Classical unified fields: physical space (original) (raw)
Related papers
A unified theory of gravity and electromagnetism: Classical and quantum aspects
Pramana
Milne cosmology has recently been shown to be in broad agreement with most cosmological data while being free of the problematic notions of standard cosmology such as the dark sector. In this paper a broken symmetric unified theory of gravity and electromagnetism is introduced which has a Milne metric under a certain geometric condition. Strikingly, particles (dyons) emerge as topological charges in this theory provided the torsion vector Γ i is curl-less.
arXiv (Cornell University), 2010
We propose in this paper a mathematicians' view of the Kaluza-Klein idea of a five dimensional space-time unifying gravitation and electromagnetism. By considering the classification of positive Einstein curvature tensors and the classical Cauchy-Choquet-Bruhat theorems in general relativity, we introduce concepts of types and rigidity. Then, abandoning the usual requirement of a Ricci-flat five dimensional space-time, we show that a unified geometrical frame can be set for gravitation and electromagnetism, giving, by projection on the classical 4-dimensional space-time, the known Einstein-Maxwell-Lorentz equations for charged fluids. Thus, although not introducing, at least at this stage, new physics, we get a very aesthetic presentation of classical physics in the spirit of general relativity. The usual physical concepts, such as mass, energy, charge, trajectory, Maxwell-Lorentz law, are shown to be only various aspects of the geometry, for example curvature, of space-time considered as a Lorentzian manifold; that is no physical objects are introduced in space-time, no laws are given, everything is only geometry! This work is therefore in the continuation of the various attempts made since Einstein, Weyl, Nordstrom, Kaluza, Klein, Rainich, Wheeler.
On the Equivalence Principle and a Unified Description of Gravitation and Electromagnetism
1999
We first investigate the form the General Relativity Theory would have taken had the gravitational mass and the inertial mass of material objects been different. We then extend this analysis to electromagnetism and postulate an equivalence principle for the electromagnetic field. We argue that to each particle with a different electric charge-to-mass ratio in superimposed gravitational and electromagnetic fields there corresponds a spacetime manifold whose metric tensor gmunug_{\mu\nu}gmunu describes the dynamical actions of gravitation and electromagnetism. The electric field outside a charged sphere asserts itself independently rather than contributing to the gravitational field. The contribution of the electric field to the spacetime metric outside the charged sphere is shown to be similar to the gravitational one in the Schwartzschild metric but with a charge-to-mass ratio dependence of the test particle instead of the Reissner - Nordstr\"om metric, resulting in a unified descripti...
General relativity as a unified fluid and field theory
Journal of Physics: Conference Series
Einstein's dream for a unified field theory of Nature is attained with a classical fluid theory founded on space, time and spin, rather than on Einstein's spacetime. An invariant quantum theory for the primordial fluid obeys the homogeneous Klein-Gordon equation, which is the same three-dimensional classical wave equation (CWE) initially tried by Schrödinger to formulate quantum mechanics (QM), but abandoned by linear superposition considerations. Primordial fluid pervades universe, obeys energy and momentum conservation, and is formed by sagions: energy-like, discrete, extended Planck-size objects of finite size, carriers of linear momentum and spin, moving in absolute 3D-curved space with speed C along straightest path. We briefly describe our novel non-harmonic and inherently quantized solutions for CWE in spherical coordinates, discovered in 1995. Solutions include a steady-state background field (possibly related to the CMB, to non-locality, and to action-at-a-distance), quantized helices, and inherently quantized functions exhibiting stable dynamic equilibrium, and isomorphism under many transformations, including the classical Doppler case, and the relativistic Lorentz, Poincaré, and Einstein transformations. Isomorphism preempts ab initio a few interpretative issues regarding relativistic and classical transformations. Mathematical fields represent the realistic physical temporal evolution of the primordial fluid in curved 3D-space.
2009
The Gravitational, Electromagnetic, Weak & the Strong force are here brought together under a single roof via an extension of Reimann geometry to a new geometry (coined Reimann-Hilbert Space); that unlike Reimann geometry, preserves both the length and the angle of a vector under parallel transport. The affine connection of this new geometry-the Reimann-Hilbert Space, is a tensor and this leads us to a geodesic law that truly upholds the Principle of Relativity. The geodesic law emerging from the General Theory of Relativity (GTR) is well known to be in contempt of the Principle of Relativity which is a principle upon which the GTR is founded. The geodesic law for particles in the GTR must be formulated in special (or privileged) coordinate systems i.e. gaussian coordinate systems whereas the Principle of Relativity clearly forbids the existence of special (or privileged) coordinate systems in manner redolent of the way the Special Theory of Relativity forbids the existence of an absolute (or privileged) frame of reference. In the low energy regime and low spacetime curvature the unified field equations derived herein are seen to reduce to the well known Maxwell-Procca equation, the none-abelian nuclear force field equations, the Lorentz equation of motion for charged particles and the Dirac Equation. Further, to the already existing four known forces, the theory predicts the existence of yet another force. We have coined this the super-force and this force obeys S U(4, 4) gauge invariance. Furthermore, unlike in the GTR, gravitation is here represented by a single scaler potential, and electromagnetic field and the nuclear forces are described by the electromagnetic vector potential (A µ) which describes the metric tensor i.e. g µν = A µ A ν. From this (g µν = A µ A ν), it is seen that gravity waves may not exist in the sense envisaged by the GTR.
On the Equivalence Principle and a Unified Metric Description of Gravitation and Electromagnetism
2017
We first investigate the form the General Relativity theory would have taken had the gravitational mass and the inertial mass of material objects been different. We then extend this analysis to electromagnetism and postulate an equivalence principle for the electromagnetic field. We argue that to each particle with a different electric charge-to-mass ratio in superimposed gravitational and electromagnetic fields there corresponds a spacetime manifold whose metric tensor gμν describes the dynamical actions of gravitation and electromagnetism. The electric field outside a charged sphere asserts itself independently rather than contributing to the gravitational field. The contribution of the electric field to the spacetime metric outside the charged sphere is shown to be similar to the gravitational one in the Schwartzschild metric but with a charge-to-mass ratio dependence of the test particle instead of the Reissner Nordström metric, resulting in a unified description of gravitation ...
A Gauge-theoretical Treatment of the Gravitational Field: Classical
2008
In the geometrodynamical setting of general relativity one is concerned mainly with Riemannian metrics over a manifold M . We show that for the space M := Riem(M), we have a natural principal fiber bundle (PFB) structure Diff(M) →֒ M π → M/Diff(M), first hinted at in [1]. This construction makes the gravitational field amenable to exactly the same gauge-theoretic treatment given in [2], where it is used to separate rotational and vibrational degrees of freedom of n-particle systems, both classically and quantum mechanically. Furthermore, we show how the gauge connection in this PFB setting can be seen as a realization of Mach’s Principle of Relative Motion, in accordance with Barbour’s et al work on timeless gravitational theories [3] using best-matching. We show Barbour’s reconstruction of GR is obtained by requiring the connection to be the one induced by the deWitt metric in M. As a simple application of the gauge theory, we put the ADM lagrangian in a Kaluza-Klein context, in wh...
A Note on the Gravitational Equations Analogous to Maxwell's Electromagnetic Equations
viXra, 2017
Ever since Oliver Heaviside's suggestion of the possible existence of a set of equations, analogous to Maxwell's equations for the electromagnetic field, to describe the gravitational field, others have considered and built on the original notion. However, if such equations do exist and really are analogous to Maxwell's electromagnetic equations, new problems could arise related to presently accepted notions concerning special relativity. This note, as well as offering a translation of a highly relevant paper by Carstoiu, addresses these concerns in the same manner as similar concerns regarding Maxwell's equations were.
An approach to electromagnetism from the general relativity
2010
Classical gravitation is so similar to the electrostatic that the possible unification has been investigated for many years. Although electromagnetism is formulated now successfully by quantum field theory, this paper proposes a simple approach to describe the electromagnetism from the macroscopic perspective of general relativity. The hypothesis is based on two charged particles that cause disturbance energy sufficient to disrupt the space-time and explain approximately Maxwell's equations. Therefore, with such this simple idea, we suggest the possibility that the geometric relationship between electromagnetism and gravitation is not yet fully exhausted.
arXiv: General Relativity and Quantum Cosmology, 2005
The formalism of electric - magnetic duality, first pioneered by Reinich and Wheeler, extends General Relativity to encompass non-Abelian fields. Several energy Tensors T^uv with non-vanishing trace matter are developed solely as a function of the field strength tensor F^uv, including the Euler tensor, and tensors for matter in flux, pressure in flux, and stationary pressure. The spacetime metric g_uv is not only a solution to the second-order Einstein equation based on T^uv, but is also constrained by a third-order equation involving the Bianchi identity together with the gravitational energy components kappa_u for each T^uv. The common appearance of F^uv in all of the T^uv and kappa_v makes it possible to obtain quantum solutions for the spacetime metric, thereby geometrizing quantum physics as a non-linear theory.