The Einstein field equation

Various aspects of the Einstein field equation are presented. First the field equation is obtained by arguing that it is the simplest equation that respects the fundamental geometric insight into gravity. Then we consider whether the equation is stable, and introduce the weak energy and dominant energy conditions. The connection between inertial motion and the distant universe (Mach’s principle) is discussed. The equation of motion of matter is obtained from the field equation, and a comparison made with electromagnetic field theory. The energy and momentum of gravitational fields in stationary conditions is discussed, and the Komar energy obtained.

Physics in curved spacetime

Electromagnetic field theory, and the physics of continuous media (fluids, solids) in curved spacetime are discussed. Generalized Maxwell’s equations are written down and their justifaction is briefly presented. Then we turn to thermodynamics and continuous media. The concept of energy and momentum conservation is carefully expounded, and then the equations for fluid flow (continuity equation and Euler equation) are developed from the divergence of the energy tensor. The Bernoulli equation and the equation for hydrostatic equilibrium are obtained. The chapter then goes on to a general discussion of how general relativity operates and how gravitational phenomena are calculated and observed. The relation between gravity and other aspects of physics such as particle physics is discussed, along with the notion of general covariance.

Building Blocks for the Development of a Self-Consistent Electromagnetic Field Theory of Consciousness

The goal of this work is to compile the basic components for the construction of an electromagnetic field theory of consciousness that meets the standards of a fundamental theory. An essential cornerstone of the conceptual framework is the vacuum state of quantum electrodynamics which, contrary to the classical notion of the vacuum, can be viewed as a vibrant ocean of energy, termed zero-point field (ZPF). Being the fundamental substrate mediating the electromagnetic force, the ubiquitous ZPF constitutes the ultimate bedrock of all electromagnetic phenomena. In particular, resonant interaction with the ZPF is critical for understanding rapidly forming, long-range coherent activity patterns that are characteristic of brain dynamics. Assuming that the entire phenomenal color palette is rooted in the vibrational spectrum of the ZPF and that each normal mode of the ZPF is associated with an elementary shade of consciousness, it stands to reason that conscious states are caused by the coupling of the brain to a particular set of normal modes selectively filtered from the full frequency spectrum of the ZPF. From this perspective, the brain is postulated to function as a resonant oscillator that couples to a specific range of ZPF modes, using these modes as a keyboard for the composition of an enormous variety of phenomenal states. Theoretical considerations suggest that the brain-ZPF interface is controlled by altering the concentrations of neurotransmitters, placing the detailed study of the neurotransmitter-ZPF interaction at the center of future research activities.

Design and Implementation of an Atmospheric Anion Monitoring System Based on Beidou Positioning

Atmospheric oxygen anions play an important role in medical health, clinical medicine, environmental health, and the ecological environment. Therefore, the concentration of atmospheric anions is an important index for measuring air quality. This paper proposes a monitoring system for atmospheric oxygen anions based on Beidou positioning and unmanned vehicles. This approach combines Beidou positioning technology, 4G pass-through, the unmanned capacitance suction method, electromagnetic field theory, and atmospheric detection technology. The proposed instrument can monitor the overall negative oxygen ion concentration, temperature, and humidity in a certain region over time and provide data visualization for the concentration of negative oxygen ions.

Near-to-Far Field Transformation in FDTD: A Comparative Study of Different Interpolation Approaches

Equivalence theorems in electromagnetic field theory stipulate that farfield radiation pattern/scattering profile of a source/scatterer can be evaluated from fictitious electric and magnetic surface currents on an equivalent imaginary surface enclosing the source/scatterer. These surface currents are in turn calculated from tangential (to the equivalent surface) magnetic and electric fields, respectively. However, due to the staggered-in-space placement of electric and magnetic fields in FDTD Yee cell, selection of a single equivalent surface harboring both tangential electric and magnetic fields is not feasible. The work-around is to select a closed surface with tangential electric (or magnetic) fields and interpolate the neighboring magnetic (or electric) fields to bring approximate magnetic (or electric) fields onto the same surface. Interpolation schemes available in the literature include averaging, geometric mean and the mixed-surface approach. In this work, we compare FDTD farfield scattering profiles of a dielectric cube calculated from surface currents that are obtained using various interpolation techniques. The results are benchmarked with those obtained from integral equation solvers available in the commercial packages FEKO and HFSS.

Using Electromagnetic Properties to Identify and Design Superconducting Materials

Superconductors have a wide array of applications, such as medical imaging, supercomputing, and electric power transmission, but superconducting materials only operate at very cold temperatures. Thus, the quest to engineer room temperature superconductors is currently a hot topic of research. To accomplish this mission, it is important to have a complete understanding of the material properties that are being used to create these superconductors. Understanding the atomic and electromagnetic properties of the prospective materials will provide tremendous insight into the best choice for the materials. Therefore, a theoretical model that incorporates electromagnetic field theory and quantum mechanics principles is utilized to explain the electrical and magnetic characteristics of superconductors. This model can be used to describe the electrical resistance response and why it vanishes at the material’s critical temperature. The model can also explain the behavior of magnetic fields and why some superconducting materials completely exclude magnetic fields while other superconductors partially exclude these fields. Thus, this theoretical analysis produces a model that describes the behavior of both type I and type II superconductors. Since there are subtle differences between superconductors and perfect conductors, this model also accounts for this distinction and explains why superconductors behave differently than perfect conductors. Therefore, this theory addresses the major properties associated with superconducting materials and thus will aid researchers in the pursuit of designing room temperature superconductors.

Origin of Gauge Theories in Electrodynamics

<div>The potential formulation has significant advantages over field formulation in solving complicated problems in electromagnetic field theory. One essential part of electromagnetic field theory's potential formulation is gauge invariance and gauge theories because it provides an extra degree of freedom. By using this extra degree of freedom, we can solve complicated electromagnetic problems quickly. Thus, it is necessary to include a systematic explanation of gauge theories in teaching electromagnetic theory. However, textbooks usually formulate gauge theories by using Maxwell's equations of electromagnetism, by using vector calculus identities. However, this method of formulation of gauge theories does not give a clear idea about the origin of gauge theories and gauge invariance in electromagnetism. Here the author formulates gauge theories from wave equations of the electric and magnetic fields instead of directly using Maxwell's equations. This method generalizes all gauge theories like Lorenz gauge theory, Coulomb gauge theory, Etc. Gauge theory, because of the way the author derives it, gives a distinct idea about the mathematical origin of the gauge theories and gauge invariance in electromagnetic field theory. Thus, the author reviews the origin of gauge theories in electromagnetic field theory and develops a distinct and effective method to introduce gauge theory in the teaching of electromagnetic field theory that can provide better understanding of the topic to undergraduate students.</div><div><br></div>

Origin of Gauge Theories in Electrodynamics

<div>The potential formulation has significant advantages over field formulation in solving complicated problems in electromagnetic field theory. One essential part of electromagnetic field theory's potential formulation is gauge invariance and gauge theories because it provides an extra degree of freedom. By using this extra degree of freedom, we can solve complicated electromagnetic problems quickly. Thus, it is necessary to include a systematic explanation of gauge theories in teaching electromagnetic theory. However, textbooks usually formulate gauge theories by using Maxwell's equations of electromagnetism, by using vector calculus identities. However, this method of formulation of gauge theories does not give a clear idea about the origin of gauge theories and gauge invariance in electromagnetism. Here the author formulates gauge theories from wave equations of the electric and magnetic fields instead of directly using Maxwell's equations. This method generalizes all gauge theories like Lorenz gauge theory, Coulomb gauge theory, Etc. Gauge theory, because of the way the author derives it, gives a distinct idea about the mathematical origin of the gauge theories and gauge invariance in electromagnetic field theory. Thus, the author reviews the origin of gauge theories in electromagnetic field theory and develops a distinct and effective method to introduce gauge theory in the teaching of electromagnetic field theory that can provide better understanding of the topic to undergraduate students.</div><div><br></div>

MATHEMATICAL MODELING OF THE ELECTRONIC STRUCTURE USING ELECTROMAGNETIC FIELD THEORY METHODS FOR EXPLORATION SYSTEMS BASED ON UAVS

In this article, the authors consider the possibility of using the method of electromagnetic field theory for mathematical modeling of the electronic structure of exploration systems on UAVs.