On a Four Dimensional Unified Field Theory of the Gravitational, Electromagnetic, Weak and the Strong Force (original) (raw)
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On a Generalized Theory of Relativity
2010
The General Theory of Relativity (GTR) is essentially a theory of gravitation. It is built on the Principle of Relativity. It is bonafide knowledge, known even to Einstein the founder, that the GTR violates the very principle upon which it is founded i.e., it violates the Principle of Relativity; because a central equation i.e., the geodesic law which emerges from the GTR, is well known to be in conflict with the Principle of Relativity because the geodesic law, must in complete violation of the Principle of Relativity, be formulated in special (or privileged) coordinate systems i.e., Gaussian coordinate systems. The Principle of Relativity clearly and strictly forbids the existence/use of special (or privileged) coordinate systems in the same way the Special Theory of Relativity forbids the existence of privileged and or special reference systems. In the pursuit of a more Generalized Theory of Relativity i.e., an all-encampusing unified field theory to include the Electromagnetic, Weak & the Strong force, Einstein and many other researchers, have successfully failed to resolve this problem. In this reading, we propose a solution to this dilemma faced by Einstein and many other researchers i.e., the dilemma of obtaining a more Generalized Theory of Relativity. Our solution brings together the Gravitational, Electromagnetic, Weak & the Strong force under a single roof via an extension of Riemann geometry to a new hybrid geometry that we have coined the Riemann-Hilbert Space (RHS). This geometry is a fusion of Riemann geometry and the Hilbert space. Unlike Riemann geometry, the RHS preserves both the length and the angle of a vector under parallel transport because the affine connection of this new geometry, is a tensor. This tensorial affine leads us to a geodesic law that truly upholds the Principle of Relativity. It is seen that the unified field equations derived herein are seen to reduce to the well known Maxwell-Procca equation, the non-Abelian nuclear force field equations, the Lorentz equation of motion for charged particles and the Dirac equation.
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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.
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.
Foundations of Relativistic Gravithermodynamics
Foundations of Relativistic Gravithermodynamics. Publishing house “TVORY”, Vinnytsia, 2022
The cardinal difference between relativistic gravithermodynamics (RGTD) and general relativity (GR) is that in RGTD the extranuclear thermodynamic characteristics of matter are used in the tensor of energy-momentum to describe only its quasi-equilibrium motion. For the description of the inertial motion in RGTD only the hypothetical intranuclear gravithermodynamic characteristics of matter are used. Exactly this fact allows avoid the necessity of nonbarionic dark matter in the Universe in principle. Evolutionary self-contraction of microobjects of lower layers of gravithermodynamically bonded matter outpaces the similar self-contraction of its upper layers. This is the exact reason of the curvature of intrinsic space of matter. That is why gravitational field itself should be primarily considered as the field of spatial inhomogeneity of evolutionary decreasing of the size of matter microobjects in the background Euclidean space of expanding Universe. In correspondence to this the gravitational field itself is the field of spatial inhomogeneity of gravithermodynamic state of dense matter of compact astronomical objects, as well as of strongly rarefied gas-dust matter of space vacuum. And, therefore, the gravitational field fundamentally cannot exist without matter. That is why it is not an independent form of matter. It is shown that equations of the gravitational field of GR should be considered as equations of spatially inhomogeneous gravithermodynamic state of only utterly cooled down matter. This matter can only be the hypothetical substances such as ideal gas, ideal liquid and the matter of absolutely solid body. The real matter will be inevitably cooling down for infinite time and never will reach the state that is described by the equations of gravitational field of the GR. Only conditional identity of inertial mass of moving matter to its gravitational mass only by gravity-quantum clock, which is located in the point, from which the matter started its inertial motion, and due to the usage of corrected value of gravitational constant in its pseudo-centric intrinsic frame of reference of spatial coordinates and time, is justified. This is related to the equivalence of inertial mass of matter to the Hamiltonian of its inert free energy, while the gravitational mass of matter is equivalent to the Lagrangian of its ordinary internal energy. It was proved that total energy of matter of inertially moving body is equal in all global gravithermodynamic frames of references of spatial coordinates and time (GT-FR) that are also inertially moving relatively to matter. The temporal invariance of not only the momentum but also of Lagrangian of ordinary internal energy and of equivalent to it gravitational mass of matter is justified. And that is precisely why there is the temporal invariance and a conform Lorentz-invariance of thermodynamic potentials and parameters in examined modification of transformations of the special theory of relativity (SR). Conformal relativistic transformations of increments of metrical spatial segments and metrical temporal intervals (instead of increments of coordinates and coordinate time of SR) were received. Exactly this fact allows avoid not only the twins paradox when twins are inertially moving but also the necessity of the dark energy in the Universe. It is also shown that the tensor of energy-momentum of matter (right side of the gravitational field equation) should be formed not being based on external thermodynamic parameters, but being based exactly on the intranuclear gravithermodynamic parameters. In this case the observed motion of astronomical objects of the galaxies is provided at arbitrary small density of mass of the matter on their periphery and, consequently, the presence of dark non-baryonic matter in the Universe is unnecessary. Of course, bodies free fall in gravitational field is an original realization of their tendency to increase the evolutionary self-contraction of microobjects of their matter, and the realization of the tendency of the whole gravitationally bonded inhomogeneous matter to the minimum of the integral values of its inert free energy and thermodynamic Gibbs free energy. Bodies that fall accelerate independently in spatially inhomogeneous medium of the outer space or atmosphere. Such bodies transform their continuously released intra-atomic energy into kinetic energy. It is shown that in case of bodies’ free fall the gravitational deceleration of the rate of their intrinsic time is completely compensated by the motion due to isotropic all-round conformal gauge self-contraction of the size of falling bodies in the background Euclidean space of the Universe. Clocks that fall free are inertially moving and, therefore, continue to count time at the same rate as when they were in the state of rest. Similarly, the rate of time of astronomical body is not changed in the process of its motion in elliptical orbit. The dilatation of intrinsic time of distant galaxies is also absent, which points on the fact that Etherington identity does not correspond to reality. The fact that Hubble’s redshift is linearly dependent on transversal comoving distance instead of luminosity distance is justified. It is shown that mentioned above fact corresponds to astronomical observations. According to this the presence of dark energy in the Universe is also unnecessary. For the collective gravithermodynamic Gibbs microstates the connection between all thermodynamic potentials and parameters of matter have been found. This connection is realized with the help of several wave functions that can take arbitrary values with certain probability. The quantum equation of gravitational field have been found, the solutions of which set the spatial distribution of gravitational radius of matter in its every new gravithermodynamic state with the polynomial function with the next more high degree. The indicator of the degree of this function of continuously cooling down matter can successively take only integer and semi-integer values. That is why the process of cooling down of the whole RGTD-bonded matter is the quantum process that is caused by its spontaneous transition to the polynomial function with more high value of degree and, therefore, to the next quantum collective state.
A Generalized Theory of Gravitation
Reviews of Modern Physics, 1948
' 'N the following we shall give a new presentation of the generalized theory of gravitation, which constitutes a certain progress in clarity as compared to the previous presentations. * It is our aim to achieve a theory of the total field by a generalization of the concepts and methods of the relativistic theory of gravitation. i. THE FIELD STRUCTURE The theory of gravitation represents the field by a symmetric tensor g;~, i.e. , g;q=gq;(i, k=&,~, 4), where the g,t ar e real functions of Xgp ' ' ' X4 In the generalized theory the total field is represented by a Hermitian tensor. The symmetry property of the (complex) g;& is gik gkiĨ f we decompose g,& into its real and imaginary components, then the former is a symmetric tensor (g;&), the latter an antisymmetric tensor (gp). The g;s are still functions of the real variables x~, .~, x4.