Towards the demystificatiom of quantum interference (original) (raw)
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Wave-Particle Duality Revitalized: Consequences, Applications and Relativistic Quantum Mechanics
2011
The proposed paper presents the unobserved inadequacies in de Broglie's given concepts of wave-particle duality and matter waves in the year 1923. The commonly admitted quantum energy or frequency expression hν=γmc 2 is shown to be inappropriate for matter waves and is acceptable only for photons, where the symbols have their usual meanings. The superluminal phase velocity expression c 2 /υ, for matter waves, is investigated in detail and is also reported to be inadequate in the proposed paper. The rectifications in the inadequate concepts of de Broglie's theory and refinements in the analogy implementation between light waves and matter waves are presented, which provides the modified frequency and phase velocity expression for matter waves. Mathematical proofs for the proposed modified frequency and phase velocity expression are also presented. In accordance with the proposed concepts, a wave-particle duality picture is presented which elucidates the questions coupled with the wave-particle duality concepts, existing in the literature. Consequently, particle type nature is shown to be a characteristic of waves only, independent from the presence of matter. The modifications introduced in the frequency expression for matter waves leads to variation in the wave function expression for a freely moving particle and its energy operators, with appropriate justifications provided in the paper. A new relation between the Kinetic energy and Momentum of the moving body is also proposed and is subsequently applied to introduce novel General and Relativistic Quantum Mechanical Wave Equations. Applications of these equations in bound state quantum mechanical systems, presented in the paper, provide the information regarding particle's general and relativistic behavior in such systems. Moreover, the proposed wave equations can also be transformed into Schrödinger's and Dirac's equations. The interrelation of Schrödinger's, Dirac's and proposed equations with the universal wave equation is also presented.
Quantum Trajectories and Physical Reality of de Broglie's Waves
An exact, ray-based general treatment is shown to hold for any kind of monochromatic wave feature-including diffraction and interference-described by Helmholtz-like equations, under the coupling action of a dispersive function (which we call "Wave Potential") encoded in the structure itself of the Helmholtz equation. Since the time-independent Schroedinger and Klein-Gordon equations (associating particles of assigned total energy with stationary de Broglie waves) are themselves Helmholtz-like equations, the same general approach is extended to the ray-based dynamics of point-like particles, whose exact trajectories and dynamical laws may be obtained without resorting to statistical concepts of any kind, thus suggesting a non-probabilistic nature of de Broglie's waves and of physical reality.
Wave mechanics, from Louis de Broglie to Schrödinger: a comparison
Studies in History and Philosophy of Science II, 2021
Erwin Schrödinger's work on wave mechanics started in late 1925, stimulated by his study of Louis de Broglie's thesis. It is well known that in his initial attempts to formulate a quantum theory of the atom Schrödinger tried to develop a relativistic theory, following de Broglie's ideas, and only afterwards he looked for a non-relativistic wave equation. It is straightforward to derive the wave equation corresponding to de Broglie's phase waves. both in the relativistic and nonrelativistic realms. In the case of his relativistic attempt, Schrödinger did indeed follow a simple approach, using de Broglie's theory. In the non-relativistic approach, he attempted to produce an independent derivation of the wave equation, following several different lines, instead of using de Broglie's results in the classical limit. This paper analyses Schrödinger's derivations of the wave equation, showing the differences and similarities between his theory and de Broglie's. It will be shown that, although it is formally possible to derive the wave equation from de Broglie's theory, there is an incompatibility between the two theories: it would be impossible to make any sense of de Broglie's ideas in the case of the rigid rotator, for instance. Schrödinger's approach was, in this sense, independent and incompatible with de Broglie's theory, and it could be easily applied to many different physical situations. This heuristic value of Schrödinger's wave equation is another very important distinction between the two theories, since de
Deconstruction of Quantum Wave Mechanics
The model of the hydrogen atom originally introduced by Erwin Schr¨odinger in 1926 is a two-body proton -electron system. It relies on the Schr¨odinger operator H and on the linear Schr¨odinger time dependent equation. Then Niels Bohr discovered that the model contradicts the basic dynamics of the atom and quantum wave mechanics was invented, with incidences here told from a deconstructive standpoint. The final section of this paper sketches a new, alternative, continuous, causal and fully deterministic wave mechanics —already mentioned in [1], [2], [3] and elsewhere— crucially relying on H and solvable in terms of its eigenvalues and eigenfunctions, but definitely non-linear. An important implication is that the deterministic hydrogen atom must be conceived as a three-body system consisting of proton , electron and photon.
Wave – particle duality interpretation: de brogile equation criticisms
Physics & Astronomy International Journal, 2020
The development of the quantum theory has been ongoing for many years. The wave-particle duality has been and is central to debates among physicists, in their endeavor to understand and bring more insight about the quantum theory. In this paper attempts by physicists to clarify the wave-particle duality are discussed. The wave or particle or both state of matter is analyzed, followed by discussion on the criticisms on de Broglie equation. Lastly, the paper concludes that debates on the wave-particle duality will continue since there is no consensus yet among physicists, and that experimental evidence should be given to substantiate claims.
General relativistic effects on quantum interference and the principle of equivalence
Physical Review D, 2002
Using a novel approach, we work out the general relativistic effects on the quantum interference of de Broglie waves associated with thermal neutrons. The unified general formula is consistent with special relativistic results in the flat space limit. It is also shown that the exact geodesic equation contains in a natural way a gravitational analog of the Aharonov-Bohm effect. We work out two examples, one in general relativity and the other in heterotic string theory, in order to obtain the first order gravitational correction terms to the quantum fringe shift. Measurement of these terms is closely related to the validity of the equivalence principle at a quantum level.
2005
The de Broglie wave phenomenon was studied in the framework of Lagrangean formulation of Relativistic Mechanics. The conclusion was made that the de Broglie wave of a particle is a relativistic phenomenon related to the field-dependent proper mass. The wave develops in a process of proper-to-kinetic mass transformation when the particle is given a momentum. The time-part of the 4-wave vector is related to the proper mass oscillation while the spacial part is due to the momentum; both parts can be treated in terms of virtual (longitudinal and scalar) photons characterizing excitation states of a mediating scalar field. It is shown that in Relativistic Mechanics with the variable proper mass both electromagnetic and gravitational force can be treated on the same footing: both are due to the same source that is, the proper mass. Consequently, the scalar mediating field provides a mechanism of unification of gravitational and electromagnetic forces. The concept of the unified divergence...
On energy, matter and wave-like behaviour
The relationship between light speed energy and the kinetic energy of non-relativistic particles is considered and an equation proposed to unify them. This leads naturally to the postulation of the de Broglie vector to represent any relativistic or non-relativistic particle. By adopting this concept, it is possible to account for the wave-particle duality associated with quantum mechanics, which is demonstrated for both diffraction and refraction. The angular momentum of the de Broglie vector can be considered as the spin of a particle, pointing along the axis of rotation. The visualisation of a particle as simply a de Broglie vector leads to the idea that all matter is an embodiment of energy trapped within a potential well. If energy escapes the potential well and reacts in a negative manner to the gravitational field of the potential well, it would reach the speed of light almost instantaneously.
The de Broglie Wave as Evidence of a Deeper Wave Structure
It is argued that the de Broglie wave is not the wave usually supposed, but the relativistically induced modulation of an underlying carrier wave that moves with the velocity of the particle. In the rest frame of the particle this underlying structure has the form of a standing wave. De Broglie too assumed the existence of this antecedent standing wave, but failed to notice its survival as a carrier wave in the Lorentz transformed wave structure. Identified as a modulation, the de Broglie wave acquires a physically reasonable ontology, evidencing a more natural unity between matter and radiation than might otherwise be contemplated, and avoiding the necessity of recovering the particle velocity from a superposition of such waves. Because the Schrödinger and other wave equations for massive particles were conceived as equations for the de Broglie wave, this interpretation of the wave is also relevant to such issues in quantum mechanics as the meaning of the wave function, the nature of wave-particle duality, and the possibility of well-defined particle trajectories