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Physical Review E

Comment on “Observation of matter wave beat phenomena in the macrodomain for electrons moving along a magnetic field”

C. S. Unnikrishnan

Published Aug 30, 2004• 6 citations
Publisher

Abstract

I show that the claim of the observation of matter wave beat phenomena in the classical macrodomain by Varma et al. [Phys. Rev. E 65, 026503 (2002)] is based on a mistaken interpretation of effects arising from multiple focusing of an electron beam in an axial magnetic field. I present the basic physical facts that mimic wavelike phenomena and suggest a classical explanation of modulations reported by Varma et al. Realization that the macroscopic "de Broglie wavelength" used by Varma et al. is the same as the focusing distance of a monoenergetic electron beam in the uniform magnetic field leads to a full classical explanation of all the effects reported by Varma et al. The reported observations are not evidence for any quantumlike phenomenon in the macrodomain, and their results do not indicate any violation of the Lorentz equation of motion.

DOI
10.1103/physreve.70.028501

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Observation of matter wave beat phenomena in the macrodomain for electrons moving along a magnetic field

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We report here the observations that exhibit the existence of matter wave phenomena with wavelength in the macrodomain of a few centimeters, for electrons moving along a magnetic field from an electron gun to a collector plate situated behind a grounded grid. These are in accordance with the predictions of a quantumlike theory for charged particles in the classical macrodomain, given by one of the authors [R. K. Varma, Phys. Rev. A 31, 3951 (1985)] with a recent generalization [R. K. Varma, Phys. Rev. E 64, 036608 (2001)]. The beats correspond to two closely spaced "frequencies" in the system, with the beat frequency given, in accordance with the characteristics of a wave phenomena, by the difference between the two frequencies. The beats ride as a modulation over a discrete energy band structure obtained with only one frequency present. The frequency here corresponds to the distance between the electron gun and the detector plate as it characterizes the variation in the energy band structure as the electron energy is swept. The second "frequency" corresponds to the gun-grid distance. These observations of the beats of matter waves in this experiment, with characteristics in accordance with the wave algorithm, then establish unambiguously the existence of macroscopic matter waves for electrons propagating along a magnetic field.

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Reply to “Comment on ‘Observation of matter wave beat phenomena in the macrodomain for electrons moving along a magnetic field’ ”

Ram K. Varma, A. M. Punithavelu, S. B. Banerjee

The so-designated ``complete classical explanation'' by Unnikrishnan in the preceding Comment, of the macroscopic wave beats reported by us recently, is based on an assumed physical mechanism that has no experimentally established basis. Through this assumed physical process and the focusing properties of an electron beam in a magnetic field, he produces what are essentially ``particle beats'' as against the ``wave beats'' observed by us. Even assuming that such a physical process does exist, the consequences of his mechanism are shown here to be in serious contradiction with our experimental observations, thereby invalidating the claim that his model explains, in purely classical terms, our observations exhibiting the existence of macroscopic matter wave beats in the charged particle motion along a magnetic field.

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I show that the claim of the observation of matter wave beat phenomena in the classical macrodomain by Varma et al. [Phys. Rev. E 65, 026503 (2002)] is based on a mistaken interpretation of effects arising from multiple focusing of an electron beam in an axial magnetic field. I present the basic physical facts that mimic wavelike phenomena and suggest a classical explanation of modulations reported by Varma et al. Realization that the macroscopic "de Broglie wavelength" used by Varma et al. is the same as the focusing distance of a monoenergetic electron beam in the uniform magnetic field leads to a full classical explanation of all the effects reported by Varma et al. The reported observations are not evidence for any quantumlike phenomenon in the macrodomain, and their results do not indicate any violation of the Lorentz equation of motion.
We report here the observations that exhibit the existence of matter wave phenomena with wavelength in the macrodomain of a few centimeters, for electrons moving along a magnetic field from an electron gun to a collector plate situated behind a grounded grid. These are in accordance with the predictions of a quantumlike theory for charged particles in the classical macrodomain, given by one of the authors [R. K. Varma, Phys. Rev. A 31, 3951 (1985)] with a recent generalization [R. K. Varma, Phys. Rev. E 64, 036608 (2001)]. The beats correspond to two closely spaced "frequencies" in the system, with the beat frequency given, in accordance with the characteristics of a wave phenomena, by the difference between the two frequencies. The beats ride as a modulation over a discrete energy band structure obtained with only one frequency present. The frequency here corresponds to the distance between the electron gun and the detector plate as it characterizes the variation in the energy band structure as the electron energy is swept. The second "frequency" corresponds to the gun-grid distance. These observations of the beats of matter waves in this experiment, with characteristics in accordance with the wave algorithm, then establish unambiguously the existence of macroscopic matter waves for electrons propagating along a magnetic field.
The so-designated ``complete classical explanation'' by Unnikrishnan in the preceding Comment, of the macroscopic wave beats reported by us recently, is based on an assumed physical mechanism that has no experimentally established basis. Through this assumed physical process and the focusing properties of an electron beam in a magnetic field, he produces what are essentially ``particle beats'' as against the ``wave beats'' observed by us. Even assuming that such a physical process does exist, the consequences of his mechanism are shown here to be in serious contradiction with our experimental observations, thereby invalidating the claim that his model explains, in purely classical terms, our observations exhibiting the existence of macroscopic matter wave beats in the charged particle motion along a magnetic field.
I present conclusive arguments to show that a recent claim of observation of quantum-like effects of the magnetic vector potential in the classical macrodomain is spurious. The `one dimensional interference patterns' referred to in the paper by R. K. Varma et al (Phys. Lett. A 303 (2002) 114-120) are not due to any quantum-like wave phenomena. The data reported in the paper are not consistent with the interpretation of interference, or with the topology of the Aharonov-Bohm effect. The assertion that they are evidence of A-B like effect in the classical macrodomain is based on inadequate appreciation of basic physical facts regarding classical motion of electrons in magnetic fields, interference phenomena, and the A-B effect.
Abstract This review describes the results of investigations on charged particle dynamics in a magnetic field carried out over a number of years. The studies have unravelled the existence of some very surprising and unusual phenomena. Though existing on the macro-scale, they are found to be of quantum origin, and are thereby not covered by the Lorentz equation, which has been regarded conventionally as the descriptor of electrodynamic phenomena on the macro-scale. These novel phenomena have been found to be attributed to the ‘quantum modulation’ of the de Broglie wave along the magnetic field. This is brought about through the scattering-induced transition across Landau levels, leading to the modulation of the plane wave state along the field as a result of the entanglement between the parallel and perpendicular degrees of freedom. These findings were motivated by the predictions of a formalism developed by the author and include such unusual phenomena as (i) macro-scale matter wave interference effects and (ii) the detection of curl-free vector potential also on the macro-scale, both attributed to quantum modulation which is a matter wave on the macro-scale. The formalism is thus described as ‘macro-quantization of guiding centre motion’.
Solutions of the Dirac wave equation are obtained representing the motion of an electron in a uniform magnetic field. These solutions are used to calculate the maximum penetration of the electrons into the field and also the average x coordinate of the current. Both results agree with the classical result to distances of the order of a de Broglie wave length. The solutions were then combined to represent a beam of electrons passing thru a slit. It was shown that the deviation of this beam from the classical path was also of the order of a de Broglie wave length. It was necessary to impose the condition that the slit be wide compared to an electron wave length - a condition amply fulfilled in all applications. This means that the slit must be so wide that diffraction of the electrons can be neglected. The conclusion is drawn that in all experiments which have been performed the differences between the classical and the quantum predictions will be too small to be observed. The differences in paths predicted will in all cases be of the order of an electron wave length.