The paper studies the inferences of wave equations for electromagnetic fields when there are gravitational fields at the same time. In the description with the algebra of octonions, the inferences of wave equations are identical with that in conventional electromagnetic theory with vector terminology. By means of the octonion exponential function, we can draw out that the electromagnetic waves are transverse waves in a vacuum, and rephrase the law of reflection, Snell's law, Fresnel formula, and total internal reflection etc. The study claims that the theoretical results of wave equations for electromagnetic strength keep unchanged in the case for coexistence of gravitational and electromagnetic fields. Meanwhile the electric and magnetic components of electromagnetic waves can not be determined simultaneously in electromagnetic fields.
It is argued that once we consider the underpinning of a Non Commutative geometry, itself symptomatic of extended particles, for example in Quantum Superstring theory, then a reconciliation between gravitation and electromagnetism is possible.
We obtain Hamilton equations for the gravitational field and demonstrate the conservation of total energy. We derive the Poisson bracket equation for a general dynamical variable.
A new geometry, called General geometry, is constructed. It is proven that its the most simplest special case is geometry underlying Electromagnetism. Another special case is Riemannian geometry. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. It is shown that equation of motion for a particle interacting with electromagnetic field coincides exactly with equation for geodesics of geometry underlying Electromagnetism. It is also shown that Electromagnetism can not be geometrized in the framework of Riemannian ge…
In the context of a Planck scale underpinning for the universe, we argue that both gravitation and electromagnetism can be characterized in a unified way, in a Sakharov like description. We also consider the issue of observed gamma radiation, which recent observations seem to indicate are caused by the annihilation of exotic $Mev$ particles, as indeed was theoretically predicted earlier. Some other problems are also considered.
The proposed temporal fluctuations model attempt for a unitary vision on gravity, electromagnetism and inertia. On obtain Newton law of gravitation and Coulomb law by starting from simple principles. On obtain too the main results of General Relativity Theory and Electromagnetism. One of the major points of present work is to obtain unified potential, which allow a unitary description of gravity and electromagnetism. As consequence, on obtain supplemental effects responsible for conservation laws violation in certain closed systems. On maintain the validity of conservation laws only if those s…
Maxwell's equations comprise both electromagnetic and gravitational fields. The transverse part of the vector potential belongs to magnetism, the longitudinal one is concerned with gravitation. The Coulomb gauge indicates that longitudinal components of the fields propagate instantaneously. The delta-function singularity of the field of the divergence of the vector potential, referred to as the dilatation center, represents an elementary agent of gravitation. Viewing a particle as a source or a scattering center of the point dilatation, the Newton's gravitation law can be reproduced.
The attempts to unify electromagnetism and gravitation have included the formulations of Herman Weyl and the Kaluza Klein theory with the fifth dimension. More recently there have been fruitful attempts in the domain of Quantum Superstrings and the author's formulation in terms of Quantum Mechanical Kerr-Newman Black Holes. Though all these appear to be widely divergent approaches, they are shown to have a unified underpinning in the context of quantized fractal space time.
We show that gravitational mass and inertial mass are correlated by an adimentional factor, which in specific electromagnetic conditions, can be reduced, nullified, negated, and increased. Some theoretical consequences of the mentioned correlation are: the generalization of Newton=92s second law for the motion (New law for Inertia); the deduction of the differential equation for entropy (second law of Thermodynamics); unification of gravitational and electromagnetic interactions .
It is argued that there is a connection between the fundamental forces of electromagnetism and gravitation. This connection occurs because of: 1) the fundamental significance of the finite and invariant velocity of light in inertial reference frames in the special theory, and 2) the reliance of the general theory of relativity upon the special theory of relativity locally in spacetime. The connection between the fundamental forces of electromagnetism and gravitation follows immediately from these two points. A brief review is provided of: 1) the role of the finite and invariant velocity of lig…
In the context of the fact that the existence of dark energy causing the accelerated expansion of the universe has been confirmed by the WMAP and the Sloan Digital Sky Survey, we re-examine gravitation itself, starting with the formulation of Sakharov and show that it is possible to obtain gravitation in terms of the electromagnetic charge of elementary particles, once the ZPF and its effects at the Compton scale are taken into account.
Does a physical field exist independently of the interaction between the field source and the test body used to measure it at a given point? What does propagate between two physical bodies when they interact? These are the fundamental questions we answer in the present work for electromagnetic and gravitational interactions. We come to the conclusion that gravitational fields as well as spacetime curvature cannot depend on the passive-gravitational to inertial mass ratio of the test bodies, because this would lead to energy conservation and causality violation except when this ratio is univers…
Monogenic functions are functions of null vector derivative and are here analysed in the geometric algebra of 5-dimensional spacetime, G(4,1), in order to derive several laws of fundamental physics. The paper introduces the working algebra and the definition of monogenic functions, showing that these generate two 4-dimensional spaces, one with Euclidean signature and the other one with Minkowski signature. The equivalence conditions between the two spaces are studied and relativistic dynamics, not entirely coincident with Einstein's general theory of relativity, is demonstrated. The monogenic …
The classical theory of electromagnetism has been revisited and the possibility of longitudinal photon wave is explored. It is shown that the emergence of longitudinal wave is a consequence of Lorenz gauge (condition) violation. Proca, Vlaenderen & Waser and Arbab theories are investigated.
Following the line of the history, if by one side the electromagnetic theory was consolidated on the 19th century, the emergence of the special and the general relativity theories on the 20th century opened possibilities of further developments, with the search for the unification of the gravitation and the electromagnetism on a single unified theory. Some attempts to the geometrization of the electromagnetism emerged in this context, where these first models resided strictly on a classical basis. Posteriorly, they were followed by more complete and embracing quantum field theories. The presen…
A theory which achieves a complete geometrical unification of gravitation and electromagnetism (GUGE) is presented. This new theory is based on a recent proposal of proper time redefinition that leads to the construction of a Riemann metric, which naturally unifies gravity and electromagnetism. The 5--dimensional Riemann metric which arises looks exactly the same as the one postulated in the Kaluza-Klein (KK) 5-dimensional theory. Nevertheless, there are deep differences between GUGE and KK. The GUGE metric is deduced while the KK metric is postulated. In the GUGE field theory there is no need…
In 1909 the brothers E. and F. Cosserat discovered a new nonlinear group theoretical approach to elasticity (EL), with the only experimental need to measure the EL constants. In a modern language, their idea has been to use the nonlinear Spencer sequence instead of the nonlinear Janet sequence for the Lie groupoid defining the group of rigid motions of space. Following H. Weyl, our purpose is to compute for the first time the nonlinear Spencer sequence for the Lie groupoid defining the conformal group of space-time in order to provide the physical foundations of both electromagnetism (EM) and …
After many fruitless decades of trying to unify electromagnetism and gravitation, it is now being realized that this can be done only in discrete spacetime, as indeed the author had demonstrated. In this context, a unified description of gravitation and electromagnetism is provided within the framework of a gauge like formulation. Following the discrete spacetime structure, we then argue that the underpinning for the universe is an array of Planck scale oscillators.
Defining the generalized charge, potential, current and generalized fields as complex quantities where real and imaginary parts represent gravitation and electromagnetism respectively, corresponding field equation, equation of motion and other quantum equations are derived in manifestly covariant manner. It has been shown that the field equations are invariant under Lorentz as well as duality transformations. It has been shown that the quaternionic formulation presented here remains invariant under quaternion transformations.
The generalization of Einstein's special theory of relativity (SRT) is proposed. In this model the possibility of unification of scalar gravity and electromagnetism into a single united field is considered. Formally, the generalization of the SRT is that instead of (1+3)-dimensional Minkowski space the (1+4)-dimensional extension G is considered. As a fifth additional coordinate the interval S is used. This value is saved under the usual Lorentz transformations in Minkowski space M, but it changes when the transformations in the extended space G are used. We call this model the extended space …
We will provide detailed arguments showing that the set of Maxwell equations, and the corresponding wave equations, do not properly describe the evolution of electromagnetic wave-fronts. We propose a nonlinear corrected version that is proven to be far more appropriate for the modellization of electromagnetic phenomena. The suitability of this approach will soon be evident to the reader, through a sequence of astonishing congruences, making the model as elegant as Maxwell's, but with increased chances of development. Actually, the new set of equations will allow us to explain many open questio…
Postulating the existence of magnetic monopole in electromagnetism and Heavisidian monopoles in gravitational interactions, a unified theory of gravi-electromagnetism has been developed on generalizing the Schwinger-Zwanziger formulation of dyon to quaternion in simple and consistent manner. Starting with the four Lorentz like forces on different charges, we have generalized the Schwinger-Zwanziger quantization parameters in order to obtain the angular momentum for unified fields of dyons and gravito-dyons (i.e. Gravi-electromagnetism). Taking the unified charge as quaternion, we have reformul…
A principle on the macroscopic motion of systems in thermodynamic equilibrium, rarely discussed in texts, is reviewed: Very small but still macroscopic parts of a fully isolated system in thermal equilibrium move as if points of a rigid body, macroscopic energy being dissipated to increase internal energy, and increase entropy along. It appears particularly important in Space physics, when dissipation involves long-range fields at Electromagnetism and Gravitation, rather than short-range contact forces. It is shown how new physics, Special Relativity as regards Electromagnetism, first Newtonia…
Using the Einstein energy-mass relation and a concept of cross-correlating material unit-fields (pp. 1-148), the quantum equation for united gravitation and electromagnetism is derived (pp. 148-164). The unified equation yields all known solutions to the Dirac equation, for example, the fine and hyperfine structure of the atom spectrum. Moreover, the model explains physical nature of the spin and anomalous gyromagnetic factor of an electron, as well as the Pauli exclusion principle. For weak fields, in the classical limit, the model simplifies to the Lorentz-Maxwell electromagnetism and the so…
Some connections between quantum mechanics and classical physics are explored. The Planck-Einstein and De Broglie relations, the wavefunction and its probabilistic interpretation, the Canonical Commutation Relations and the Maxwell--Lorentz Equation may be understood in a simple way by comparing classical electromagnetism and the photonic description of light provided by classical relativistic kinematics. The method used may be described as `inverse correspondence' since quantum phenomena become apparent on considering the low photon number density limit of classical electromagnetism. Generali…
An attempt has been made to analyse the the role of octonions in various unified field theories associated with dyons and the dark matter. Starting with the split octonion al- gebra and its properties, we have discussed the octonionic unified gauge formulation for SU(2) ?X U(1) electroweak theory and SU(3) X? SU(2) ?X U(1) grand unified theory. De- scribing the octonion eight dimensional space as the combination of two quaternionic spaces (namely associated with the electromagnetic interaction (EM-space) and linear gravitational interaction (G-space)), we have reexamined the unified picture of…
The mere principle of relativity and Lorentz transformations for the mass current predict, in close analogy to electromagnetism, the existence of gravitomagnetic fields. With the reasonable assumption of the non existence of a gravitomagnetic mass, a parameter-free set of equations for "effective" vector gravitoelectromagnetism results. As a consequence gravity propagates at the speed of light in a flat Minkowski space and quadrupole gravitational radiation, consistent with energy balance, is predicted with the same value of GR. Heuristic considerations relate gravitational radiation to the st…
A fraction of energy is theoretically predicted to be captured from electromagnetic field to form a gravitating mass, when a low-mass charged particle enters the strong field from a region of no electromagnetism. In this paper the mass variation has been calculated for a charged particle on free-fall in the constraint electromagnetic field. It has been shown that there is an evident effect to the variation in mass when the low-mass charged particle is in the strong field.
Based on first principles solutions in a unified framework of quantum mechanics and electromagnetism we predict the presence of a universal attractive depolarisation radiation (DR) Lorentz force ($F$) between quantum entities, each being either an IED matter particle or light quantum, in a vacuuonic dielectric vacuum. Given two quantum entities $i=1,2$ of either kind, of characteristic frequencies $ν_i^0$, masses $m_i^0=hν_i^0 / c^2$ and separated at a distance r^0, the solution is $F=- G m_1^0 m_2^0/ (r^0)^2$, where $G= χ_0^2 e^4/12 π^2 ε_0^2 ρ_λ$, $χ_0$ is the susceptibility and $ρ_λ$ is the…
This paper is intended to investigate the relation between electrodynamics in anisotropic material media and its analogous formulation in an spacetime, with non-null Riemann curvature tensor. After discussing the electromagnetism via chiral differential forms, we point out the optical activity of a given material medium, closely related to topological spin, and the Faraday rotation, associated to topological torsion. Both quantities are defined in terms of the magnetic potential and the electric and magnetic fields and excitations. We revisit some properties of material media and the associate…
A Lagrangian depending on geometric variables (metric, affine connection, gauge group generators) is given which maintains compatibility with General Relativity. It generates the dynamics for Electromagnetism and other Gauge Fields along with Gravitation, at the time it gives a geometric foundation for the stress-energy tensor of continuous matter. The geometric-invariance principle under this integration is exposed and the resulting field equations are obtained. The theory is developed over the tangent space of a four-dimensional real manifold and the generators become those from the Homogeno…
Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal coframe theta and a (metric compatible) Lorentz connection Gamma. These two potentials yield the field strengths torsion T and curvature R. Evans tried to infuse electromagnetic properties into this geometrical framework by putting the coframe theta to be proportional to four extended electromagnetic potentials A; these are assumed to encompass the conventional Maxwellian potential in a suit…
