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.
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 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.
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.
The preceding Comment challenged my claim that potentials might be just auxiliary mathematical tools and that they are not necessary for explaining physical phenomena. The Comment did not confront my explanation without the potentials of the Aharonov-Bohm effects that appeared in the original article, but stated that I cannot apply this explanation for seven other examples. In my reply, using my method, I provide explanations of one of the examples, show that two other examples are not relevant, and agree that the remaining examples require further analysis. However, I argue that none of the examples provides robust counterexamples to my claim, similar to the original Aharonov-Bohm setups which were explained in my article, so the Comment does not refute my claim.
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.
It has been widely thought that the ontology of quantum mechanics is real, physical fields. In this paper, I will present a new argument against the field ontology of quantum mechanics by analyzing one-body systems such as an electron. First, I argue that if the physical entity described by the wave function of an electron is a field, then this field is massive and charged. Next, I argue that if a field is massive and charged, then any two parts of the field in space will have gravitational and electromagnetic interactions, while the existence of such self-interactions for an electron contradicts quantum mechanics and experimental observations. This poses a serious difficulty for the field ontology of quantum mechanics. Third, I argue that a particle ontological interpretation of the wave function may avoid the difficulty by providing a plausible explanation of the non-existence of self-interactions. According to this explanation, the wave function of an electron is a description of the state of the random motion of the electron as a particle, and in particular, the modulus squared of the wave function gives the probability density that the electron appears in every possible position in space. Finally, I answer a major objection to the explanation of the non-existence of self-interactions in terms of particle ontology.