An Outline of the Grand Unified Theory of Gauge Fields

This paper attempts to propose a grand unified guiding principle of gauge fields from the mathematical and physical picture of fiber bundles: it is believed that our universe may have more fundamental interactions than the four fundamental interactions, and the gauge fields of these fundamental interactions are just a unified gauge potential on the fiber bundle manifold or the components connected to the bottom manifold, that is, our universe;these components can meet the transformation of gauge potential, and even can be transformed from a fundamental interaction gauge potential to another fundamental interaction gauge potential, and can be summarized into a unified equation, namely the expression of the generalized gauge equation, corresponding to the gauge transformation invariance;so gauge transformation invariance is a necessary condition to unify field theory, but quantization of field is not a necessary condition;the four (or more) fundamental interaction fields of the universe are unified into a universal gauge field defined by the connection of the principal fiber bundle on the cosmic base manifold.

Unified Field Theory

In the Einstein field equations, the geometry or the curvature of space-time defined as depended on the distribution of mass and energy principally resides on the left-hand side is set identical to a non-geometrical tensorial representation of matter on the right-hand side. In one or another form, general relativity accords a direct geometrical significance only to the gravitational field while the other physical fields are not of space time. They reside only in space time. Less well known, though of comparable importance is Einstein’s dissatisfaction with the fundamental asymmetry between gravitational and non-gravitational fields and his contributions to develop a completely relativistic geometrical field theory of all fundamental interactions, a unified field theory. Of special note in this context and equally significant is Einstein’s demand to replace the symmetrical tensor field by a non-symmetrical one and to drop the condition gik = gki for the field components. Historically, many other attempts were made too, to extend the general theory of relativity’s geometrization of gravitation to non-gravitational interactions, in particular, to electromagnetism. Still, progress has been very slow. It is the purpose of this publication to provide a unified field theory in which the gravitational field, the electromagnetic field and other fields are only different components or manifestations of the same unified field by mathematizing the relationship between cause and effect under conditions of general theory of relativity.

A New Version of Unified Field Theory—Stochastic Quantum Space Theory on Particle Physics and Cosmology

Stochastic Quantum Space (SQS) theory is a new version of unified field theory based on three fundamental postulations: Gaussian Probability Postulation, Prime Numbers Postulation, Vacuon Postulation. It build a framework with theoretical results agree with many experimental data well. For more information, please refer to the PDF.

A NEW MODELLING METHOD FOR EVALUATING EXTERNAL DISTURBING POTENTIAL BASED ON THEORY OF UNIFIED REPRESENTATION OF GRAVITATIONAL FIELD

For a special use a new modelling method of evaluating external disturbing potential is presented in this paper.Being different from classical methods in physical geodesy this method is grounded upon the theory of unified representation of gravitational field.The models created in this way are particularly satisfactory for a high_speed computation of gravitational field in low altitude because they take account of topographic effects and have their kernel functions with simple structure and weak singularity.

Unified Field Theory in a Nutshell—Elicit Dreams of a Final Theory Series

The present reading is part of our on-going attempt at the foremost endeavour of physics since man began to comprehend the heavens and the earth. We present a much more improved Unified Field Theory of all the forces of Nature i.e. the gravitational, the electromagnetic, the weak and the strong nuclear forces. The proposed theory is a radical improvement of Professor Hermann Weyl’s supposedly failed attempt at a unified theory of gravitation and electromagnetism. As is the case with Professor Weyl’s theory, unit vectors in the proposed theory vary from one point to the next, albeit, in a manner such that they are—for better or for worse;compelled to yield tensorial affinities. In a separate reading, the Dirac equation is shown to emerge as part of the description of the these variable unit vectors. The nuclear force fields—i.e., electromagnetic, weak and the strong— together with the gravitational force field are seen to be described by a four-vector field Aμ, which forms part of the body of the variable unit vectors and hence the metric of spacetime. The resulting theory very strongly appears to be a logically consistent and coherent unification of classical and quantum physics and at the same time a grand unity of all the forces of Nature. Unlike most unification theories, the present proposal is unique in that it achieves unification on a fourdimensional continuum of spacetime without the need for extra-dimensions.

A NON-DUALISTIC UNIFIED FIELD THEORY OF GRAVITATION,ELECTROMAGNETISM AND SPIN

The wisdom of classicalunified field theories in the conceptual framework of Weyl, Eddington, Einstein and Schrodinger has often been doubted and in particular there does not appear to be any empirical reason why the Einstein-Maxwell (E-MJ theory needs to be geometrized. The crux of the matter is, however not whether the E-M theory is aesthetically satisfactory but whether it answers all the modern questions within the classical context. In particular, the E-M theory does not provide a classical platform from which the Dirac equation can be derived in the way Schrodinger's equation is derived from classical mechanics via the energy equation and the Correspondence Principle. The present paper presents a non-dualistic unified field theory (UFT) in the said conceptual framework as propounded by M. A. Tonnelat. By allowing the metric form ds2=g,dx dx and the non-degenerate two-form F=(1/2t)rdx dx to enter symmetrically into the theory we obtain a UFT which contains Einstein's General Relativity and the Born-Infeld electrodynamics as special cases. Above all, it is shown that the Dirac equation describing the electron in an 'external' gravito-electromagnetic field can be derived from the non-dualistic Einstein equation by a simple factorization if the Correspondence Principle is assumed.

A Very Simple Model Concerning the Unified Field Theory Basing on the Kronig-Penney-Model

In this paper, a very simple novel model is presented concerning the unified field theory (“theory of everything”). In the scope of this novel theory, it is assumed that matter, space and time are quantized. It is assumed that the space is subdivided into cubic elementary cells (space quanta), and in each of its eight corners a Delta potential is positioned. That means the Delta potentials are equidistantly arranged, so that the Delta potentials are forming a lattice similar to a crystal lattice in solid state physics. The novel theory is analogue to the Kronig-Penney model well-known in solid state physics: a crystal lattice comprises Delta potentials arranged equidistantly to one another, so the lattice space can be considered as being quantized by an array of equally spaced Delta potentials or the lattice space is divided into cubic elementary cells (space quanta). But instead of electrons, material quanta are inserted into the cubic elementary cells or space quanta. So the material quanta are not freely vibrating (unbound state), but are vibrating in a bound state with discrete energy levels separated by an energy gap. This is due to the presence of the array of Delta potentials. In the frame of this novel theory the Schr?dinger Equation for the Kronig-Penney-Model is not solved by differentiation, but the Schr?dinger Equation is integrated yielding the formula , by whose discussion the existence of an energy gap is revealed. This energy gap is responsible if the material quantum occurs as light quantum (photon) or mass quantum.

The Oscillating Universe Theory (To the Unified Field Theory)

This paper represents model of oscillating universe theory. We try to realize model of both electromagnetic waves and spectrum of elementary particles from the unified point of view. Consideration of problems of the gravitational optics and dark matter is developing from the solid crystal model for the vacuum. The vacuum is represented as a three-dimensional crystal lattice matter with a very small lattice period, much less than 10-26 cm. The oscillators are located at the nodes of an infinite lattice. It is shown that an infinite set of equations to describe the coupled oscillations of moving oscillators converges to a system of twelve equations. We have obtained the combined equations for a multicomponent order parameter in the form of the electric and magnetic vacuum polarization, which defines the spectrum and symmetry of normal oscillations in the form of elementary particles. Two order parameters—a polar vector and an axial vector— had to be introduced as electrical and magnetic polarization, correspondingly, in order to describe dynamic properties of vacuum. Vacuum susceptibility has been determined to be equal to the fine structure constant a. Unified interaction constant g for all particles equal to the double charge of Dirac monopole has been found (g = e/a, where e—electron charge). The fundamental vacuum constants are: g, a, parameters of length and parameters of time for electron and nucleon oscillations, correspondingly. Energy of elementary particles has been expressed in terms of the fundamental vacuum parameters, light velocity being equal to . The term mass of particle has been shown to have no independent meaning. Particle energy does have physical sense as wave packet energy related to vacuum excitation. Exact equation for particle movement in the gravitational field has been derived, the equation being applied to any relatively compact object: planet, satellite, electron, proton, photon and neutrino. The situation has been examined according to the cosmological principle when galaxies are distributed around an infinite space. In this case the recession of galaxies is impossible, so the red shift of far galaxies’ radiation has to be interpreted as the blue time shift of atomic spectra;it follows that zero-energy, and consequently electron mass are being increased at the time. Since physical vacuum has existed eternally, vacuum parameters can be either constant, or oscillating with time. It is the time oscillation of the parameters that leads to the growth of electron mass within the last 15 billion years and that is displayed in the red shift;the proton mass being decreased that is displayed in planet radiation.

Unified Theory of Fundamental Interactions

Based on local gauge invariance, four different kinds of fundamental interactions in nature are unified in a theory which has Gravitational Gauge Group gauge symmetry. In this approach, gravitational field, like electromagnetic field, intermediate gauge field, and gluon field, is represented by gauge potential. Four kinds of fundamental interactions are formulated in the similar manner, and therefore can be unified in a direct or semi-direct product group. The model discussed in this paper is a renormalizable quantum model and can be regarded as an extension of the standard model to gravitational interactions, so it can be used to study quantum effects of gravitational interactions.

A Perdurable Defence to Weyl’s Unified Theory

Einstein dealt a lethal blow to Weyl’s unified theory by arguing that Weyl’s theory was at the very best—beautiful, and at the very least, un-physical, because its concept of variation of the length of a vector from one point of space to the other meant that certain absolute quantities, such as the “fixed” spacing of atomic spectral lines and the Compton wavelength of an Electron for example, would change arbitrarily as they would have to depend on their prehistories. This venomous criticism of Einstein to Weyl’s theory remains much alive today as it was on the first day Einstein pronounced it. We demonstrate herein that one can overcome Einstein’s criticism by recasting Weyl’s theory into a new Weyl-kind of theory were the length of vectors are preserved as is the case in Riemann geometry. In this New Weyl Theory, the Weyl gauge transformation of the Riemann metric gμν?and the Maxwellian electromagnetic field Aμ?are preserved.

Unification of Non-Abelian SU(N) Gauge Theory and Gravitational Gauge Theory

In this paper, a general theory on unification of non-Abelian SU(N) gauge interactions and gravitationalinteractions is discussed. SU(N) gauge interactions and gravitational interactions are formulated on the similar basisand are unified in a semi-direct product group GSU(N). Based on this model, we can discuss unification of fundamentalinteractions of Nature.

考虑围岩膨胀特性的深埋圆形隧道弹塑性统一解

针对隧道及地下工程中围岩吸水膨胀导致应力与位移场变化难以量化的问题,基于弹塑性与湿度应力场理论,采用统一强度理论与非关联流动法则,推导考虑中间主应力效应与围岩吸水膨胀特性的深埋圆形隧道弹塑性统一解.首先,结合考虑湿度变化的平衡方程与本构方程,获得围岩弹性状态下的应力与位移解;然后,提出围岩弹塑性状态的判定方法,并基于统一强度理论推导围岩塑性状态下的解析解;最后,通过算例对比分析验证本文所推统一解的准确性,并进一步探究中间主应力、湿度膨胀系数以及含水率变化对围岩应力场与塑性区半径的影响规律,研究结果表明:本文与已有文献所求塑性区半径偏差仅为0.136%,验证了本文所推统一解的合理性;在所提供支护抗力相同的前提下,考虑围岩膨胀特性计算所得塑性区半径扩大,弹-塑性界面的环向应力增加,考虑围岩膨胀特性所得塑性区半径与环向应力是不考虑膨胀特性的1.06倍;当统一强度理论参数从0.0增加到1.0时,弹-塑性界面的环向应力增幅为6.6%,塑性区半径降幅为13.9%,隧道洞壁位移降幅为16.0%;当湿度膨胀系数分别取值0.00与0.10时,由于湿度膨胀系数影响引起的弹-塑性界面环向应力与塑性区半径增量分别达17.98%与27.4%;当最大含水率从0.00增加到0.06时,弹-塑性界面的环向应力增幅为16.9%,塑性区半径增幅为23.1%,隧道洞壁位移增幅为100%.研究成果可为膨胀岩隧道结构设计提供理论依据.

Analysis of the Electromagnetic Characteristics and the Mechanism Underlying Bio-Medical Function of Longitudinal Electromagnetic (LEM) Waves

Based on theoretical system of current Maxwell’s equations, the Maxwell’s equations for LEM waves concealed in full current law and Faraday’s law of electromagnetic induction (Faraday’s law) are proposed. Then, taking them as the fundamental equations, the wave equation and energy equation of LEM waves are established, and a new electromagnetic wave propagation mode based on the mutual induction of scalar electromagnetic fields/vortex magneto-electric fields, which was overlooked in current Maxwell’s equations, are put forward. Moreover, through theoretical derivation based on vacuum LEM waves, the Maxwell’s equations of the gravitational field generated by vacuum LEM waves, the wave equations of the electromagnetic scalar potential/magnetic vector potential and the constraint equation governing the wave phase-velocities between LEM/TEM waves are discovered. Finally, on the basis of these theoretical research results, the electromagnetic properties of vacuum LEM waves are analyzed in detail, encompassing the speed of light, harmless penetrability to the human body, absorption and stable storage by water, the possibility of generating artificial gravitational fields, and the capability of extracting free energy. This reveals the medical functional mechanism of LEM waves and establishes a solid theoretical basis for the application of LEM waves in the fields of medicine and energy.

Between Quantum Mechanics and General Relativity

The origin of elementary particle mass is considered as a function of n-valued graviton quanta. To develop this concept we begin in a cold region of “empty space” comprised of only microscopic gravitons oscillating at angular frequency ω. From opposite directions enters a pair of stray protons. Upon colliding, heat and energy are released. Customarily, this phase and what follows afterward would be described by Quantum Chromodynamics (QCD). Instead, we argue for an intermediary step. One in which neighboring gravitons absorb discrete amounts of plane-wave energy. Captured by the graviton, the planewave becomes a standing wave, whereupon its electromagnetic energy densities are converted into gravitational quanta. Immediately thereafter an elementary particle is formed and emitted, having both mass and spin. From absorption to conversion to emission occurs in less than 3.7 × 10−16 s. During this basic unit of hybrid time, general relativity and quantum physics unite into a common set of physical laws. As additional stray protons collide the process continues. Over eons, vast regions of spacetime become populated with low-mass particles. These we recognize to be dark matter by its effects on large scale structures in the universe. Its counterpart, dark energy, arises when the conversion of gravitational quanta to particle emission is interrupted. This causes the gravitational quanta to be ejected. It is recognized by its large scale effects on the universe.

Next Frontier in Physics—Space as a Complex Tension Field

We hypothesize that 100% of the energy of our cosmic system is held by a physically real Complex Tension Field (CTF). We are using an old methodology of thinking used by our forefather engineers long before the advent of modern scientific thinking. We call it Interaction Process Mapping Epistemology or IPM-E. We apply this IPM-E on to the prevailing Measurable Data Modeling Epistemology or MDM-E. This approach helped us analyze the “Measurement Problem”, recognized during the rise of quantum mechanics (QM), and helped us recover a universal property of all linear waves, that they do not interact, or interfere, with each other. This Non-Interaction of Waves, or the NIW-property, should be obvious through daily observations and through the Huygens-Fresnel diffraction integral and through critical evaluation of contradictory hypotheses we have been assigning to photons through ages. This implicates that the time-frequency Fourier theorem, although mathematically correct, and is used universally in all branches of science;does not map the real physical interaction processes for most optical phenomena. Accordingly, we present the necessary modifications for a few selected phenomena in classical and quantum optics to validate the NIW-property. In the process we find that accepting photons as non-interacting, but diffractively propagating linear wave packets crossing the entire cosmic space, requires CTF as a physical medium. Then we develop logical arguments in support of stable elementary particles as nonlinear but resonant vortex-like undulations of this same CTF. These vortex-like particles impose various secondary potential gradients around themselves giving rise to the four forces we know. Thus, CTF can serve as the cosmic substrate to develop a unified field theory without the need of dark matter and dark energy. In the process, we demonstrate a path to add ontologic thinking on our biologically successful epistemic thinking.

Unification of Electromagnetic Interactions and Gravitational Interactions

Unified theory of gravitational interactions and electromagnetic interactions is discussed in this paper.Based on gauge principle, electromagnetic interactions and gravitational interactions are formulated in the same mannerand are unified in a semi-direct product group of U(1) Abelian gauge group and gravitational gauge group.

Unification of Electromagnetic Interactions and Gravitational Interactions

Unified theory of gravitational interactions and electromagnetic interactions is discussed in this paper.Based on gauge principle, electromagnetic interactions and gravitational interactions are formulated in the same mannerand are unified in a semi-direct product group of U(1) Abelian gauge group and gravitational gauge group.

Theory of Electro Relativity

A unified field theory is created by using a simple dipole antenna to model the Earth’s electrical fields. From Maxwell’s equation a set of standard radio field equations are presented for the Electrostatic, Inductive and Radiative field. By inserting three gravity field equations (1/r, 1/r2 and 1/r3) a new set of field equations are created that can be used to define space, time, gravity and the electromagnetic field at any point P in the field.

The Geometrization of the Electromagnetic Field

Einstein used the term “unified field theory” in a title of a publication for the first time in 1925. Somewhat paradoxically, an adequate historical, physical and philosophical understanding of the dimension of Einstein’s unification program cannot be understood without fully acknowledging one of Einstein’s philosophical principles. Despite many disappointments, without finding a solution besides of the many different approaches along the unified field theory program and in ever increasing scientific isolation, Einstein insisted on the unity of objective reality as the foundation of the unity of science. Einstein’s engagement along his unification program was burdened with a number of difficulties and lastly in vain. Nevertheless, a successful geometrization of the gravitational and the electromagnetic fields within the framework of the general theory of relativity is possible. Thus far, it is a purpose of the present contribution to geometrize the electromagnetic field within the framework of the general theory of relativity.

The Explanation for the Origin of the Higgs Scalar and for the Yukawa Couplings by the Spin-Charge-Family Theory

The spin-charge-family theory is a kind of the Kaluza-Klein theories, but with two kinds of the spin connection fields, which are the gauge fields of the two kinds of spins. The SO(13,1) representation of one kind of spins manifests in d = (3 + 1) all the properties of family members as assumed by the standard model;the second kind of spins explains the appearance of families. The gauge fields of the first kind, carrying the space index m = (0,...,3), manifest in d = (3 + 1) all the vector gauge fields assumed by the standard model. The gauge fields of both kinds of spins, which carry the space index (7, 8) gaining at the electroweak break nonzero vacuum expectation values, manifest in d = (3 + 1) as scalar fields with the properties of the Higgs scalar of the standard model with respect to the weak and the hyper charge ( and , respectively), while they carry additional quantum numbers in adjoint representations, offering correspondingly the explanation for the scalar Higgs and the Yukawa couplings, predicting the fourth family and the existence of several scalar fields. The paper 1) explains why in this theory the gauge fields are with the scalar index s = (5,6,7,8) doublets with respect to the weak and the hyper charge, while they are with respect to all the other charges in the adjoint representations;2) demonstrates that the spin connection fields manifest as the Kaluza-Klein vector gauge fields, which arise from the vielbeins;and 3) explains the role of the vielbeins and of both kinds of the spin connection fields.