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

International Journal for Research in Applied Science and Engineering Technology

An analysis on Quantum mechanical Stability of Regular Polygons on a Point Base Using Heisenberg Uncertainty Principle

Anurag Chapagain

Published Oct 6, 2021• 0 citations
Publisher

Abstract

Abstract: It is a well-known fact in physics that classical mechanics describes the macro-world, and quantum mechanics describes the atomic and sub-atomic world. However, principles of quantum mechanics, such as Heisenberg’s Uncertainty Principle, can create visible real-life effects. One of the most commonly known of those effects is the stability problem, whereby a one-dimensional point base object in a gravity environment cannot remain stable beyond a time frame. This paper expands the stability question from 1- dimensional rod to 2-dimensional highly symmetrical structures, such as an even-sided polygon. Using principles of classical mechanics, and Heisenberg’s uncertainty principle, a stability equation is derived. The stability problem is discussed both quantitatively as well as qualitatively. Using the graphical analysis of the result, the relation between stability time and the number of sides of polygon is determined. In an environment with gravity forces only existing, it is determined that stability increases with the number of sides of a polygon. Using the equation to find results for circles, it was found that a circle has the highest degree of stability. These results and the numerical calculation can be utilized for architectural purposes and high-precision experiments. The result is also helpful for minimizing the perception that quantum mechanical effects have no visible effects other than in the atomic, and subatomic world. Keywords: Quantum mechanics, Heisenberg Uncertainty principle, degree of stability, polygon, the highest degree of stability

DOI
10.22214/ijraset.2021.38321

Related papers

A brief analysis of the physical significance of Heisenberg's uncertainty principle

Guannan Zhou

The principle of uncertainty is one of the essential principles of quantum mechanics as it outlines that there is a reflective limit to the measurement of microscopic particle motion. However it is impossible to measure at once and accurately both the position and momentum data of any microscopic particle no matter what means are used to do so. This paper starts by discussing the notion and mathematical derivation of the uncertainty principle as put forth by Heisenberg explaining the physical relevance of the principle. It introduces the natural uncertainty the principle introduces to the dynamics of particles in the microscopic world, and the significant part it plays in the theory of quantum mechanics. The article overviews the explanations of the principle on phenomena including atomic stability and scanning tunneling microscopes, and the interference of measurement actions on the states of particles and the shortcomings of measurement precision. According to the wave-particle duality of quantum mechanics, this article gives a required theoretical basis of microscopic phenomena. Likewise, the use of the research theory on the uncertainty principle by distinguished scholars in the physics fraternity helps the readers in achieving the knowledge in related subjects more easily.

Advances in Engineering Innovation•Apr 7, 2026•0 citations

Heisenberg's Uncertainty Principle from Gravity

Shibdas Roy

We propose that Heisenberg's uncertainty principle is a consequence of gravity. While quantum mechanics and gravity are widely considered incompatible, we show that Heisenberg's uncertainty principle, which is a central tenet in quantum mechanics, in fact, arises from non-diminishing finite gravity between a particle and another identical particle. We observe that it is impossible to know the position or momentum of the particle with unlimited precision, unless the gravity is infinite or zero, respectively, between the particles. We derive upper and lower bounds on the uncertainties in position and momentum of the particle, based on the uncertainty principle emerging from gravity. Accordingly, the quantum-classical boundary is identified, beyond which gravity behaves classically.

•Jan 30, 2024•2 citations

Snapshot And Story: On the Structural Origins of the Uncertainty Principle

Geoffrey Ejiga

Abstract The Heisenberg uncertainty principle is typically presented as a peculiarity of quantum mechanics — a strange constraint that emerges at subatomic scales and has no classical counterpart. This paper argues otherwise. Beginning with a simple observation — that determining an object's position requires freezing it in time, while determining its velocity requires watching it move, and that these are fundamentally incompatible acts of description — we trace a structural tension between what we call "point-properties" (like position) and "neighborhood-properties" (like velocity) from Zeno's Arrow Paradox through Bergson's philosophy of duration, through the active debate in contemporary philosophy of physics (Arntzenius, Butterfield, Lange), and into the mathematical architecture of mechanics itself. We show that this tension is formalized in the symplectic geometry shared by classical and quantum mechanics, where position and momentum live in mathematically dual spaces. Drawing on Hamilton's optico-mechanical analogy of 1831 — which Schrödinger cited in the opening sentence of his wave mechanics — we argue that classical mechanics is the short-wavelength limit of quantum mechanics, and that the two theories share the same structure at different scales of resolution. The Fourier conjugacy between position and momentum, from which the uncertainty principle follows as a mathematical theorem, was always latent in classical mechanics; quantum mechanics is what emerges when nature's finite Planck constant makes the wave nature of matter physically consequential. We introduce a three-regime framing: at ħ = 0, the wave nature vanishes and classical determinism holds; at ħ → ∞, all structure dissolves into total delocalization; at the actual finite value of ħ, neither the snapshot nor the story fully wins, producing the specific blend of determinacy and indeterminacy that characterizes our universe. An anthropic argument is offered: observers can only exist in the narrow band where ħ is large enough to permit quantum chemistry but small enough to permit stable structure. The tension between position and momentum is not a problem to be solved but a precondition for the existence of anything complex enough to notice it. The paper concludes that the uncertainty principle is not where physics gets strange but where it gets honest — where nature enforces a duality between complementary descriptions that was always present in the mathematical architecture of mechanics, from Zeno to Schrödinger.

•Apr 6, 2026•0 citations

Anti Heisenberg—Refutation Of Heisenberg’s Uncertainty Relation

Ilija Barukčić

The quantum mechanical uncertainty principle for position and momentum plays an important role in many treatments on the (philosophical, physical and other) implications of quantum mechanics. Roughly speaking, the more precisely the momentum (position) of a (quantum mechanical) object is given, the less precisely can one say what its position (momentum) is. This quantum mechanical measurement problem is not just an interpretational difficulty, it raises broader issues as well. The measurement (of a property) of a (quantum mechanical) object determines the existence of the measured. In brief, the quantum mechanical uncertainty principle challenges some fundamental principles of Science and especially the principle of causality. In particular, an independently existing (external) objective reality is denied. As we shall see, that the quantum mechanical uncertainty principle for position and momentum is based on the assumption that 1⩽0, which is a logical contradiction.

AIP conference proceedings•Jan 1, 2011•15 citations

Anti Heisenberg—Refutation Of Heisenberg’s Uncertainty Relation

Ilija Barukčić, Andrei Yu. Khrennikov, Gregg S. Jaeger +2 more

The quantum mechanical uncertainty principle for position and momentum plays an important role in many treatments on the (philosophical, physical and other) implications of quantum mechanics. Roughly speaking, the more precisely the momentum (position) of a (quantum mechanical) object is given, the less precisely can one say what its position (momentum) is. This quantum mechanical measurement problem is not just an interpretational difficulty, it raises broader issues as well. The measurement (of a property) of a (quantum mechanical) object determines the existence of the measured. In brief, the quantum mechanical uncertainty principle challenges some fundamental principles of Science and especially the principle of causality. In particular, an independently existing (external) objective reality is denied. As we shall see, that the quantum mechanical uncertainty principle for position and momentum is based on the assumption that 1⩽0, which is a logical contradiction.

AIP conference proceedings•Jan 1, 2011•0 citations

On the stability of the hydrogen atom

G.W. Sauer, W Kuhn

Reference to the solution of the Schrodinger equation does not give much physical insight into the problem of stability because it is far from obvious how the conclusion follows from the equation. The common arguments derived from the Heisenberg uncertainty principle are not sufficient to establish the existence of a stable ground state. The proof for a lower bound of the hydrogen hamiltonian may be recast into physical terms by introducing an effective localisation potential.

European Journal of Physics•Jul 1, 1982•1 citation
Abstract: It is a well-known fact in physics that classical mechanics describes the macro-world, and quantum mechanics describes the atomic and sub-atomic world. However, principles of quantum mechanics, such as Heisenberg’s Uncertainty Principle, can create visible real-life effects. One of the most commonly known of those effects is the stability problem, whereby a one-dimensional point base object in a gravity environment cannot remain stable beyond a time frame. This paper expands the stability question from 1- dimensional rod to 2-dimensional highly symmetrical structures, such as an even-sided polygon. Using principles of classical mechanics, and Heisenberg’s uncertainty principle, a stability equation is derived. The stability problem is discussed both quantitatively as well as qualitatively. Using the graphical analysis of the result, the relation between stability time and the number of sides of polygon is determined. In an environment with gravity forces only existing, it is determined that stability increases with the number of sides of a polygon. Using the equation to find results for circles, it was found that a circle has the highest degree of stability. These results and the numerical calculation can be utilized for architectural purposes and high-precision experiments. The result is also helpful for minimizing the perception that quantum mechanical effects have no visible effects other than in the atomic, and subatomic world. Keywords: Quantum mechanics, Heisenberg Uncertainty principle, degree of stability, polygon, the highest degree of stability
The principle of uncertainty is one of the essential principles of quantum mechanics as it outlines that there is a reflective limit to the measurement of microscopic particle motion. However it is impossible to measure at once and accurately both the position and momentum data of any microscopic particle no matter what means are used to do so. This paper starts by discussing the notion and mathematical derivation of the uncertainty principle as put forth by Heisenberg explaining the physical relevance of the principle. It introduces the natural uncertainty the principle introduces to the dynamics of particles in the microscopic world, and the significant part it plays in the theory of quantum mechanics. The article overviews the explanations of the principle on phenomena including atomic stability and scanning tunneling microscopes, and the interference of measurement actions on the states of particles and the shortcomings of measurement precision. According to the wave-particle duality of quantum mechanics, this article gives a required theoretical basis of microscopic phenomena. Likewise, the use of the research theory on the uncertainty principle by distinguished scholars in the physics fraternity helps the readers in achieving the knowledge in related subjects more easily.
We propose that Heisenberg's uncertainty principle is a consequence of gravity. While quantum mechanics and gravity are widely considered incompatible, we show that Heisenberg's uncertainty principle, which is a central tenet in quantum mechanics, in fact, arises from non-diminishing finite gravity between a particle and another identical particle. We observe that it is impossible to know the position or momentum of the particle with unlimited precision, unless the gravity is infinite or zero, respectively, between the particles. We derive upper and lower bounds on the uncertainties in position and momentum of the particle, based on the uncertainty principle emerging from gravity. Accordingly, the quantum-classical boundary is identified, beyond which gravity behaves classically.
Abstract The Heisenberg uncertainty principle is typically presented as a peculiarity of quantum mechanics — a strange constraint that emerges at subatomic scales and has no classical counterpart. This paper argues otherwise. Beginning with a simple observation — that determining an object's position requires freezing it in time, while determining its velocity requires watching it move, and that these are fundamentally incompatible acts of description — we trace a structural tension between what we call "point-properties" (like position) and "neighborhood-properties" (like velocity) from Zeno's Arrow Paradox through Bergson's philosophy of duration, through the active debate in contemporary philosophy of physics (Arntzenius, Butterfield, Lange), and into the mathematical architecture of mechanics itself. We show that this tension is formalized in the symplectic geometry shared by classical and quantum mechanics, where position and momentum live in mathematically dual spaces. Drawing on Hamilton's optico-mechanical analogy of 1831 — which Schrödinger cited in the opening sentence of his wave mechanics — we argue that classical mechanics is the short-wavelength limit of quantum mechanics, and that the two theories share the same structure at different scales of resolution. The Fourier conjugacy between position and momentum, from which the uncertainty principle follows as a mathematical theorem, was always latent in classical mechanics; quantum mechanics is what emerges when nature's finite Planck constant makes the wave nature of matter physically consequential. We introduce a three-regime framing: at ħ = 0, the wave nature vanishes and classical determinism holds; at ħ → ∞, all structure dissolves into total delocalization; at the actual finite value of ħ, neither the snapshot nor the story fully wins, producing the specific blend of determinacy and indeterminacy that characterizes our universe. An anthropic argument is offered: observers can only exist in the narrow band where ħ is large enough to permit quantum chemistry but small enough to permit stable structure. The tension between position and momentum is not a problem to be solved but a precondition for the existence of anything complex enough to notice it. The paper concludes that the uncertainty principle is not where physics gets strange but where it gets honest — where nature enforces a duality between complementary descriptions that was always present in the mathematical architecture of mechanics, from Zeno to Schrödinger.
The quantum mechanical uncertainty principle for position and momentum plays an important role in many treatments on the (philosophical, physical and other) implications of quantum mechanics. Roughly speaking, the more precisely the momentum (position) of a (quantum mechanical) object is given, the less precisely can one say what its position (momentum) is. This quantum mechanical measurement problem is not just an interpretational difficulty, it raises broader issues as well. The measurement (of a property) of a (quantum mechanical) object determines the existence of the measured. In brief, the quantum mechanical uncertainty principle challenges some fundamental principles of Science and especially the principle of causality. In particular, an independently existing (external) objective reality is denied. As we shall see, that the quantum mechanical uncertainty principle for position and momentum is based on the assumption that 1⩽0, which is a logical contradiction.
The quantum mechanical uncertainty principle for position and momentum plays an important role in many treatments on the (philosophical, physical and other) implications of quantum mechanics. Roughly speaking, the more precisely the momentum (position) of a (quantum mechanical) object is given, the less precisely can one say what its position (momentum) is. This quantum mechanical measurement problem is not just an interpretational difficulty, it raises broader issues as well. The measurement (of a property) of a (quantum mechanical) object determines the existence of the measured. In brief, the quantum mechanical uncertainty principle challenges some fundamental principles of Science and especially the principle of causality. In particular, an independently existing (external) objective reality is denied. As we shall see, that the quantum mechanical uncertainty principle for position and momentum is based on the assumption that 1⩽0, which is a logical contradiction.