A geometric framework for directly visualizing relativistic effects on space and time in special and general relativity

Siva’s theories explained the necessity of new theory for description of the Universe, space ,time ,space-time and matter. It explained the formation of ‘space time continuum’ in terms of ‘Films of the universe’ and an effect of consciousness associated to living things. Thus it is required to bring consciousness in to physical laws and transformations. The relation between physical world and consciousness has been analyzed clearly and explained that consciousness, if we interpret in physics, must be an inertial frame of reference which can be transformed in to inertial frames defined by ‘Special Theory of Relativity’. It is possible only by changing the signal velocity from ‘c’ to ‘c√2’ . Thus the ‘Special Theory of Relativity’ has been modified and named as ‘Super theory of Relativity’. The relativistic factor for it is also calculated as [1+(v2/c2)]1/2 where v = vo [{1- (vo2/c2)}]-1/2 here vo is its absolute velocity .The necessity to adopt a new signal velocity which is greater than that of light has been discussed and the ‘Principle of Relativity’ and ‘Principle of simultaneity’ which are basics for transformation has been applied to interpret it in terms of relativity. It has been concluded that velocity of light is a part of signal velocity and photon will have rest mass. It says that the observable velocity is a result of absolute velocity multiplied by relativistic factor for ‘Super Theory of Relativity’. Thus infinite signal transformation is introduced for transformation between Inertial frames of reference. Infinite signal velocity will explain the ‘Quantum entanglement’ in terms of transformation of physical laws from one frame to another as explained in ‘Special & General Theories of Relativity’.

This paper shows that gravitational results of general relativity (GR) can be reached by using special relativity (SR) via a SR Lagrangian that derives from the corresponding GR time dilation and vice versa. It also presents a new SR gravitational central scalar generalized potential V=V(r,r.,ϕ.), where r is the distance from the center of gravity and r.,ϕ. are the radial and angular velocity, respectively. This is associated with the Schwarzschild GR time dilation from where a SR scalar generalized potential is obtained, which is exactly equivalent to the Schwarzschild metric. Thus, the Precession of Mercury’s Perihelion, the Gravitational Deflection of Light, the Shapiro time delay, the Gravitational Red Shift, etc., are explained with the use of SR only. The techniques used in this paper can be applied to any GR spacetime metric, Teleparallel Gravity, etc., in order to obtain the corresponding SR gravitational scalar generalized potential and vice versa. Thus, the case study of Newtonian Gravitational Potential according to SR leads to the corresponding non-Riemannian metric of GR. Finally, it is shown that the mainstream consideration of the Gravitational Red Shift contains two approximations, which are valid in weak gravitational fields only.

The happiest thought of Einstein's life

When Euclidean coordinate lengths are replaced by the metric lengths of a curved geometry within Newton’s second law of motion, the metric form of the second law can be shown to be identical to the geodesic equation of motion of general relativity. The metric coefficients are contained in the metric lengths and satisfy the field equations of general relativity. Because metric lengths are the physically measured lengths, their use makes it possible to understand general relativity directly in terms of physical quantities such as energy and momentum within a curved space–time. The metric form of the second law contains gravitational effects in exactly the same manner as occurs in relativity. Its mathematical derivation uses vectors rather than tensors, and nongravitational forces can occur in this modified second law without a tensor form. Because quantum mechanics is based on Newtonian concepts of energy and momentum, it is shown that when metric lengths replace coordinate lengths in Dirac’s wave equation, it has a covariant form under a metric transformation of the physically measured distances themselves, rather than a coordinate transformation. Metric transformations are also used to describe the Dirac equation for the gravitational central field in a Schwarzschild metric.

This research investigates the advanced scientific concepts of space-time curvature, wormholes, and time dilation as fundamental natural principles described in the Quran centuries before their modern discovery. Surah Al-Kahf is particularly significant in this context, as it directly addresses wormholes, space-time curvature, and gravitational effects. To fully comprehend this, firstly we must understand what “Al-Kahf” truly represents in the Quran. This study explores the scientific properties of Al-Kahf and its relation to relativity, gravitational lensing, and space-time warping, etc.While modern science views Spacetime Curvature, wormholes and time dilation etc., as extraordinary phenomena, The Quran presents them as fundamental aspects of the universe, and are also utilized in divine operations—just as it describes the water cycle, planetary motion, and celestial mechanics etc. These principles are not isolated mentions but are woven throughout the Quran, highlighting the Quran’s deep engagement with the fabric of space-time.Among the key Quranic verses that encapsulate this concept, Surah Al-Kahf 18:17 [7] stands as the most crucial, as it directly defines and completes the key properties of Al-Kahf by describing the Spacetime Curvature, bending of light and gravitational lensing effects etc., in a most fascinating and unbelievable way, without any illogical interpretation but direct meaning of verses, from existing translations like Sahih International etc. and we have just converted it into a visual diagram/figure. While an understanding of Al-Kahf as a space-time phenomenon is possible from other Quranic descriptions, verse 18:17 serves as the “ULTIMATE KEY” to establish this concept with certainty. If one fully comprehends Quran 18:17, with Quran 18:25,29 etc. then the true nature of Al-Kahf becomes undeniably clear—revealing its nature of space-time curvature, time dilation, and gravitational lensing etc. This verse is 18:17 not only foundational but also the pinnacle of understanding, ensuring that any doubts regarding Al-Kahf’s relation to relativity and space-time distortions are completely resolved.Furthermore, once one will understand what “Al Kahf” truly represents, it will unlock a deeper understanding of entire (CHAPTER) “Surah Al-Kahf” which can ultimately help us to understand & reveal the secrets of the universe deeply including wormholes, space-time curvature, and gravitational effects, as Al-Kahf is treasure of these things. It is a complete dedicated chapter about wormholes, space-time curvature, and gravitational effects etc. Without grasping the concept of Al-Kahf from the initial part of the chapter, the rest of Surah Al-Kahf cannot be fully comprehended. This foundational understanding is not just limited to this chapter—it extends to the entire Quran, where relativity, time dilation, gravitational lensing, and space-time curvature/Anomalies are referenced in various verses. When we will establish Al-Kahf as a space-time concept, it will illuminate the meaning of other parts of Surah Al-Kahf and numerous other Quranic verses that describes these cosmic principles throughout the Quranic text.By integrating Quranic insights with General Relativity and modern astrophysics, this paper challenges conventional narratives of scientific history, advocating for a reassessment of the Quran’s contributions to humanity’s understanding of space-time and relativity. This interdisciplinary approach highlights that the Quran contains detailed direct descriptions of these cosmic phenomenon (wormholes, space-time curvature, space-time distortions and gravitational effects etc.) that align with cutting-edge physics, reinforcing the need for a historical reevaluation of scientific knowledge.

In the general theory of relativity, the four‐dimensional space‐time of describing a mass body accelerated motion or in a gravitational field, although it is a curved Riemannian geometric space from the perspective of “integral geometry”, but for any instantaneous position of the moving mass body, there is a local Flat Space of Riemannian geometric space. The local Flat Space is a Mincowski space in which the inertial coordinate system can be used in the local small area. Between the proper coordinate systems of two interacting moving masses, or between a series of following proper coordinate systems experienced by a mass body moving in any way, there should be a coordinate transformation relationship similar to the traditional special theory of relativity. However, they have an important difference: in these instantaneous local inertial systems, the speed of light is no longer the constant c of vacuum, the effect of gravitational field or acceleration on the speed of light is the same as that of a medium with a dielectric constant of ε and a magnetic permeability of μ. Using the special theory of relativity with variable speed of light that the author has established can discuss relevant relativity physics issues in these instantaneous local inertial systems. This article uses the special theory of relativity with variable speed of light to derive the functional relationship between a moving mass and the change of speed. In addition to obtain the traditional continuous increasing function relationship, a step function relationship with stepped discontinuous changes is also obtained. At the same speed, the mass can have two values, such as a ladder upgrade one level; the same mass can be matched with two different speeds, such as one step extension forward on the same step stair. From the perspective of the increase in speed, the mass is stagnant on the step platform (the speed increases, the mass does not change), and it jumps in the step up ladder (the speed does not change, the mass has a jump change). This obviously incorporates the main image of quantum theory into the theory of relativity, which is the result that all physics researchers care about and expect.

The gravity in the context of General Relativity (GR) as dynamical curvature of spacetime remains a principal impediment not only to its unification with the other fundamental interactions, but also to the formulation of quantum gravity. One possible resolution involves considering gravity in the context of Special Relativity (SR). This paper presents a procedure, which correlates the GR metrics of curved spacetime and the SR Gravitational Scalar Generalized Potential (GSGP). The GR time dilation is the key-point for the correlation of the two gravities, which implies the corresponding SR Lagrangian. Previous papers have already demonstrated the procedure and the results in cases of FLRW metric, wormholes with spherical symmetry, and Schwarzschild metric (where not only the gravitational motions (free falls) in the context of SR are exactly the same as those in the context of GR with stationary metric, but also the SR and GR Gravitational Red Shift). This paper analytically derives the general formulae of Equations of Motion in Spacetime endowed with Stationary metric in the context of GR and the ones in the context of SR, proving that they are exactly the same. Finally, it presents the case studies of gravitational motions around Schwarzschild blackhole, Kerr rotating blackhole and Standard Ellis-Bronnikov wormhole. Thus, it is shown that these motions have an equivalent SR viewpoint.

Gravity: An Introduction to Einstein's General Relativity

We give a definition of rigid congruences in both General and Special Relativity, and we try to make the definition plausible. To this end we recall Fermat's principle in General Relativity and we show that this principle allows us to reinterpret the “quotient metric” as the quadratic form which defines the optical length in a gravitational field. We apply the definition to the Earth-Sun system in the post-Newtonian approximation. Furthermore we compute the Fermat tensor and the corresponding relative variation of the speed of light in a Michelson-Morley like experiment performed on the Earth's surface. According to all measurements to date, this quantity is extremely small (10 -13 ).

We study the behaviour of relativistic quantum particles in the space-time generated by a moving mass current, in the weak field approximation. We solve the Dirac equation in this gravitational field and calculate the current associated with the particles. The study of the behaviour of quantum systems under the influence of curved space-times goes back to the end of the 1920s and to the beginning of the 1930s[1], when the generalization of the Schr ¨ odinger and Dirac equations to curved spaces has been discussed, motivated by the idea of constructing a theory combining quantum physics and general relativity. Along this line of research the hydrogen atom has been studied in particular curved space-times[2, 3]. These investigations showed that the energy levels of an atom placed in a gravitational field is shifted as a result of the interaction of the atom with the space-time curvature[3]-[5]. This shift in the energy of each atomic level would depend on the features of the space-time. The general theory of relativity, as a metric theory, predicts that gravitation is manifested as the curvature of space-time. Therefore, it is of interest to know how the curvature of spacetime at the position of the atom affects its spectrum. On the other hand, we know that there are situations in which particles are constrained to move in a region where the Riemann curvature tensor vanishes and even in this case they exhibit gravitational effects arising from a region of non-zero curvature from which they are excluded[6]. In a more general sense, we have the case in which particles are constrained to move in a region where the Riemann curvature tensor does not vanish but does depend on certain parameter of the metric such as the velocity or the angular momentum of the source. In this case we have effects on the system associated with parameters which do not influence the curvature of the space-time as we will see. In what follows we present the study concerning the behaviour of a relativistic particle placed in the gravitational field generated by a cylindrical distribution of matter with uniform density along the z-axis moving slowly, whose metric reads[7]

Science sets itself apart from other paths to truth by recognizing that even its greate practitioners sometimes err.

Relativity means that physically it is impossible to detect absolute motion. This can be stated as a “symmetry in physics”. Special relativity (SR) is the symmetry with respect to coordinate transformations among inertial frames, general relativity (GR) among more general frames, including the accelerating coordinate systems. GR is also the relativistic theory of gravitation, and SR is valid only in the absence of gravity. Einstein's motivations to develop GR are reviewed, and his basic idea of curved spacetime as the gravitation field is outlined. Relativity represents a new understanding of space and time. GR provides the natural conceptual framework for cosmology. Experimental foundation of GR will be emphasized in our presentation. The necessary mathematics is introduced as it is needed.

本文系统地分析了广义相对论的理论架构，主要预言，实验检验及其对物理科学其他分支的影响，指出爱因斯坦引力场方程除了(0,0)分量能够在线性场近似下得到牛顿的万有引力定律，张量方程的所有其他分量或者导致无穷大发散，或者与光速极限原理相悖，或者毫无物理意义。文章详细地分析了广义相对论的三个经典实验检验，指出所有三个检验都站不住脚。同时，本文也分析了最近宣布证实了引力波和黑洞的两个实验(BICEP2和LIGO实验)都经不起分析，根本不能为广义相对论提供证据。文章指出，由于相对性原理要求任何理论都必须具有平动和转动相对性，必须存在一个施瓦兹查尔德度规和科尔度规之间的转动变换。计算表明，这一变换和相对论的光速极限原理相悖，因而广义相对论违背相对性原理。本文还详尽地讨论了广义相对论的一个重要概念：时空弯曲造成引力，或者引力使时空弯曲。文章指出短程线描述的是某一物体在引力场中的运动轨迹。轨迹的弯曲不是时空的弯曲。另一方面，引力场方程描述的是等位面的形状。等位面的弯曲不是时空的弯曲。时空弯曲的量度是黎曼曲率R。计算表明，爱因斯坦场方程的两个解析解—施瓦兹查尔德解和科尔解的黎曼曲率和里奇张量都是零，所以时空是平坦的。所谓引力使时空弯曲和时空弯曲产生引力的概念都是错的。本文得出结论说，牛顿的经典引力理论是建立在开普勒实验定律所包含的无数实验观测结果之上的，经过了几百年科学实验和工程实践的检验，并且继续在科学和工程中接受广泛的检验，从来没有一个例子证明牛顿万有引力定律的错误。相反，爱因斯坦的广义相对论从基本假设，理论框架，实验检验和实际应用都存在根本性的不自洽或违背基本的物理事实。因此，说牛顿引力理论只是近似正确，广义相对论是比牛顿万有引力定律更精确的引力理论，是不正确的。至于从广义相对论演变而来的黑洞理论和大爆炸宇宙学，更是违背科学逻辑的星相学理论和数学创造论。作者坚决反对将一些违背科学的观念，诸如将多重宇宙，因果倒转，时空穿越，高维空间，宇宙创生，等等一系列星相学和创造论概念灌输给年轻的学子，主张理论物理必须在新的世纪科学复兴，从神学和星相学思维回归科学经典。 This article gives a systematic review of the theoretical framework, major predictions, experimental evidences of general relativity and its implications to other branches of science. It has been pointed out that, other than the (0,0) component of Einstein’s tensor field equation which reduces to the Newtonian law of gravitation under linear approximation, all other components either lead to divergence, or are in conflict with the fundamental postulation of relativity that no speed should exceed the speed of light, or defies physical interpretation. The review gives a detailed analysis of the three classical evidences of general relativity and has shown that none of these experimental evidences can stand scrutiny. The article also analyzed the two recent experiments (BICEP2 and LIGO) that claimed to have found experimental evidences of gravitational wave and black hole, and demonstrated their fallacies. It has been pointed out that the principle of relativity demands that any viable theory must have translational as well as rotational relativity, which requires general relativity to have a rotational transformation that can transform the Schwarzschild metric into the Kerr metric and vice versa. Calculations show that a general rotational transformation is in conflict with one of the fundamental postulations of relativity—no speed should exceed the speed of light, i.e., general relativity violates the principle of relativity. The article also gives a thorough analysis of one of the most important concept of general relativity—gravity comes from the curvature of space time, and gravity warps the space time. It has been pointed out that the curving of a geodesic is merely the bending of the trajectory of an object moving in gravitational field, which is not the curving of the space time itself. Moreover, the field equation describes the shape of equipotential, the curving of which is not the curving of space time either. The measure of curvature of space time is the Riemann curvature scalar R. Calculations show that the Riemann curvature and Ricii tensor of both the Schwarzschild metric and the Kerr metric—the only two known analytical solutions to Einstein’s field equation, vanish, which means that the space time is flat. The concept that gravity comes from the curvature of space time and gravity warps the space time is invalid. The review concludes that the Newtonian law of gravity is built upon the Keplers laws that represent enormous results of observational astronomy and has stood hundreds of years’ test by scientific research and engineering practice. It is still been checked every day by science and engineering, and has never failed the test. On the other hand, Einstein’s general relativity has a multitude of unsolvable inconsistencies in its fundamental postulations, theoretical framework, experimental tests, and it is completely powerless in practical applications. It is therefore incorrect to say that the Newtonian law of gravitation is only an approximation of the more accurate general relativity. As to the black home and the Big Bang cosmology derived and developed from general relativity, these are astrological theories that violate scientific logic. The author is strongly against brain washing the younger generations with the astrological and theological concepts such as multiverse, reverse of causality, time travel, high dimension, creation of the universe and so on. Physical science needs nothing less than a renaissance in the new century, returning to classical science from astrological paradigm.

Yang–Mills equations, originally derived for the isospin gauge group SU(2), provide the first example of gauge field equations for a non-Abelian gauge group. This gauge group appears as an internal or local symmetry group of the theory. In fact, the theory can be extended easily to include the other classical Lie groups as gauge groups. Historically, the classical Lie groups appeared in physical theories, mainly in the form of global symmetry groups of dynamical systems. Noether’s theorem established an important relation between symmetry and conservation laws of classical dynamical systems. It turns out that this relationship also extends to quantum mechanical systems. Weyl made fundamental contributions to the theory of representations of the classical groups [401] and to their application to quantum mechanics. The Lorentz group also appears first as the global symmetry group of the Minkowski space in the special theory of relativity. It then reappears as the structure group of the principal bundle of orthonormal frames (or the inertial frames) on a space-time manifold M in Einstein’s general theory of relativity. In general relativity a gravitational field is defined in terms of the Lorentz metric of M and the corresponding Levi-Civita connection on M. Thus, a gravitational field is essentially determined by geometrical quantities intrinsically associated with the space-time manifold subject to the gravitational field equations. This geometrization of gravity must be considered one of the greatest events in the history of mathematical physics.

The mainstream approach of gravitational field is the development of Geometric theories of gravitation and the application of the Dynamics of General Relativity (GR). Besides, the Generalized Special Relativity (GSR) contains the fundamental parameter (ξI) of Theories of Physics (TPs). Thus, it expresses at the same time Newtonian Physics (NPs) for ξI→0 and Einstein Relativity Theory (ERT) for ξI=1. Moreover, the Equivalence Principle (EP) in the context of GSR, has two possible interpretations: mG = m (1), or mG=γ(ξI,β)m (2), where β=υ/c and mG, m, γ are the gravitational mass, inertial rest mass and Lorentz γ-factor, respectively. In this paper we initially present a new central scalar potential V=V(k,r), where k=k(ξI) and r is the distance from the center of gravity. We demand that ‘this new GSR gravitational field in accordance with EP (1), gives the same precession of Mercury’s orbit as Schwarzschild Metric (SM) does’ and we obtain k=6-ξI2. This emerges Einsteinian SR-horizon at r=5rS, while NPs extends the horizon at six Schwarzschild radius (6rS).We can also explain the Gravitational Red Shift (GRS), if only the proposed GSR Gravitational field strength g=g(k,r) is combined with EP (2). We modify the aforementioned central scalar potential as V=V(h,k,r), where h=h(r). The combination of the above with MOND interpolating functions, or distributions of Dark Matter (DM) in galaxies, provides six different functions h=h(r). Thus, we obtain a new GSR central Gravitational field strength g=g(h,k,r), which not only explains the Precession of Mercury’s Perihelion, but also the Rotation Curves in Galaxies, eliminating Dark Matter.