A Possible Modification of Einstein＇s Theory of General Relativity

This article suggests a new metric theory of gravitation, in which metric field is determined not only by matter and nongravitational field but also by vector graviton field, and in principle there is no need to introduce the Einstein's tensor. In order to satisfy automatically the geodesic postulate, an additional coordinate condition is needed. For the spherically symmetric static field, it leads us to quite different conclusions from those of Einstein's general relativity in the interior region of the surface of infinite redshift. Accurate to the first order of , it obtains the same results about the four experimental tests of general relativity.

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.

Einstein’s Theory of Relativity in the Scenario of the Higgs Quantum Space Dynamics

This work is concerned about the true physical mechanism of gravity. The Higgs theory introduces important changes in Einstein’s view about the nature of empty space, about the meaning of motions and about the nature of the gravitational physics. The Higgs Quantum Space (HQS) is a real quantum fluid spatial medium, giving inertial mass to the elementary particles by the Higgs mechanism. Therefore, the HQS rules the inertial motion of matter-energy and is the local ultimate reference for rest and for motions. In this new scenario, velocity with respect to the local HQS and not relative velocity is the origin of all the effects of motion. The HQS also necessarily is responsible for the gravitational fields because it is mass that creates the gravitational fields. The observed absence of the gravitational slowing of the GPS clocks by the solar field and the absence of light anisotropy with respect to earth are both the obvious signature of the true physical mechanism of gravity in action. These observations show that the HQS is moving itself round the sun according to a Keplerian velocity field, consistent with the planetary motions, which will be shown to accurately create, besides the observed gravitational dynamics, all the observed effects of the gravitational fields on light and on clocks. Current theories explain the absence of the solar gravitational slowing of the GPS clocks with base in the principle of equivalence. In the language of the present work, the HQS materializes the local Lorentz frames (LFs), turning them into local proper LFs, intrinsically stationary with respect to the local moving HQS. In its motions, the HQS carries these local proper LFs with it round the sun, so that the planets of the solar system are stationary with respect to them, which directly predicts the absence of the gravitational slowing of the GPS clocks by the solar field, the absence of light anisotropy with respect to earth and all the other effects of the gravitational fields observed on earth.

The Generalized Lagrangians of Gravitational Theory With Torsion and Their Invariances Under (ε^(mn), ξ~μ) Transformations

The generalized Lagrangians of matter field and gravitational fields are specified and their invariances under (ε^(mn), ξ~μ) transformations in the space-time with torsion are studied. The possible forms of coupling between gravitational fields and matter field as well as the possible types of gravitational Lagrangian are derived. Some physical quantities are introduced and several interesting conclusions are discussed.

A Possible Interpretation on Distance-Dependent Effect of Gravitational Constant in Newton＇s Theory of Gravitation

Based on the new metric theory of gravitation suggested by the author of this article, it gives a possible theoretical interpretation on the famous experiment done by D.R. Long in 1976, i.e. the distance-dependent effect of the gravitational constant in Newton's theory of gravitation.

Gauge Gravitational Field in a Fractal Space-Time

Considering the fractal structure of space-time, the scale relativity theory in the topological dimension DT = 2 is built. In such a conjecture, the geodesics of this space-time imply the hydrodynamic model of the quantum mechanics. Subsequently, the gauge gravitational field on a fractal space-time is given. Then, the gauge group, the gauge-covariant derivative, the strength tensor of the gauge field, the gauge-invariant Lagrangean, the field equations of the gauge potentials and the gauge energy-momentum tensor are determined. Finally, using this model, a Reissner- Nordstrom type metric is obtained.

The Implications of the Sun’s Dragging Effect on Gravitational Experiments

Experimental determinations of Newton’s gravitational constant, Big G, have increased, in number and precision, during the last 30 years. There is, however, a persistent discrepancy between various authors. After examining some literature proposing that the differences in Big G might be a function of the length of the day along the years, this paper proposes an alternative hypothesis in which the periodicity of said variation is a function of the relative periodicity of the Sun-Earth distance. The hypothesis introduced here becomes a direct application of the Kerr Metric that describes a massive rotating star. The Kerr solution for the equations of the General Theory of Relativity of Albert Einstein fits well with this relative periodicity and adequately predicts the arrangement of the ex-perimental G values reported by sixteen different laboratories. Also, the author explains how the Sun disturbs gravity on the surface of the Earth.

Quantum Gravitational Energy Simplifies Gravitational Physics and Gives a New Einstein Inspired Quantum Field Equation without G

We show the simplest form with which one can express the gravity force, and that still gives all the same predictions of observable phenomena as does standard Newton gravity and general relativity theory. In addition, we show a new field equation that gives all the same predictions as general relativity theory, but that it is simpler as the only constant needed is the speed of light and that also gives quantum gravity. This new form to express gravity, through quantum gravitational energy, requires less constants to predict gravity phenomena than standard gravity theory. This alone should make the physics community interested in investigating this approach. It shows that gravitational energy, and other types of energy are a collision-length in their most complete and deepest form and that quantization of gravity is related to the reduced Compton frequency of the gravitational mass per Planck time. While general relativity theory needs two constants to predict gravity phenomena, that is G and c, our new theory, based on gravity energy, only needs one constant, cg, that is easily found from gravitational observations with no prior knowledge of any constants. Further, we will show that, at the deepest quantum level, quantum gravity needs two constants, cg and the Planck length, while the standard formulation here needs c, h and lp. Thus our theory gives a reduction in constants and simpler formulas than does standard gravity theory. Most important we by this seems to have a fully consistent framework for quantum gravity.

Re-examination of the Two-Body Problem Using Our New General System Theory

It is well-known that philosophical conflicts exist among classical mechanics,quantum mechanics and relativistic mechanics.In order to use the framework of general system theory to unify these three mechanics subjects,a new general system theory is developed based on a new ontology of ether and minds as the fundamental existences in the world.The two-body problem is the simplest model in mechanics and in this paper,it is re-examined by using our new general system theory.It is found that the current description of the classical full two-body problem is inappropriate since the observer and the measurement apparatus have not been explicitly considered.After considering these,it is actually a three-body problem while only the special case of the Kepler problem is the two-body problem.By introducing the concepts of psychic force and psychic field,all the possible movement states in the two-body problem can be explained within the framework of classical mechanics.There is no need to change the meanings of many fundamental concepts,such as time,space,matter,mass,and energy as done in quantum mechanics and relativity theory.This points out a new direction for the unification of different theories.

Precise Measurements of the Gravitational Constant: Revaluation by the Information Approach

The gravitational constant discovered by Newton is still measured with a relative uncertainty that is several orders of magnitude larger than the relative uncertainty of other fundamental constants. Numerous methods are used to measure it. This article discusses the information-oriented approach for analyzing the achievable relative measurement uncertainty, in which the magnitude of the gravitational constant can be considered as plausible. A comparison is made and the advantages and disadvantages of various methods are discussed in terms of the possibility of achieving higher accuracy using a new metric called comparative uncertainty, which was proposed by Brillouin.

Higgs Quantum Space Dynamics and the Nature of the Gravitational Fields

This work discusses the implications of the Higgs theory on Einstein’s General Relativity, showing that these implications accurately lead to all the experimental observations. The Higgs theory introduces the Higgs field breaking the electroweak symmetry and filling up the universe with the Higgs quantum condensate. This Higgs Quantum Space (HQS) gives inertial mass to elementary particles by the Higgs mechanism and hence necessarily is the local ultimate reference for rest and for motions. Velocity with respect to the local HQS and not relative velocity is the origin of all the effects of motion on matter-energy. Within this scenario, the observed absence of the gravitational slowing of the GPS clocks by the solar field, as well as the absence of light anisotropy with respect to earth, demonstrates that earth and also the other planets of the solar system are very nearly stationary with respect to the local HQS. This can make a sense only if the HQS is itself moving round the sun according to a Keplerian velocity field, consistent with the planetary motions. The current theories explain the absence of the solar gravitational slowing of the GPS clocks with base in the principle of equivalence. Accordingly, the local Lorentz frame (LF), moving with earth round the sun, cancels the spacetime curvature and reproduces locally the environment of special relativity. In this local environment, earth and the GPS clocks are stationary and therefore display proper time. In the scenario of the present HQS dynamics, the local HQS materializes the local LFs, turning them into local proper LFs, stationary with respect to the local HQS. In its motion, the HQS carries these local proper LFs with it round the sun. The orbiting earth is stationary with respect to the local moving HQS and necessarily too with respect to these local proper LFs, thereby canceling the effects of the gravitational field and perfectly implementing the principle of equivalence. The present work shows moreover that this Keplerian velocity field of the HQS accurately creates the observed gravitational dynamics and all the effects of the gravitational fields on matter, on light and on clocks.

A Classical Field Theory of Gravity and Electromagnetism

A classical field theory of gravity and electromagnetism is developed. The starting point of the theory is the Maxwell equations which are directly tied to the Riemann-Christoffel curvature tensor. This is done through the derivatives of the Maxwell tensor which are equated to a vector field ?contracted with the curvature tensor, i.e., . The electromagnetic portion of the theory is shown to be equivalent to the classical Maxwell equations with the addition of a hidden variable. Because the proposed equations describing electromagnetism and gravity differ from the classical Maxwell-Einstein equations, their ability to describe classical physics is shown for several situations by direct calculation. The inclusion of antimatter and its behavior in a gravitational field, and the possibility of particle-like solutions exhibiting quantized charge, mass and angular momentum are discussed.

Influence of Infinitesimal Neglected Effects by Current Theory of Gravitation and Experiments on the Stability of the Universe

From the hypotheses compatible with microphysics theory, this paper establishes a new theoretical model of static universal gravitation and deduces new formula of the theory of universal gravitation. In a first order approximation, the new formula shows the inverse-square law consistent with Newton formula, which would indicate that the new theory is consistent with the experimental results that can be reasonably explained by the current theory of gravitation. The parameters and higher order terms among the coefficients of this paper reveal the numerous infinitesimal neglected effects by current theory and experiments. In the first order approximation, the meanings of the physical parameters included in coefficients are analyzed and the infinitesimal neglected effects are applied in the study of the stability of the universe, which overcomes the difficulty of singularity in the cosmology of Newton, Einstein, etc., and concludes that the boundary of universe is unlimited, without any need of the hypothesis that the universe starts off with the big bang. Therefore, this paper establishes a harmonious and ingenious relationship between microphysics and macrophysics theories. In addition, through the analysis of the formula derived from the theory of this paper, it is found that: in general, the gravitational constant is not always a constant in the gravitation formula requiring high precision;from the perspective of the interaction of field quantum, the acting force may not be equal to counter-acting force under the interaction of indirect contact;the gravity process is an exothermic process;in the gravitational process, annihilation effects may exist amongst gravitons;reciprocal translation may exist amongst fundamental forces.

Why Gravitational Waves Cannot Exist

The purpose of this short but difficult paper is to revisit the mathematical foundations of both General Relativity (GR) and Gauge Theory (GT) in the light of a modern approach to nonlinear systems of ordinary or partial differential equations, using new methods from Differential Geometry (D.C. Spencer, 1970), Differential Algebra (J.F. Ritt, 1950 and E. Kolchin, 1973) and Algebraic Analysis (M. Kashiwara, 1970). The main idea is to identify the differential indeterminates of Ritt and Kolchin with the jet coordinates of Spencer, in order to study Differential Duality by using only linear differential operators with coefficients in a differential field K. In particular, the linearized second order Einstein operator and the formal adjoint of the Ricci operator are both parametrizing the 4 first order Cauchy stress equations but cannot themselves be parametrized. In the framework of Homological Algebra, this result is not coherent with the vanishing of a certain second extension module and leads to question the proper origin and existence of gravitational waves. As a byproduct, we also prove that gravitation and electromagnetism only depend on the second order jets (called elations by E. Cartan in 1922) of the system of conformal Killing equations because any 1-form with value in the bundle of elations can be decomposed uniquely into the direct sum (R, F) where R is a section of the Ricci bundle of symmetric covariant 2-tensors and the EM field F is a section of the vector bundle of skew-symmetric 2-tensors. No one of these purely mathematical results could have been obtained by any classical approach. Up to the knowledge of the author, it is also the first time that differential algebra in a modern setting is applied to study the specific algebraic feature of most equations to be found in mathematical physics, particularly in GR.

Ashtekar-Kodama Gravity as a Classical and Quantum Extension of Loop Quantum Gravity

This paper presents a new theory of gravity, called here Ashtekar-Kodama (AK) gravity, which is based on the Ashtekar-Kodama formulation of loop quantum gravity (LQG), yields in the limit the Einstein equations, and in the quantum regime a full renormalizable quantum gauge field theory. The three fundamental constraints (hamiltonian, gaussian and diffeomorphism) were formulated in 3-dimensional spatial form within LQG in Ashtekar formulation using the notion of the Kodama state with positive cosmological constant Λ. We introduce a 4-dimensional covariant version of the 3-dimensional (spatial) hamiltonian, gaussian and diffeomorphism constraints of LQG. We obtain 32 partial differential equations for the 16 variables Emn (E-tensor, inverse densitized tetrad of the metric) and 16 variables Amn (A-tensor, gravitational wave tensor). We impose the boundary condition: for large distance the E-generated metric g(E) becomes the GR-metric g (normally Schwarzschild-spacetime). The theory based on these Ashtekar-Kodama (AK) equations, and called in the following Ashtekar-Kodama (AK-) gravity has the following properties. • For Λ = 0 the AK equations become Einstein equations, A-tensor is trivial (constant), and the E-generated metric g(E) is identical with the GR-metric g. • When the AK-equations are developed into a Λ-power series, the Λ-term yields a gravitational wave equation, which has only at least quadrupole wave solutions and becomes in the limit of large distance r the (normal electromagnetic) wave equation. • AK-gravity, as opposed to GR, has no singularity at the horizon: the singularity in the metric becomes a (very high) peak. • AK-gravity has a limit scale of the gravitational quantum region 39 μm, which emerges as the limit scale in the objective wave collapse theory of Gherardi-Rimini-Weber. In the quantum region, the AK-gravity becomes a quantum gauge theory (AK quantum gravity) with the Lie group extended SU(2) = ε-tensor-group(four generators) as gauge group and a corresponding covariant derivative. • AK quantum gravity is fully renormalizable, we derive its Lagrangian, which is dimensionally renormalizable, the normalized one-graviton wave function, the graviton propagator, and demonstrate the calculation of cross-section from Feynman diagrams.

Refinement of Newton Gravitation Law

According to the theory of general relativity and experiments with atomic clocks in gravitation field, presence of the field shall cause time dilation of clock at rest in the field. This means that the gravitation constant G is not a true physical constant, but rather a function of the location of the setup in the field when measuring the parameter. This is because the definition of G includes a unit of time, and duration of that time unit is influenced by clock’s location in the field. However, the theory assumes a prior that G shall remain constant in gravitation field, even though this may not be the case. On the other hand, relativistic gravitation phenomena can be derived without contradiction from a refined version of Newton’s law of gravitation that complies with Einstein’s law of mass-energy equivalence.

The Gravitational Potential and the Gravitational Force According to the Correct Schwarzschild Metric

In a recent article, we have corrected the traditional derivation of the Schwarzschild metric, thus obtaining the formulation of the correct Schwarzschild metric, which is different from the traditional Schwarzschild metric. In this article, by starting from this correct Schwarzschild metric, we obtain the formulas of the correct gravitational potential and of the correct gravitational force in the case described by this metric. Moreover, we analyse these correct results and their consequences. Finally, we propose some possible crucial experiments between the commonly accepted theory and the same theory corrected according to this article.

视广义相对论及新广义相对论为广义引力理论特殊情况的研究

根据广义引力理论的基本公式导出了广义相对论和新广义相对论的引力场方程和粒子运动方程．结果表明了广义相对论和新广义相对论均是广义引力理论的特殊情况．阐述了这种方法在理论上和运算上的一些优点．

τ-Rickart模和相对τ-Rickart模

设τ=■表示遗传挠理论.提出了τ-Rickart模和相对τ-Rickart模的概念,讨论了τ-Rickart模的性质和等价刻画,给出了Rickart模与τ-Rickart模之间没有相互蕴含关系的例子;证明了直和因子包含τ-挠子模的τ-Rickart模具有SIP性质;证明了对任意i,j∈{1,2},若Mi是M,-C2模,则M是τ-Rickart模当且仅当对任意i,j∈{1,2},Mi是Mj-τ-Rickart模,其中M=M1⊕M2.

从引力波谈爱因斯坦的幸运

在引力波被直接探测之际,从独特的视角回顾了爱因斯坦创立广义相对论、预言引力波、引进宇宙学常数的历程,也介绍分析了他的若干论文的发表情况,从而将爱因斯坦的若干科学事件有机地融合起来。