Ratio of Gravitational Force to Electric Force from Empirical Equations in Terms of the Cosmic Microwave Background Temperature

Previously, we presented several empirical equations using the cosmic microwave background (CMB) temperature. Next, we propose an empirical equation for the fine-structure constant. Considering the compatibility among these empirical equations, the CMB temperature (Tc) and gravitational constant (G) were calculated to be 2.726312 K and 6.673778 × 10−11 m3∙kg−1∙s−2, respectively. Every equation could be explained in terms of the Compton length of an electron (λe), the Compton length of a proton (λp) and a. Furthermore, every equation could also be explained in terms of Avogadro’s number and the number of electrons in 1 C. However, the ratio of the gravitational force to the electric force cannot be uniquely determined when the unit of the Planck constant (Js) is changed. In this study, we showed that every equation can be described in terms of Planck constant. From the assumption of minimum mass, the ratio of gravitational force to electric force could be elucidated.

Weakly Singular Symmetric Galerkin Boundary Element Method for Fracture Analysis of Three-Dimensional Structures Considering Rotational Inertia and Gravitational Forces

The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures,because only boundary and crack-surface elements are needed.However,for engineering structures subjected to body forces such as rotational inertia and gravitational loads,additional domain integral terms in the Galerkin boundary integral equation will necessitate meshing of the interior of the domain.In this study,weakly-singular SGBEM for fracture analysis of three-dimensional structures considering rotational inertia and gravitational forces are developed.By using divergence theorem or alternatively the radial integration method,the domain integral terms caused by body forces are transformed into boundary integrals.And due to the weak singularity of the formulated boundary integral equations,a simple Gauss-Legendre quadrature with a few integral points is sufficient for numerically evaluating the SGBEM equations.Some numerical examples are presented to verify this approach and results are compared with benchmark solutions.

The Gravitational Force Quantum and its Value

Gravitation is one of the basic phenomena of the world. Tremendous number of theoretical works on origin, nature, essentials, consequences, etc. of the gravitation and related phenomena were published so far. The most prominent ones are based on the Albert Einstein＇s general theory of relativity. The author of this communication based his approach to the gravitation on Isaac Newton＇s law of the universal gravitation and related quantities, i.e. gravitational forces of matter objects, distance and motion. Namely on the fact, that the gravitation force is - as well as the inertia, mass, space ＂occupied＂ and other properties are - principal features/attributes/properties of matter objects. Gravitation is an additive property of matter objects. Taking into account other positivistic quantities like mass of the Earth, standard acceleration of gravity, and the value of the atomic unit of mass, the author defined a gravitational force of atomic unit （or ＂the Gravitational Force Quantum＂） as a gravitational force which exerts one atomic unit of Earth＇s mass on 1 kilogram of a mass on Earth＇s surface, and he calculated its value： GFO = 1.4958 × 10^-54 N. This quantity can be useful for further development of the ＂quantum mechanical＂ approach to the description and general notion about the world.

An experiment discovery about gravitational force changes in materials due to temperature variation

The authors discovered in first time that the weight of materials or its gravitational force by earth related to its temperature and its ferromagnetism. An experiment was designed to elevate the temperatures of six different materials （Au, Ag, Cu, Fe, Al, Ni） up to 600 ℃and precisely measured their weights. It is found all the materials weigh about 0.33 ‰ - 0. 82 ‰ less. For example the weight of silver sample weighted by a precision electronic scale in a manner of special design decreases about 0.8 ‰, when its temperature is elevated to 600 ℃. Thus different metals＇ gravitational forces or weights are adjusted with temperature variation.

Classical Gravitational Interactions and Gravitational Lorentz Force

In quantum gauge theory of gravity, the gravitational field is represented by gravitational gauge field.The field strength of gravitational gauge field has both gravitoelectric component and gravitomagnetic component. In classical level, gauge theory of gravity gives classical Newtonian gravitational interactions in a relativistic form. Besides,it gives gravitational Lorentz force, which is the gravitational force on a moving object in gravitomagnetic field The direction of gravitational Lorentz force is not the same as that of classical gravitational Newtonian force. Effects of gravitational Lorentz force should be detectable, and these effects can be used to discriminate gravitomagnetic field from ordinary electromagnetic magnetic field.

Algorithms for Empirical Equations in Terms of the Cosmic Microwave Background Temperature

Previously, we presented several empirical equations using the cosmic microwave background (CMB) temperature. Next, we propose an empirical equation for the fine-structure constant. Considering the compatibility among these empirical equations, the CMB temperature (Tc) and gravitational constant (G) were calculated to be 2.726312 K and 6.673778 × 10−11 m3∙kg−1∙s−2, respectively. Every equation can be explained numerically in terms of the Compton length of an electron (λe), the Compton length of a proton (λp) and α. Furthermore, every equation can also be explained in terms of the Avogadro number and the number of electrons at 1 C. We show that every equation can be described in terms of the Planck constant. Then, the ratio of the gravitational force to the electric force can be uniquely determined with the assumption of minimum mass. In this report, we describe the algorithms used to explain these equations in detail. Thus, there are no dimension mismatch problems.

The Elementary Gravitational Charge and Its Value

In the article ＂The Gravitational Force Quantum and its Value＂ [1 ], the author defined a gravitational force of the atomic unit （＂the Gravitational Force Quantum＂） as a gravitational force which exerts one atomic unit of the Earth＇s mass on l kilogram of a mass on the Earth＇s surface, and he calculated its value as： GFQEarth = 1.4958 × 10.54 N. In the present contribution, he extended the Gravitational Force Quantum concept to further Objects of the Solar Planetary System and for the Pluto. He calculated values of the GFQo on the analogous basis, i.e. of the mass and the standard acceleration of the gravity of individual objects and of the atomic unit of the mass. He received GFQo values for the Mercury 102.1427 × 1055N, the Venus 16,60012 × 10-55N, the Earth 14.97839 × l0-55 N, the Mars 52.91869 × 10-55N, the Jupiter 0.124391×1055 N, the Saturn 0.17929 ×1055N, the Uranus 0.945178 ×1055N, the Neptune 1.002845 × 10-55N, for the Pluto 458.9124 × 10-55N, and for the Sun 0.001257 × 10-55N, respectively. He multiplied the GFQo values by second power of the radii of the individual objects （O）, receiving values denoted as the ＂Elementary Gravitational Charge＂ （Go）. The Elementary Gravitational Charge represents a gravitational force of one atomic unit of mass in the （radius） distance of 1 meter. They were found of the same value： GMe= Gv = GE= GMa= Gj= Gs = Gp= GSun= 6.079675463 × 10-41N. The values were the same as the calculated one on the basis of the ＂classical＂ Newton＇s formula： FG = И × M × m / R2, for the gravitational force between the atomic unit mass and a mass of 1 kg at a distance of 1 meter, which value was calculated as G = 6.079675463 ×1041 N. The quantity of the Elementary Gravitational Charge can be supposed to be analogous to the Elementary （Electric） Charge （e =1.6021766208（98） × 10-19 C） quantity.

Gravitational Space-Time Curve Generation via Accelerated Charged Particles

A force with an acceleration that is equal to multiples greater than the speed of light per unit time is exerted on a cloud of charged particles. The particles are resultantly accelerated to within an infinitesimal fraction of the speed of light. As the force or acceleration increases, the particles’ velocity asymptotically approaches but never achieves the speed of light obeying relativity. The asymptotic increase in the particles’ velocity toward the speed of light as acceleration increasingly surpasses the speed of light per unit time does not compensate for the momentum value produced on the particles at sub-light velocities. Hence, the particles’ inertial mass value must increase as acceleration increases. This increase in the particles’ inertial mass as the particles are accelerated produce a gravitational field which is believed to occur in the oscillation of quarks achieving velocities close to the speed of light. The increased inertial mass of the density of accelerated charged particles becomes the source mass (or Big “M”) in Newton’s equation for gravitational force. This implies that a space-time curve is generated by the accelerated particles. Thus, it is shown that the acceleration number (or multiple of the speed of light greater than 1 per unit of time) and the number of charged particles in the cloud density are surjectively mapped to points on a differential manifold or space-time curved surface. Two aspects of Einstein’s field equations are used to describe the correspondence between the gravitational field produced by the accelerated particles and the resultant space-time curve. The two aspects are the Schwarzchild metric and the stress energy tensor. Lastly, the possibility of producing a sufficient acceleration or electromagnetic force on the charged particles to produce a gravitational field is shown through the Lorentz force equation. Moreover, it is shown that a sufficient voltage can be generated to produce an acceleration/force on the particles that is multiples greater than the speed of light per unit time thereby generating gravity.

Energy of the Gravitational Field as an Equivalent of the Dark Energy of the Universe

Determination of the structural foundations and parameters of the Universe is an important urgent task since it enables us to understand and explain the structure and basic parameters of the material world. Herewith, it is necessary to be aware of modern problems of physics and possible ways to solve them. Among such problems, hypotheses concerning dark matter and the energy of the Universe occupy an important place. However, the determination of their on the basis of modern theories still leads to abstract equations that do not give concrete results;therefore, they have a level of hypotheses. A number of initial scientific propositions based on this abstract of mathematical dependencies have controversial meanings. Elimination of this disadvantage is the main goal of the work performed. Its main difference and scientific novelty are the justification of the energy parameters of the gravitational field of the Universe, the magnitude of which can replace its dark energy and dark mass. The solution to this problem is justified by strict physical dependencies, which are obtained on the basis of fundamental physical constants. It is an urgent and important scientific and applied problem, since it develops knowledge about the gravitational field and the material world in general. The performed work is based on the methods of deduction and induction in the research of the material world based on the application of the well-known reliable laws of physics and the general principles of the development of the theory of knowledge. Other research methods are still unknown, since the work performed is associated with new scientific discoveries, the search for which is difficult to formalize by technique methods. The results of the study consist of the analysis of wave, force and energy parameters of the relict gravitational field of the Universe. The calculated value of this energy is 1.58 × 1070 J. This energy is enough to cover the amount of dark energy and mass in the Universe, which casts doubt on their existence. Conclusions: This paper can supplement previously performed research on the dark mass and energy of the Universe, which requires further for their reconciliation.

On the Origin of Gravity and the Emergence of a Black Hole

We show the theoretical origin of gravitational force and explain why it is the weakest force of nature. Further, we report that if the gravity of any object at any point is larger than a certain value, from that point on it will be a black hole-like object;this might be a new criterion to define a black hole. It might offer fresh insight into the origin of gravity and black hole.

The Nature and Origin of Inertia

This paper aims to present a new theory that explains the mechanism of inertia at providing a satisfying explanation for the yet unknown mechanism for inertia. By considering the vacuum as a liquid with a measurable density, hydrodynamics laws are used to describe the behaviour of the vacuum when it is dragged by moving body. The inertia is the result of the initial resistance between the moving bodies against the static vacuum. The moving body drags the resisting vacuum during acceleration, till the point that the vacuum travels with the moving body and has the same velocity. When the body decelerates, the vacuum continues to flow and to push the body at the same direction of the original flow till its complete stop. Formulations based on Planck theory derived to prove its equivalence to Newton inertia law. Formulation based on hydrodynamics is derived to confirm the theory that the force exerted by the vacuum on static body in gravity and on moving body in inertia is equivalent to Newton law. The strong equivalence principle is reaffirmed and, consequently, Einstein’s equations are preserved.

Rotating Lepton Model of Pions and Kaons: Mechanics at fm Distances

The present article is a continuation of a recently published paper [1] in which we have modeled the composition and structure of neutrons and other hadrons using the Rotating Lepton Model (RLM) which is a Bohr type model employing the relativistic gravitational attraction between three ultrafast rotating neutrinos as the centripetal force. The RLM accounts for special relativity and also for the De Broglie equation of quantum mechanics. In this way this force was shown to reach the value of the Strong Force while the values of the masses of the rotating relativistic neutrinos reach those of quarks. Masses computed for twelve hadrons and bosons are in very close (~2%) agreement with the experimental values. Here we use the same RLM approach to describe the composition and structure and to compute the masses of Pions and Kaons which are important zero spin mesons. Contrary to hadrons and bosons which have been found via the RLM to comprise the heaviest neutrino eigenmass m3, in the case of mesons the intermediate neutrino mass eigenstate m2 is found to play the dominant role. This can explain why the lowest masses of mesons are generally smaller than those of hadrons and bosons. Thus in the case of Pions it is found that they comprise three rotating m2 mass eigenstate neutrinos and the computed mass of 136.6 MeV/c2 is in good agreement with the experimental value of 134.977 MeV/c2. The Kaon structure is found to consist of six m2 mass eigenstate neutrinos arranged in two parallel pion-type rotating triads. The computed Kaon mass differs less that 2% from the experimental K± and K°values of 493.677 MeV/c2 and 497.648 MeV/c2 respectively. This, in conjunction with the experimentally observed decay products of the Kaons, provides strong support for the proposed K structure.