant with the certain values of momentum-position and energy-time. The principle of certainty proves that the calculation of θ ≥π/2 between the particle and the wave involved in the particle leads to uncertainty. But calculating with θ=0 does not bring uncertainty. Again, if the total energy E of the particle is measured accurately in the laboratory, the momentum and position can be measured with certainty. Quantum certainty mechanics has been established by combining Newtonian mechanics, relativity theory and quantum mechanics. Quantum entanglement can be explained by protecting the conservation law of energy.
One of the aspects of quantum theory which has attracted the most general attention, is the novelty of the logical notions which it presupposes. It asserts that even a complete mathematical description of a physical system S does not in general enable one to predict with certainty the result of an experiment on S, and that in particular one can never predict with certainty both the position and the momentum of S, (Heisenberg’s Uncertainty Principle). It further asserts that most pairs of observations are incompatible, and cannot be made on S, simultaneously (Principle of Non-commutativity of Observations).
The uncertainty principle places fundamental limits on the accuracy with which we are able to measure the values of different physical quantities (Heisenberg 1949 The Physical Principles of the Quantum Theory (New York: Dover); Robertson 1929 Phys. Rev. 34 127). This has profound effects not only on the microscopic but also on the macroscopic level of physical systems. The most familiar form of the uncertainty principle relates the uncertainties in position and linear momentum. Other manifestations include those relating uncertainty in energy to uncertainty in time duration, phase of an electromagnetic field to photon number and angular position to angular momentum (Vaccaro and Pegg 1990 J. Mod. Opt. 37 17; Barnett and Pegg 1990 Phys. Rev. A 41 3427). In this paper, we report the first observation of the last of these uncertainty relations and derive the associated states that satisfy the equality in the uncertainty relation. We confirm the form of these states by detailed measurement of the angular momentum of a light beam after passage through an appropriate angular aperture. The angular uncertainty principle applies to all physical systems and is particularly important for systems with cylindrical symmetry.
Heisenberg's uncertainty principle, which he announced in 1927, grow out of his attempts to explain some of the quantum mechanics peculiarities. This principle holds that it is impossible to determine simultaneously, with any certainty, the position, and the particle's momentum, the more accurately the investigator determines one, the less accurate by he can know the other, according to the metric expression: Δx·Δp x ≥ h. On this article I aim the philosophical certainty of Quantum Mechanics, because one effect of Heisenberg's research was to transform some physical laws into probability's statements.
I consider in this book a formulation of Quantum Mechanics. Usually QM is formulated based on the notion of time and space, both of which are thought a priori given quantities or notions. However, when we try to define the notion of velocity or momentum, we encounter a difficulty as we will see in chapter 1. The problem is that if the notion of time is given a priori, the velocity is definitely determined when given a position, which contradicts the uncertainty principle of Heisenberg. We then set the basis of QM on the notion of position and momentum operators as in chapter 2. Time of a local system then is defined approximately as a ratio ∣x∣/∣v∣|x|/|v|∣x∣/∣v∣ between the space coordinate xxx and the velocity vvv. In this formulation of QM, we can keep the uncertainty principle, and time is a quantity that does not have precise values unlike the usually supposed notion of time has. The feature of local time is that it is a time proper to each local system, which is defined as a finite set of quantum mechanical particles. We now have an infinite number of local times that are unique and proper to each local system. Based on the notion of local time, the motion inside a local system is described by the usual Schrodinger equation. We investigate such motion in a given local system in part II. This is a usual quantum mechanics. After some excursion of the investigation of local motion, we consider in part III the relative relation or motion between plural local systems. In the final part IV, we will prove that there is at least one Universe wave function ϕ\phiϕ in which all local systems have local motions and thus local times. This concludes our formulation of Quantum Mechanics.