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Feynman-path analysis of Hardy's paradox: Measurements and the uncertainty principle

D. Sokolovski, Irene Puerto Gimenez, R. Sala Mayato

arXiv:0903.4795Physics Letters AMar 12, 200811 citations

Bell's Theorem Main Hidden Assumption

Jacques Poitevineau, Yves‐Henri Sanejouand

We show that the proofs of Bell’s theorem regarding the Einstein, Podolsky, Rosen paradox about incompleteness of Quantum Mechanics implicitly use a negation of Heisenberg’s uncertainty principle, for particles taken separately. Moreover, we show that the entanglement of the pair of particules, hidden variables and locality property are not necessary to establish the theorem. In other words, the theorem only speaks about Heisenberg’s principle and its experimental violation is simply another demonstration of the fundamental character of this principle. Therefore, the paradox is still alive and abandoning the locality property, as often advocated, is premature.We show that the proofs of Bell’s theorem regarding the Einstein, Podolsky, Rosen paradox about incompleteness of Quantum Mechanics implicitly use a negation of Heisenberg’s uncertainty principle, for particles taken separately. Moreover, we show that the entanglement of the pair of particules, hidden variables and locality property are not necessary to establish the theorem. In other words, the theorem only speaks about Heisenberg’s principle and its experimental violation is simply another demonstration of the fundamental character of this principle. Therefore, the paradox is still alive and abandoning the locality property, as often advocated, is premature.

Jan 1, 20260 citations

On Derivations of the Uncertainty Principle

Ernest R. Davidson

The Journal of Chemical PhysicsFeb 15, 196521 citations

Schrdinger equation for various quantum systems based on Heisenberg's uncertainty principle

Kexin An

This article establishes the proof of the Schrdinger equation for numerous quantum systems, utilizing Heisenberg's uncertainty principle. The Fourier transform connects functions in the time and frequency domains, resulting in the mathematical inequality that is the foundation of the uncertainty principle. In the part of Methods and Theory, the article derives the uncertainty principle through Fourier transforms by defining the mean and variance of angular frequency and time, and subsequently expanding the integral. This establishes the fundamental connection between time and frequency domains, illustrating the constraints imposed by quantum mechanics. In the part of Results and Application, the article applies the uncertainty principle to derive the Schrdinger equation under different conditions: free particle, particle in a box, harmonic oscillator, and hydrogen atom. For each case, the article assumes wave function solutions, uses the uncertainty in position and momentum to estimate kinetic and potential energies, and shows that the total energy matches the ground state energy derived from the Schrdinger equation. The results highlight the critical role of Heisenberg's uncertainty principle in understanding key aspects of quantum mechanics, providing a unified framework for these diverse systems.This article establishes the proof of the Schrdinger equation for numerous quantum systems, utilizing Heisenberg's uncertainty principle. The Fourier transform connects functions in the time and frequency domains, resulting in the mathematical inequality that is the foundation of the uncertainty principle. In the part of Methods and Theory, the article derives the uncertainty principle through Fourier transforms by defining the mean and variance of angular frequency and time, and subsequently expanding the integral. This establishes the fundamental connection between time and frequency domains, illustrating the constraints imposed by quantum mechanics. In the part of Results and Application, the article applies the uncertainty principle to derive the Schrdinger equation under different conditions: free particle, particle in a box, harmonic oscillator, and hydrogen atom. For each case, the article assumes wave function solutions, uses the uncertainty in position and momentum to estimate kinetic and potential energies, and shows that the total energy matches the ground state energy derived from the Schrdinger equation. The results highlight the critical role of Heisenberg's uncertainty principle in understanding key aspects of quantum mechanics, providing a unified framework for these diverse systems.

Theoretical and Natural ScienceSep 27, 20240 citations

Uncertainty principle and uncertainty relations

Jos Uffink, Jan Hilgevoord

Foundations of PhysicsSep 1, 1985174 citations

An Introduction to the Uncertainty Principle

Sundaram Thangavelu

Birkhäuser Boston eBooksJan 1, 2004116 citations

Paradoxes from the uncertainty principle

Abstract

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Paradoxes from the uncertainty principle

Abstract

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