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Journal of Southwest China Normal University

The Defects in the Interpretation of the Uncertainty Relation with Single-Slit Diffraction Experiment

Changfang Zhang

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

The single-slit diffraction experiment is often used to explain the uncertainty relation,ΔxΔpx≈ h,in College Physics teaching.Such an approach means non-scientific knowledge of this relation,which is apedagogical virus affecting not only the students but also the teachers.Some of the defects are analyzed in this paper,and it is hoped that this work will be useful for the teachers in the teaching of the uncertainty relation.

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The single-slit diffraction experiment is often used to explain the uncertainty relation,ΔxΔpx≈ h,in College Physics teaching.Such an approach means non-scientific knowledge of this relation,which is apedagogical virus affecting not only the students but also the teachers.Some of the defects are analyzed in this paper,and it is hoped that this work will be useful for the teachers in the teaching of the uncertainty relation.
It is generally accepted that the disturbance interpretation cannot explain Heisenberg's uncertainty relation DxDp=h. In this paper a clear distinction will be made between the notions of state preparation and measurement, noting that the disturbance that is referred to in Heisenberg's disturbance interpretation is usually caused by the measurement. The main goal of this paper is to examine and discuss to what extent disturbance during the state preparation plays a role in the interpretation of Heisenberg's uncertainty relation. This examination will be done in the context of a single-slit experiment. To conclude this paper a novel single-slit experiment will be proposed and discussed with which a clearer insight could be gained into the exact role of disturbance when a quantum system passes a single-slit.
This experiment investigates the Heisenberg Uncertainty Principle (HUP) through an optical analogue using Single-slit diffraction of a monochromatic He–Ne laser. The spatial confinement of light through slits of varying width is compared with the resulting diffraction patterns, providing a means to examine the relationship between position uncertainty ∆x and transverse momentum uncertainty ∆px. Diffraction patterns were recorded using a photodiode detector, and the angular positions of the first minima were determined and used to estimate the spread in momentum via the de-Broglie relation. The results demonstrates and are consistent with the expected inverse relationship. The measured diffraction patterns were also found to adhere to the Fraunhofer diffraction relation, supporting the validity of the experimental model and the goodness of fit of the data.The calculated uncertainty products were further found to be consistent with the expected magnitude of Planck's constant. and therefore the the findings support the interpretation of diffraction as a classifcal manifestation of the Foruier relation between position and momentum space. Thus providing a physically intuituve demonstration of Heisenberg's Uncertainty Principle.
This paper reports on a study of student understanding of the wave nature of matter in the context of the pattern produced by the diffraction and interference of particles. Students in first-year, second-year, and third-year physics courses were asked to predict and explain how a single change in an experimental setup would affect the pattern produced when electrons or other particles are incident on a single slit, double slit, or crystal lattice. The errors made by students after standard instruction indicated the presence of similar conceptual and reasoning difficulties at all levels. Among the most serious was an inability to interpret diffraction and interference in terms of a basic wave model. Other errors revealed a lack of a functional understanding of the de Broglie wavelength. Students often treated it as a fixed property of a particle, not as a function of the momentum. An important goal of this investigation was to provide a research base for the design of instruction to help students develop and apply a basic wave model for matter.
A thought experiment, in which a light beam is sent through slits of different sizes thereby producing a diffraction pattern, is used to illustrate the uncertainty principle. Attempts to reduce the uncertainty in the measurement of the position of the light beam ( ) succeed, but at the expense of increasing the uncertainty in the measurement of the momentum ( ), so that the product of the two magnitudes, x, is still larger than h, Planck's constant. This experiment introduces the idea that one can know the value of a physical observable with as high a precision as necessary, but the act of measuring this observable has an effect on how much we can know about another observable. This thought experiment can be physically performed using a diode laser and a series of slits. A derivation is presented to relate the uncertainties in position and momentum to variables that can be measured with a ruler in a classroom or laboratory. Data from a typical experiment are also presented.
This paper investigates the “private” interpretations that students of quantum mechanics develop concerning this theory. By means of questionaires, we analyze their conceptions with respect to the double slit experiment, uncertainty principle, quantum state, retrodiction, and projection postulate. Correlating the students’ answers, we observe that different private interpretations are frequently employed for analyzing different problems. Other conclusions about the cognitive processes of the students are also obtained.