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Annalen der Physik

Remarks on the Relationship between Electron Interference and Electron Polarization

P. S. Fargo

Published Jan 1, 1967• 1 citation
Publisher

Abstract

Abstract In relation to a recent paper by INTHOFF it is pointed out that it is legitimate to describe the polarization accompanying the interference of electron beams as resulting from the spin‐dependence of the wavelength of the electrons while they are in an electromagnetic field. Using a semi‐classical argument it is shown furthermore that an electron optic “biprism” would give a detectable polarization effect only if on account of its very high gradient the field constituting the biprism could not be considered constant over a region whose linear dimensions are comparable with the Compton wave length of the electron.

DOI
10.1002/andp.19674750108

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Abstract In relation to a recent paper by INTHOFF it is pointed out that it is legitimate to describe the polarization accompanying the interference of electron beams as resulting from the spin‐dependence of the wavelength of the electrons while they are in an electromagnetic field. Using a semi‐classical argument it is shown furthermore that an electron optic “biprism” would give a detectable polarization effect only if on account of its very high gradient the field constituting the biprism could not be considered constant over a region whose linear dimensions are comparable with the Compton wave length of the electron.
The interference effect produced by two independent sources can be understood in terms of the detection process, owing to the inability of the detector to know from which of the two sources the photons come. Detection based on the Compton effect seems to be a powerful method for recording the interference between high-frequency coherent fields. It is shown that by taking advantage of the uncertainty over the photon momenta, the scattering probability for an electron in an interference fringe is very high when the electrons are not relativistic. When the fields have the same frequency in the laboratory system, relativistic electrons can "see" the interference only when the angles between the fields are very small. In general, relativistic electrons see interference when the fields are suitably shifted in frequency in the laboratory system.
Electron interference phenomena are now easily observable with the advent of bright and yet coherent field-emission electron beams. The interaction of electron waves with electromagnetic fields is essentially described by the Aharonov–Bohm (AB) effect. However, the AB effect has long been disputed due to a feature that cannot be understood in terms of classical electrodynamics. This paper describes the experiments that confirmed its existence and discusses its expanding applications to the observation of electromagnetic fields in the microscopic region.
This paper further explores the structural similarities between the elementary quantum-mechanical wavefunction and circularly polarized electromagnetic waves to further tune a possible physical interpretation of the wavefunction. The interpretation that is offered analyzes the real and the imaginary part of the wavefunction as oscillations which each carry half of the total energy of the particle. These oscillations are perpendicular to each other, and the interplay between both may describe how energy propagates through space over time. The model is based on three fundamental premises: 1.The dimension of the matter-wave field vector is force per unit mass (N/kg), as opposed to the force per unit charge (N/C) dimension of the electric field vector. This dimension is an acceleration (m/s2), which is the dimension of the gravitational field. 2.This gravitational disturbance may cause a charged mass to move about some center, combining linear and circular motion. This interpretation may reconcile the wave-particle duality to some extent: fields interfere but if, at the same time, they do drive a pointlike particle, this may explain why, as Feynman puts it, “when you do find the electron some place, the entire charge is there.” This hybrid hypothesis is supported by an elegant yet simple derivation of the Compton radius of an electron. 3.In light of the direction of the magnetic moment of an electron in an inhomogeneous magnetic field, the plane which circumscribes the circulatory motion of the electron should also comprise the direction of its linear motion. Hence, unlike an electromagnetic wave, the plane of the two-dimensional oscillation cannot be perpendicular to the direction of motion of our electron. Finally, this paper addresses an issue which has hampered other physical interpretations of the wavefunction: amplitude transformations when going from one representation (or reference frame) to another. Indeed, the author re-visits the original mathematical arguments here and shows that the proposed model, and the related physical interpretation of the wavefunction, are not incompatible with the key results and mainstream logic in this regard.
The wave function describing the electron interference produced by an electrostatic biprism derived from the perturbation theory involves an integral which is not easy to evaluate numerically. Using the method of stationary phase it is shown in the paper that the expression of this integral in terms of the Fresnel integrals considerably facilitates the calculations. Physically this expression corresponds to the superposition of two waves emerging from two virtual images of the source diffracted by two opaque half-planes of opposite orientation. In such a way the model widely used for discussions of the interference of this type is justified.
Remarkable progress can be observed in recent years in the controlled emission, guiding, and detection of coherent, free electrons. Those methods were applied in matter wave interferometers leading to high phase sensitivities and precise sensor technologies for dephasing influences such as mechanical vibrations or electromagnetic frequencies. However, the previous devices have been large laboratory setups. For future sensor applications or tests of the coherence properties of an electron source, small, portable interferometers are required. Here, we demonstrate a compact biprism electron interferometer that can be used for mobile applications. The design was optimized for small dimensions by beam path simulations. The interferometer has a length between the tip and the superposition plane before magnification of only 47 mm and provides electron interference patterns with a contrast up to 42.7%. The detection of two dephasing frequencies at 50 and 150 Hz was demonstrated applying second order correlation and Fourier analysis of the interference data.