This article examines the use of fractals to estimate the probability of classical events controlled by quantum processes. A hypothesis explaining the opposite charges of the positron and electron is discussed, as well as the relationship with the main modern theories of quantum mechanics, such as quantum electrodynamics (QED), string theory, etc. The relationship with the tunnel effect and the pulsed tunnel effect is considered. Examples of practical application of fractals are given, for example, in photocatalysts. The concepts of the effective mass of a photon and the quantum nature of elementary particles, the idea of their internal structure and the formation of matter from the point of view of quantum mechanics are touched upon. Particular attention is paid to the fractal structure of the quantum field as a probability associated with the formation of a positron or electron, and the mathematical connection with the Dirac equation, QED and the Schrödinger equation.
This article examines the use of fractals to estimate the probability of classical events controlled by quantum processes. A hypothesis explaining the opposite charges of the positron and electron is discussed, as well as the relationship with the main modern theories of quantum mechanics, such as quantum electrodynamics (QED), string theory, etc. The relationship with the tunnel effect and the pulsed tunnel effect is considered. Examples of practical application of fractals are given, for example, in photocatalysts. The concepts of the effective mass of a photon and the quantum nature of elementary particles, the idea of their internal structure and the formation of matter from the point of view of quantum mechanics are touched upon. Particular attention is paid to the fractal structure of the quantum field as a probability associated with the formation of a positron or electron, and the mathematical connection with the Dirac equation, QED and the Schrödinger equation.
This article provides a comprehensive review of the quantum tunneling effect, one of the most important phenomena in quantum mechanics. According to the laws of classical physics, a particle cannot overcome a potential barrier if it has insufficient energy. However, in quantum mechanics, due to the wave nature of the particle, the probability of penetrating the barrier is non-zero. This work analyzes in detail the theoretical foundations of the tunneling effect, its description via the Schrödinger equation, probability amplitudes, boundary conditions for wave functions, and their physical meaning. Furthermore, the application of this effect in semiconductor physics, nuclear physics, scanning tunneling microscopy, and nanotechnology is discussed. Based on the work of Kazakh scientists, the place and significance of the tunneling effect in modern physics are determined. The research results provide a deeper understanding of quantum phenomena and promote the development of their practical applications.
A new application of a fractal concept to quantum physics has been developed. The fractional path integrals over the paths of the Levy flights are defined. It is shown that if fractality of the Brownian trajectories leads to standard quantum mechanics, then the fractality of the Levy paths leads to fractional quantum mechanics. The fractional quantum mechanics has been developed via the new fractional path integrals approach. A fractional generalization of the Schrodinger equation has been discovered. The new relationship between the energy and the momentum of the nonrelativistic fractional quantum-mechanical particle has been established, and the Levy wave packet has been introduced into quantum mechanics. The equation for the fractional plane wave function has been found. We have derived a free particle quantum-mechanical kernel using Fox's H-function. A fractional generalization of the Heisenberg uncertainty relation has been found. As physical applications of the fractional quantum mechanics we have studied a free particle in a square infinite potential well, the fractional "Bohr atom" and have developed a new fractional approach to the QCD problem of quarkonium. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum mechanics. (c) 2000 American Institute of Physics.
In this article, we start our discussion on the Aharonov-Bohm effect then raise a plausible interpretation within the quantum electrodynamics (QED) framework. We provide a quantum treatment of the source of the electromagnetic potential and argue that the underlying mechanism in AB effect can be viewed as interactions between electrons described by QED theory where the interactions are mediated by virtue photons. On further analysis, we claim that the framework of one particle quantum mechanics (OPQM) can be shown, in general, as a mathematically approximated model which can be reformulated from QED theory. In addition, the classical Maxwell equations are derived from QED scattering process while both classical electromagnetic fields and potentials serve as mathematical tools that are constructed to approximate the interactions among elementary particles described by QED physics, i.e. neither classical fields nor potentials represent any real entities of nature. At the conclusion of this article, we make a few remarks on the hypnosis of the existence of magnetic monopoles.
In quantum open systems, transport coejcients such as crosssections or conductance fluctuate as functions of the relevant parameters. These fluctuations give rise to complicated patterns. An important question is their possible fractality. In this paper we present a historical review of fractal fluctuations in quantum systems and their relation to the properties of their classical counterparts. We discuss the original semiclassical predictions and various numerical and experimental results. Some numerical simulations claim explanations based on pure quantum grounds. We thus report an argument that traces fractality back to the statistical properties of the S -matrix poles. Although full understanding of the reasons for fractal fluctuations might seema secondary problem, it could lead to a deeper comprehension of quantum mechanics and its interplay with classical mechanics.
This article provides a compact scientific entry to the broader G-theory research corpus. The central hypothesis of the programme is that G-theory should be understood not as a competing replacement for quantum mechanics, quantum field theory, QED, gauge theory, or relativity, but as a possible common root substrate from which physically admissible theories, fields, particle sectors, and measurement realizations may arise as typed secondary structures in their proper domains. The article introduces the basic root vocabulary of the programme, including the primary harmonic root Hₒ, the minimally sufficient control coordinate 1gk, the structural deviation coordinate ΔH, and the levelwise energy–control relation E ⊙ K = Σ. It explains the role of exact and covariant inheritance between levels, the distinction between dimensional modality and physical spacetime dimension, and the reconstruction of a common fermionic lineage leading to charge-conjugate electron–positron sectors rather than two independently inserted particle models. The article also summarizes the relation of this programme to the G–Noether line, the Yang–Mills mass-gap research architecture, the prediction and validation framework of Appendix V, and the current open frontiers of absolute mass and charge population, continuum/infrared completion, and independent empirical identification. A separate part is devoted to the Tonomura single-electron interference experiment, where the G-substrate interpretation is carried through a coherent realization, measurement interaction, event algebra, and localized readable event while preserving standard quantum probabilities. This construction is explicitly not presented as a new probability law or as an independent solution of the single-outcome problem. The purpose of the article is therefore not to replace the detailed proofs contained in the full corpus, but to provide physicists with a concise map of the programme, its main mathematical structures, its completed internal results, its current limitations, and its experimentally testable frontier.
Models of an individual photon having joint wave‐particle properties, needle‐like geometry, and spin cannot be based on conventional theory, but be deduced in terms of a revised quantum electrodynamic approach. In this paper the latter is applied to two‐slit configurations and electron‐positron pair formation: (a) Two‐slit experiments performed earlier by Tsuchiya et al. and recently by Afshar et al. demonstrate the joint wave‐particle properties of the individual photon, and agree with Einstein’s argument against Complementarity. The present theory is consistent with these results, (b) The elementary electron‐positron pair formation process is considered, with special attention to the involved orbits, conservation of energy, spin, and electric charge. The obtained model appears to be consistent with the process in which the created electron and positron move along two rays and have original directions along the path of the incoming photon. The nonzero electric field divergence of the theory is associated with an intrinsic local electric charge density. This may explain that the photon can decay on account of the impact from an external electric field.