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Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

A deterministic interpretation of the commutation and uncertainty relations of quantum theory and a redefinition of Planck’s constant as a coupling condition

Terence William Barrett

Published Jun 1, 1978• 10 citations
Publisher
DOI
10.1007/bf02894686

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A Relational Interpretation of the Heisenberg Uncertainty Principle and the Role of Planck's Constant

Barry Kieran Radcliffe

This paper presents a conceptual reinterpretation of the Heisenberg Uncertainty Principle within the relational framework developed in the preceding papers of this series. In conventional quantum mechanics, the uncertainty relation between position and momentum is typically understood as a limitation on the simultaneous precision with which these quantities can be measured. In this work, we explore an alternative interpretation in which the uncertainty principle reflects a structural constraint on the types of physical states that can exist within spacetime. Within the relational lens framework, physical systems exist between two fundamental limiting conditions: gravitational singularities, representing perfect spatial localization, and the speed of light, representing maximal propagation through spacetime. From this perspective, position and momentum can be interpreted as expressions of two complementary tendencies—localization and propagation—that define the allowable configurations of physical systems. Under this interpretation, the uncertainty relation expresses the minimum balance that must exist between these tendencies for a physical system to remain within spacetime. Planck’s constant (ħ) therefore represents the smallest relational scale separating these two boundary conditions. Rather than reflecting a limitation of measurement alone, the uncertainty principle may be understood as a structural feature of relational spacetime itself. This paper is conceptual in nature and does not introduce new empirical claims. Instead, it proposes a relational interpretation of the uncertainty principle that links quantum behavior with the broader boundary structure explored in earlier papers in this series.

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A simple experimental checking of Heisenberg's uncertainty relations

Selim Pašić, Ozren Gamulin, Zoran Tocilj

We show that the quantum mechanical interpretation of the diffraction of light on a slit, when a wave function is assigned to a photon, can be used for a direct experimental study of Heisenberg’s position-momentum and equivalent positionwave vector uncertainty relation for the photon. Results of an experimental test of the position-wave vector uncertainty relation, where the wavelength is used as the input parameter, are given and they very well confirm our approach. The same experimental results can also be used for a test of the position-momentum uncertainty relation when the momentum p0 of a photon is known as the input parameter. We show that a measurement of p0, independent of the knowledge of the value of the Planck’s constant, is possible. Using that value of p0, a test of the position-momentum uncertainty relation could be regarded as a method for a direct measurement of the Planck’s constant. This is discussed, since the diffraction pattern is also well described by classical electrodynamics in the considered experimental conditions. This approach for testing the Heisenberg’s uncertainty relations is very simple and consequently suitable as a quantitative exercise in undergraduate experimental courses, as well as a visual and attractive demonstration of the Heisenberg’s uncertainty principle in courses of quantum mechanics.

Fizika A•Nov 10, 2006•2 citations
This paper presents a conceptual reinterpretation of the Heisenberg Uncertainty Principle within the relational framework developed in the preceding papers of this series. In conventional quantum mechanics, the uncertainty relation between position and momentum is typically understood as a limitation on the simultaneous precision with which these quantities can be measured. In this work, we explore an alternative interpretation in which the uncertainty principle reflects a structural constraint on the types of physical states that can exist within spacetime. Within the relational lens framework, physical systems exist between two fundamental limiting conditions: gravitational singularities, representing perfect spatial localization, and the speed of light, representing maximal propagation through spacetime. From this perspective, position and momentum can be interpreted as expressions of two complementary tendencies—localization and propagation—that define the allowable configurations of physical systems. Under this interpretation, the uncertainty relation expresses the minimum balance that must exist between these tendencies for a physical system to remain within spacetime. Planck’s constant (ħ) therefore represents the smallest relational scale separating these two boundary conditions. Rather than reflecting a limitation of measurement alone, the uncertainty principle may be understood as a structural feature of relational spacetime itself. This paper is conceptual in nature and does not introduce new empirical claims. Instead, it proposes a relational interpretation of the uncertainty principle that links quantum behavior with the broader boundary structure explored in earlier papers in this series.
We show that the quantum mechanical interpretation of the diffraction of light on a slit, when a wave function is assigned to a photon, can be used for a direct experimental study of Heisenberg’s position-momentum and equivalent positionwave vector uncertainty relation for the photon. Results of an experimental test of the position-wave vector uncertainty relation, where the wavelength is used as the input parameter, are given and they very well confirm our approach. The same experimental results can also be used for a test of the position-momentum uncertainty relation when the momentum p0 of a photon is known as the input parameter. We show that a measurement of p0, independent of the knowledge of the value of the Planck’s constant, is possible. Using that value of p0, a test of the position-momentum uncertainty relation could be regarded as a method for a direct measurement of the Planck’s constant. This is discussed, since the diffraction pattern is also well described by classical electrodynamics in the considered experimental conditions. This approach for testing the Heisenberg’s uncertainty relations is very simple and consequently suitable as a quantitative exercise in undergraduate experimental courses, as well as a visual and attractive demonstration of the Heisenberg’s uncertainty principle in courses of quantum mechanics.