Toward Nonlocal Electrodynamics of Accelerated Systems

We revisit acceleration-induced nonlocal electrodynamics and the phenomenon of photon spin-rotation coupling. The kernel of the theory for the electromagnetic field tensor involves parity violation under the assumption of linearity of the field kernel in the acceleration tensor. However, we show that parity conservation can be maintained by extending the field kernel to include quadratic terms in the acceleration tensor. The field kernel must vanish in the absence of acceleration; otherwise, a general dependence of the kernel on the acceleration tensor cannot be theoretically excluded. The physical implications of the quadratic kernel are briefly discussed.

A Scale-Invariant, Machian Theory of Gravitation and Electrodynamics Unified

As gravitation and electromagnetism are closely analogous long-range interactions, and gravitation is formulated in terms of geometry in general relativity (GR), we expect the latter also to appear through the geometry. This unification has however remained an unfulfilled goal. The goal is achieved here in a new theory, which results from the principles of equivalence and Mach supplemented with a novel insight that the field tensors in a geometric theory of gravitation and electromagnetism must be traceless, since these long-range interactions are mediated by virtual exchange of massless particles whose mass is expected to be related to the trace of the field tensors. Hence the Riemann tensor, like the analogous electromagnetic field tensor, must be traceless. Thence emerges a scale- invariant, Machian theory of gravitation and electrodynamics unified, wherein the vanishing of the Ricci tensor appears as a boundary condition. While the field equations of the theory are given by the vanishing divergence of the respective field tensors and their duals, the matter and charge emerge from the spacetime. A quantitative formulation of the emergent fields embodied in ‘energymomentum super tensors’ follows from the respective Bianchi identities for the two fields. The resulting theory is valid at all scales and explains the observations without invoking the non-baryonic dark matter, dark energy or inflation. Moreover, it answers the questions that the GR-based standard paradigm could not address.

A scale-invariant, Machian theory of gravitation and electrodynamics unified

As gravitation and electromagnetism are closely analogous long-range interactions, and the current formulation of gravitation is given in terms of geometry, we expect the latter also to appear through the geometry. This unification has however, remained an unfulfilled goal. The goal is achieved here in a new theory, which results from the principles of equivalence and Mach supplemented with a novel insight that the field tensors in a geometric theory of gravitation and electromagnetism must be traceless, since these long-range interactions are mediated by virtual exchange of massless particles whose mass is expected to be related to the trace of the field tensors. Hence, the Riemann tensor, like the analogous electromagnetic field tensor, must be traceless. Thence emerges a scale-invariant, Machian theory of gravitation and electrodynamics unified, wherein the vanishing of the Ricci tensor appears as a boundary condition. While the field equations of the theory are given by the vanishing divergence of the respective field tensors and their duals, the matter and charge emerge from the spacetime. A quantitative formulation thereof, embodied in “energy-momentum super tensors”, follows from the respective Bianchi identities for the two fields. The resulting theory is valid at all scales and explains the observations without invoking the non-baryonic dark matter, dark energy or inflation. Moreover, it answers the questions that the general relativity-based standard paradigm could not address.

A Scale-Invariant, Machian Theory of Gravitation and Electrodynamics Unified

As gravitation and electromagnetism are closely analogous long-range interactions, and gravitation is formulated in terms of geometry in general relativity (GR), we expect the latter also to appear through the geometry. This unification has however remained an unfulfilled goal. The goal is achieved here in a new theory, which results from the principles of equivalence and Mach supplemented with a novel insight that the field tensors in a geometric theory of gravitation and electromagnetism must be traceless, since these long-range interactions are mediated by virtual exchange of massless particles whose mass is expected to be related to the trace of the field tensors. Hence the Riemann tensor, like the analogous electromagnetic field tensor, must be traceless. Thence emerges a scale- invariant, Machian theory of gravitation and electrodynamics unified, wherein the vanishing of the Ricci tensor appears as a boundary condition. While the field equations of the theory are given by the vanishing divergence of the respective field tensors and their duals, the matter and charge emerge from the spacetime. A quantitative formulation of the emergent fields embodied in ‘energymomentum super tensors’ follows from the respective Bianchi identities for the two fields. The resulting theory is valid at all scales and explains the observations without invoking the non-baryonic dark matter, dark energy or inflation. Moreover, it answers the questions that the GR-based standard paradigm could not address.

Electromagnetism and special relativity

In 1905, when Einstein published his theory of special relativity, Maxwell’s work was already about forty years old. It is therefore both remarkable and ironic (recalling the old arguments about the aether being the ‘preferred’ reference frame for describing wave propagation) that classical electrodynamics turned out to be a relativistically correct theory. In this chapter, a range of questions in electromagnetism are considered as they relate to special relativity. In Questions 12.1–12.4 the behaviour of various physical quantities under Lorentz transformation is considered. This leads to the important concept of an invariant. Several of these are encountered, and used frequently throughout this chapter. Other topics considered include the transformationof E- and B-fields between inertial reference frames, the validity of Gauss’s law for an arbitrarily moving point charge (demonstrated numerically), the electromagnetic field tensor, Maxwell’s equations in covariant form and Larmor’s formula for a relativistic charge.

Solved Problems in Classical Electromagnetism

Apart from an introductory chapter which focuses mainly on some important mathematical concepts and analytical techniques, this book consists entirely of questions and solutions on topics in classical electromagnetism. The questions are divided into three categories according to their ‘level of difficulty’, and the book should appeal to students who are at different stages in their respective degrees. A wide range of topics are treated which include: the basic experimental laws of electricity and magnetism, Maxwell’s equations, electric and magnetic fields in vacuum and in matter, electromagnetic waves with applications to waveguides and antennas, the electromagnetic potentials, multipole expansions and multipole moments, gauge transformations, electric circuits, electromagnetic radiation, the electromagnetic field tensor and covariance. The solutions are usually followed by a set of comments intended to stimulate inductive reasoning and provide additional information of interest (including points of historical significance). Both analytical and numerical techniques are used to obtain and analyse solutions. The computer calculations use Mathematica (version 10), and the relevant code is given in the text. The book will be useful to students and lecturers in undergraduate and graduate-level courses on classical electromagnetism and in computational physics.

A Scale-Invariant, Machian Theory of Gravitation and Electrodynamics Unified

As gravitation and electromagnetism are closely analogous long-range interactions, and gravitation is formulated in terms of geometry in general relativity (GR), we expect the latter also to appear through the geometry. This unification has however remained an unfulfilled goal. The goal is achieved here in a new theory, which results from the principles of equivalence and Mach supplemented with a novel insight that the field tensors in a geometric theory of gravitation and electromagnetism must be traceless, since these long-range interactions are mediated by virtual exchange of massless particles whose mass is expected to be related to the trace of the field tensors. Hence the Riemann tensor, like the analogous electromagnetic field tensor, must be traceless. Thence emerges a scale- invariant, Machian theory of gravitation and electrodynamics unified, wherein the vanishing of the Ricci tensor appears as a boundary condition. While the field equations of the theory are given by the vanishing divergence of the respective field tensors and their duals, the matter and charge emerge from the spacetime. A quantitative formulation of the emergent fields embodied in ‘energymomentum super tensors’ follows from the respective Bianchi identities for the two fields. The resulting theory is valid at all scales and explains the observations without invoking the non-baryonic dark matter, dark energy or inflation. Moreover, it answers the questions that the GR-based standard paradigm could not address.

Lorentz force and ponderomotive force in the presence of a minimal length

In this work, according to the electromagnetic field tensor in the framework of generalized uncertainty principle (GUP), we obtain the Lorentz force and Faraday’s law of induction in the presence of a minimal length. Also, the ponderomotive force and ponderomotive pressure in the presence of a measurable minimal length are found. It is shown that in the limit [Formula: see text], the generalized Lorentz force and ponderomotive force become the usual forms. The upper bound on the isotropic minimal length is estimated.

VARIATIONAL FORMULATION OF EISENHART'S UNIFIED THEORY

Eisenhart's classical unified field theory is based on a non-Riemannian affine connection related to the covariant derivative of the electromagnetic field tensor. The sourceless field equations of this theory arise from vanishing of the torsion trace and the symmetrized Ricci tensor. We formulate Eisenhart's theory from the metric-affine variational principle. In this formulation, a Lagrange multiplier constraining the torsion becomes the source for the Maxwell equations.

Accelerated Lyra's Cosmology Driven by Electromagnetic Field in Inhomogeneous Universe

A new class of cylindrically symmetric inhomogeneous cosmological models for perfect fluid distribution with electromagnetic field is obtained in the context of Lyra's geometry. We have obtained solutions by considering the time dependent displacement field. The source of the magnetic field is due to an electric current produced along thez-axis. OnlyF12is a nonvanishing component of electromagnetic field tensor. To get the deterministic solution, it has been assumed that the expansionθin the model is proportional to the shearσ. It has been found that the solutions are consistent with the recent observations of type Ia supernovae, and the displacement vectorβ(t)affects entropy. Physical and geometric aspects of the models are also discussed in presence and absence of magnetic field.