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arXiv:1012.4544 · American Journal of Physics

Refraction in spacetime

M. Jääskeläinen, Marijke Lombard, Ulrich Zülicke

Published May 13, 2011• 3 citations
arXivHTMLPDF

Abstract

Refraction, interference, and diffraction are distinguishing features of wavelike phenomena. Although they are usually associated only with a purely spatial wave-propagation pattern, analogs to interference and diffraction involving the spatio-temporal dynamics of waves in one dimension have been discussed. We complete the triplet of analogies by discussing how spatio-temporal analogs to refraction are exhibited by a quantum particle in one dimension that is scattering off a step barrier. Similarly, birefringence in spacetime occurs for a spin-1/2 particle in a magnetic field.

DOI
10.1119/1.3553459

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Refraction, interference, and diffraction are distinguishing features of wavelike phenomena. Although they are usually associated only with a purely spatial wave-propagation pattern, analogs to interference and diffraction involving the spatio-temporal dynamics of waves in one dimension have been discussed. We complete the triplet of analogies by discussing how spatio-temporal analogs to refraction are exhibited by a quantum particle in one dimension that is scattering off a step barrier. Similarly, birefringence in spacetime occurs for a spin-1/2 particle in a magnetic field.
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We study the quantum slit diffraction problem in three dimensions. In the treatment of diffraction of particles by a slit, it is usually assumed that the motion perpendicular to the slit is classical. Here we take into account the effect of the quantum nature of the motion perpendicular to the slit using the Green function approach [18]. We treat the diffraction of a Gaussian wave packet for general boundary conditions on the shutter. The difference between the standard and our three-dimensional slit diffraction models is analogous to the diffraction in time phenomenon introduced in [16]. We derive corrections to the standard formula for the diffraction pattern, and we point out situations in which this might be observable. In particular, we discuss the diffraction in space and time in the presence of gravity.
Abstract Chapter 11 introduces the essential mystery of quantum mechanics, shows how it is resolved, and then goes on to examine related phenomena. The mystery is how individual photons, not electromagnetic waves, can give rise to the interference pattern seen in the two-slit experiment. They are shown to do so because the relevant quantum amplitude is a linear combination of two terms, leading to the pattern when neither slit is identified as the one the photon went through, but collapsing to one term and no pattern if the slit is identified. Similar results are shown to occur when individual electrons are incident on the two slits, and when large molecules, which have de Broglie wavelengths, are scattered by diffraction gratings. Many other interference experiments are described, including those where a photon was shown to be in two places simultaneously and one where a photon displayed both wave and particle features.
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