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European Journal of Physics

Verification of the uncertainty principle by using diffraction of light waves

D Nikolic, Lj. Nesic

Published Feb 2, 2011• 10 citations
Publisher

Abstract

We described a simple idea for experimental verification of the uncertainty principle for light waves. We used a single-slit diffraction of a laser beam for measuring the angular width of zero-order diffraction maximum and obtained the corresponding wave number uncertainty. We will assume that the uncertainty in position is the slit width. For the acquisition of the experimental data and their further analysis, we used a computer. Because of its simplicity this experiment is very suitable for demonstration, as well as for a quantitative exercise at universities and final year of high school studies.

DOI
10.1088/0143-0807/32/2/018

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We described a simple idea for experimental verification of the uncertainty principle for light waves. We used a single-slit diffraction of a laser beam for measuring the angular width of zero-order diffraction maximum and obtained the corresponding wave number uncertainty. We will assume that the uncertainty in position is the slit width. For the acquisition of the experimental data and their further analysis, we used a computer. Because of its simplicity this experiment is very suitable for demonstration, as well as for a quantitative exercise at universities and final year of high school studies.
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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.
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.
The goal of this project was to create an intuitive and clear demonstrator of the dening properties of quantum mechanics using single slit diraction of light, which has quantum mechanical properties because of light's waveparticle duality. In this report we will describe the process and thoughts behind our project of creating a portable demonstration of the uncertainty principle. By designing and building both a physical setup with a laser, a slit, mirrors, lenses, beam-splitters, attenuators and cameras, and developing software which displays images from the cameras in a clear user interface with calculations we hope that students from high schools and gymnasiums that visit Vetenskapens Hus at Alba Nova will learn something new while using the demonstrator.
At present, the theory of light diffraction only has the simple wave-optical approach. In this paper, we study light diffraction with the relativistic quantum theory approach. We find that the slit length, slit width, slit thickness and wavelength of light affect the diffraction intensity and form of diffraction pattern. However, the effect of slit thickness on the diffraction pattern cannot be explained by wave-optical approach, but it can be explained in quantum theory. We compare the theoretical results with single- and multiple-slits experimental data, and find the theoretical results are in accordance with the experimental data. In addition, we give some theory predictions. We think all new predictions will be tested by the light diffraction experiment.