Gauge Invariance of Gravitodynamical Potentials in the Jefimenko’s Generalized Theory of Gravitation

In the Jefimenko’s generalized theory of gravitation, it is proposed the existence of certain potentials to help us to calculate the gravitational and cogravitational fields, such potentials are also presumed non-invariant under certain gauge transformations. In return, we propose that there is a way to perform the calculation of certain potentials that can be derived without using some kind of gauge transformation, and to achieve this we apply the Helmholtz’s theorem. This procedure leads to the conclusion that both gravitational and cogravitational fields propagate simultaneously in a delayed and in an instant manner. On the other hand, it is also concluded that these potentials thus obtained can be real physical quantities, unlike potentials obtained by Jefimenko, which are only used as a mathematical tool for calculating gravitational and cogravitational fields.

Meso-scale available gravitational potential in the world oceans

The pitfalls of applying the commonly used definition of available gravitational potential energy （AGPE） to the world oceans are re-examined. It is proposed that such definition should apply to the meso-scale problems in the oceans, not the global scale. Based on WOA98 climatological data, the meso-scale AGPE in the world oceans is estimated. Unlike previous results by Oort et al. , the meso-scale AGPE is large wherever there is a strong horizontal density gradient. The distribution of meso-scale AGPE reveals the close connection between the baroclinic instability and the release of gravitational potential energy stored within the scale of Rossby deformation radius.

Gravitational Time Dilation inside the Solid Sphere

Gravitational time dilation directly reflects the difference between gravitational potentials at different altitudes in the gravitational field. At the same time this phenomenon is expected to obey the Einstein’s equivalence principle, one of two pillars (apart from general covariance) of general relativity. The experiments aimed at detecting the gravitational time dilation are therefore described as the tests of general relativity or, alternatively, the tests of equivalence principle. When applied to the exterior of a solid sphere, these two interpretations are fully compatible both theoretically and experimentally. However, when applied to the interior of a solid sphere (e.g., to the interior of Earth), they seem to contradict each other. Namely, a strict dependence of the gravitational time dilation on the gravitational potential inside the sphere proves to be at odds with the equivalence principle. This paper reveals this problem and provides solution to it. As a consequence, it is concluded that, contrary to the current belief, the Earth’s center is older, not younger, than the Earth’s surface. Since all the previous experiments have been performed either on or above the Earth’s surface, an experiment performed below the Earth’s surface is proposed.

Crustal density structures and isostasy beneath the Western North China craton,Trans-North China Orogen,and surrounding regions

To determine the lateral and vertical variations in crustal structure and their influence on the seismicity of the Western North China Craton,the Trans-North China Orogen,and the surrounding regions,the wavelet multi-scale structures,Moho depth,crustal density structures,and isostatic state are modelled using Bouguer gravity anomaly data,topography,and earthquake focal mechanisms.We obtained homogeneous crustal densities and deviations of<1 km between the crustal thicknesses estimated from the isostatic model and those inverted from the Bouguer gravity anomalies in the Ordos Block,the Inner Mongolia Suture Zone,the Sichuan Basin,and the Jizhong Depression.These results provide new evidence for relatively simple and stable continental crustal structures,and indicate that these regions will remain stable in both the vertical and lateral directions.The Hetao Graben,Yinchuan Graben,Weihe Basin,and Shanxi graben system have heterogeneous crustal densities and are isostatically over-compensated.In contrast,the crust beneath the Yinshan Uplift,Lvliang Uplift,and northern and central Taihang Uplift is thin and under-compensated.The heterogeneous crustal densities and non-isostatic state beneath the Tibetan Plateau and Qinling Central China Orogen indicate that these two blocks are unstable in the vertical and lateral directions.Although Cenozoic deformation of the North China Craton is thought to be driven by lithospheric stresses related to the India-Eurasia collision and Pacific slab retreat in South East Asia,we suggest that gravitational potential energy created by the heterogeneous crustal structure modulates these first-order forces.The results of this study could constrain the causes of seismicity in systems surrounding the Ordos Block.

A Study of the Pit-Aided Construction of Egyptian Pyramids

Pyramids,symbols of the Ancient Egyptian civilization,are visited by tourists and studied by researchers from all around the world.However,the techniques used by Ancient Egyptians to construct the pyramid,specifically,how such a tall structure could have been constructed from huge blocks of stone with the limited productive forces at the time,remains a mystery to the world.Though numerous theories,such as the use of ramps,levers,pulleys,fluid buoyancy,and cast-in-place concrete,have been proposed in academia,no consensus has been reached to date.Based on mechanical principles and the productive forces available at the time,the famous Pyramid of Khufu is used as a case study in this paper to propose a theory of pit-aided construction.The main steps include the digging of the pit,the transportation of stone blocks into the pit,the layer-by-layer construction,and the layer-by-layer filling of soil until the top of the pyramid is completed.The main idea of the pit-aided construction was to use the self-weight of the stone material to achieve the transportation of stone blocks by converting potential energy to kinetic energy,thereby avoiding the large amounts of work that must be done to elevate the huge blocks of stone.The proposed theory of pit-aided construction is consistent with the cultural custom of burial that is associated with tomb construction,namely laying the deceased to rest through burial,and is also consistent with the productive forces available in Ancient Egypt at the time.

How Quantum Mechanics and General Relativity Can Be Brought Together

This paper describes an easy and teaching way how quantum mechanics (QM) and general relativity (GR) can be brought together. The method consists of formulating Schrödinger’s equation of a free quantum wave of a massive particle in curved space-time of GR using the Schwarzschild metric. The result is a Schrödinger equation of the particle which is automatically subjected to Newtons’s gravitational potential.

Characteristics and geological significance of the stress state of the lithosphere in the Qinghai-Tibetan Plateau and its neighboring areas

The present-day lithospheric stress state of the Qinghai-Tibetan Plateau and neighboring areas is controlled by both the lithosphere itself and the underlying mantle.In other words,the stress is affected by the gravitational potential energy(GPE)difference caused by the change in the density distribution within the lithosphere and the drag force on the base of the lithosphere caused by mantle convection.The study of the lithospheric stress state plays an important role in further understanding the dynamic background and mechanism for the evolution of the Qinghai-Tibetan Plateau.In this study,the Crust1.0 crustal density model combined with the S40RTS mantle shear wave velocity variation model was used to calculate the GPE.The EGM2008gravity field model was used to calculate the drag force from mantle convection at the base of the lithosphere.The lithospheric and joint stress fields of the two sources were obtained by solving the force balance under the thin sheet approximation.This way,we could comprehensively analyze the characteristics of the stress state within the Plateau.Six regions were classified according to the GPE stress field,mantle drag force stress field,the relative magnitude of the two stress fields,and correlation between the two stress fields and surface deformation.The lithospheric stress fields of the Tarim Basin and other stable blocks are mainly controlled by the GPE difference.The lithospheric stress field in the collision zone between the Indian Plate and the QinghaiTibetan Plateau is predominantly controlled by the deep mantle drag force.The lithospheric stress field in the interior of the Plateau is controlled by both GPE and mantle drag.The correlation between the lithospheric stress field and surface deformation at the southeast margin of the Qinghai-Tibetan Plateau is poor.It is hypothesized that the presence of lower crustal flow with lower effective viscosity leads to crust-mantle decoupling,and the mantle drag force has a weaker influence on the shallow crust,resulting in the inconsistency between the average lithospheric stress field and surface deformation.

A Well-Balanced Kinetic Scheme for Gas Dynamic Equations under Gravitational Field

In this paper,a well-balanced kinetic scheme for the gas dynamic equations under gravitational field is developed.In order to construct such a scheme,the physical process of particles transport through a potential barrier at a cell interface is considered,where the amount of particle penetration and reflection is evaluated according to the incident particle velocity.This work extends the approach of Perthame and Simeoni for the shallow water equations[Calcolo,38(2001),pp.201-231]to the Euler equations under gravitational field.For an isolated system,this scheme is probably the only well-balanced method which can precisely preserve an isothermal steady state solution under time-independent gravitational potential.A few numerical examples are used to validate the above approach.