Newton’s gravitational constant G is the product of two natural constants, which explains the “anomalous” increase in the eccentricity of the lunar orbit

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

Black Holes and the Supermassive Compact Object at the Galactic Center: Multi-arts of Thought and Nature

On Poincaré gauge theory of gravity, its equations of motion, and Gravity Probe B

Newtonian Quantum Gravity (NQG) unifies quantum physics with Newton's theory of gravity and calculates the so-called “general relativistic” phenomena more precisely and in a much simpler way than General Relativity, whose complicated theoretical construct is no longer needed. Newton's theory of gravity is less accurate than Albert Einstein's theory of general relativity. Famous examples are the precise predictions of General Relativity at binary pulsars. This is the reason why relativistic physicists claim that there can be no doubt that Einstein's theory of relativity correctly describes our physical reality. With the example of the famous “Hulse-Taylor binary” (also known as PSR 1913 + 16 or PSR B1913 + 16), the author proves that the so-called “general relativistic phenomena” observed at this binary solar system can be calculated without having any knowledge on relativistic physics. According to philosophical and epistemological criteria, this should not be possible, if Einstein's theory of relativity indeed described our physical reality. Einstein obviously merely developed an alternative method to calculate these phenomena without quantum physics. The reason was that in those days quantum physics was not yet generally taken into account. It is not the first time that a lack of knowledge of the underlying physical phenomena has to be compensated by complicated mathematics. Einstein's theory of general relativity indirectly already includes additional quantum physical effects of gravitation. This is the reason why it cannot be possible to unite Einstein's theory of general relativity with quantum physics, unless one uses “mathematical tricks” that make the additional quantum physical effects disappear again in the end.

The Newtonian physics, quantum physics and the theories of relativity suffer from a major Incompleteness on the ground of being unable to offer the topologies and the dimensionalities of the numerous physical variables. Out of the three very familiar dimensions of physical variables in conventional physics length (L), mass (M) and time (T), the two variables, namely mass and time are fully arbitrary and abstract. In Newtonian physics L, M and T are fully independent variables since no mathematical equation linking the said three variables have been proposed. It is an established fact and a matter of everyday experience that L, M and T are very much linked to each other and otherwise which, the universe could have taken either the infinite number of shapes of desire arising out of endless permutations and combinations of L, M and T or could have merged to fully length (LM°T°) or fully mass (L°MT°) or fully time (L°M° T). Max Planck tied up the five numbers of basic physical variables, length, time, mass, electric charge and temperature to the same source by linking all of them to the Newton’s Gravitational constant (G) and Planck constant (h). However, this attempt was also incomplete since the topologies of G and h, could not be put forward. Later on, the quantum physics even, could not erase the stamp of ‘abstractness’ as put on the physical variables like mass, time, temperature, gravitation, photon waves and many others. Neither the Newtonian physics nor the quantum physics can depict the dimensionalities of entropy, force, energy, acceleration, black hole, plasma state, etc. and as well cannot also tell us how a ‘photon’ looks alike or what the ‘gravitons’ are in reality. The recently discovered topological theory of quantum gravity (TTQG) revealed the following: 1. The phenomenon of gravitation is being linked to the intermolecular attractive forces. 2. Have defined all the above said physical variables as ‘gravitons’ in regard to entropy. 3. Presented the topologies and dimensionalities of the physical variables. 4. Introduced the inverse dimensionality concept in physics. 5. Proposed the mathematical equation relating L, M and T 6. Reformulated the basics of Newtonian physics, quantum physics and the special and general theories of relativity. 7. All the cosmic phenomena of the universe have been represented by a singularity graviton originated universal graviton cycle.

Born in Ulm, Württemberg (now Germany), Einstein was a theoretical physicist who initiated a scientific revolution with his theory of general relativity. Challenging classical mechanics and its basis in Newtonian science, Einstein replaced the Euclidean model of geometry with four-dimensional spacetime and, from the axiom of the absolute speed of light, logically deduced the relativity of time. Subsequent to the advent of relativity theory, there is no longer any absolute temporal metric for defining the real. Einstein published two seminal papers, "Zur Elektrodynamik bewegter Körper" (1905; "The Special Theory of Relativity") and "Die Grundlage der allgemeinen Relativitätstheorie" (1916; "The General Theory of Relativity"), and in 1921 was awarded the Nobel Prize in Physics. His name and iconic visage have become synonymous with modern science, leaving an ineradicable imprint on 20th-century culture far beyond the enclaves of scientific research, a status partly achieved by his willingness to popularize his work. Einstein made lasting contributions to gravitational field theory, astrophysics and quantum mechanics, and much fame has accrued around his groundbreaking formula E = mc2, with its articulation of mass-energy equivalence. But it is with the theory and concept of time-relativity that Einstein’s thought crosses over into cultural and aesthetic modernism.

In this thesis we examine several ways in which we can explore the early universe through gravitational-waves and the fundamental nature of gravity through cosmology and observations of dynamics within the solar system. Both of these topics have taken center stage, as we are living at a unique time which promises to bring fundamental insights into the nature of gravity with the discovery of new binary pulsar systems, the building of increasingly precise solar system and tabletop experiments and the birth of gravitational-wave observatories-- to name a few recent and upcoming advances. We first discuss whether we may be able to directly detect gravitational waves from inflation using future space-based interferometers. We then describe how the direct detection of inflationary gravitational waves will allow us to probe the fundamental physics that operated at the earliest moments of the universe. Next, a new constraint to a general cosmological gravitational wave background is presented using the observations of the cosmic microwave background. Moving away from general relativity, we consider alternative theories of gravity. One reason to consider alternative theories of gravity is the observation that the expansion of the universe is currently accelerating. It is possible that this accelerated expansion is due to a modification of gravity. However, any theory that modifies gravity in order to produce accelerated expansion must also conform to the dynamics that we observe within the Solar System. We discuss how the observation of the deflection of light around the Sun places severe limitations on a particular modified gravity theory, known as f(R) gravity. Our discussion of f(R) gravity leads us to ask whether the parameterized post Newtonian parameter, γPPN, takes on a universal value. We identify measurements made of strong lensing around early type galaxies in the Sloan Lens ACS (SLACS) survey as a first step in performing this new test of gravity. Finally, we explore some consequences of Chern-Simons gravity. One of the unique aspects of Chern-Simons gravity is that it introduces parity violation into the gravitational sector. As a consequence, it predicts a different gravitomagnetic field around the rotating Earth than is predicted in general relativity. We show how recent measurements of this gravitomagnetic field made by observing the two LAser GEOdynamics Satellites (LAGEOS) and Gravity Probe B satellites constrain Chern-Simons gravity. Finally, we discuss how future observations of binary pulsar systems may allow for a more general exploration of the gravitomagnetic structure around rotating objects.

Gravity: An Introduction to Einstein's General Relativity

We recall a classical theory of torsion gravity with an asymmetric metric, sourced by a Nambu–Goto + Kalb–Ramond string [R. T. Hammond, Rep. Prog. Phys. 65, 599 (2002)]. We explain why this is a significant gravitational theory and in what sense classical general relativity is an approximation to it. We propose that a noncommutative generalisation of this theory (in the sense of Connes’ noncommutative geometry and Adler’s trace dynamics) is a “quantum theory of gravity.” The theory is in fact a classical matrix dynamics with only two fundamental constants – the square of the Planck length and the speed of light, along with the two string tensions as parameters. The guiding symmetry principle is that the theory should be covariant under general coordinate transformations of noncommuting coordinates. The action for this noncommutative torsion gravity can be elegantly expressed as an invariant area integral and represents an atom of space–time–matter. The statistical thermodynamics of a large number of such atoms yields the laws of quantum gravity and quantum field theory, at thermodynamic equilibrium. Spontaneous localisation caused by large fluctuations away from equilibrium is responsible for the emergence of classical space–time and the field equations of classical general relativity. The resolution of the quantum measurement problem by spontaneous collapse is an inevitable consequence of this process. Quantum theory and general relativity are both seen as emergent phenomena, resulting from coarse graining of the underlying noncommutative geometry. We explain the profound role played by entanglement in this theory: entanglement describes interaction between the atoms of space–time–matter, and indeed entanglement appears to be more fundamental than quantum theory or space–time. We also comment on possible implications for black hole entropy and evaporation and for cosmology. We list the intermediate mathematical analysis that remains to be done to complete this programme.

# The Dawn of Gravitation: # The Mathematical Principles of Natural Philosophy (I Newton) # On the Dynamics of the Electron (H Poincare) # Einstein's Deepest Insight and Its Early Impacts: # Outline of a Generalized Theory of Relativity and of a Theory of Gravitation (A Einstein & M Grossmann) # The Foundation of the General Theory of Relativity (A Einstein) # On a Generalization of the Concept of Riemann Curvature and Spaces with Torsion (E Cartan) # The Scalar-Tensor Theory of Gravity: # Formation of the Stars and Development of the Universe (P Jordan) # Yang-Mills' Deepest Insight and Its Relation to Gravity: # Conservation of Isotopic Spin and Isotopic Gauge Invariance (C N Yang & R L Mills) # Conservation of Heavy Particles and Generalized Gauge Transformations (T D Lee & C N Yang) # Invariant Theoretical Interpretation of Interaction (R Utiyama) # Accelerated Frames: Generalizing the Lorentz Transformations: # On Homogeneous Gravitational Fields in the General Theory of Relativity and the Clock Paradox (C Moller) # The Clock Paradox in the Relativity Theory (T Y Wu & Y C Lee) # Four-dimensional Symmetry of Taiji Relativity and Coordinate Transformations Based on a Weaker Postulate for the Speed of Light (J P Hsu & L Hsu) # Quantum Gravity and 'Ghosts': # Quantum Theory of Gravitation (R P Feynman) # Quantum Theory of Gravity, III Applications of the Covariant Theory (B S DeWitt) # Feynman Diagram for the Yang-Mills Field (L D Faddeev & V N Popov) # Missed Opportunities (F J Dyson) # Gauge Theories of Gravity: # Extended Translation Invariance and Associated Gauge Fields (K Hayashi & T Nakano) # Gravitational Field as a Generalized Gauge Field (R Utiyama & T Fukuyama) # Alternate Approaches to Gravity: Roads Less Traveled By: # Fixation of Coordinates in the Hamiltonian Theory of Gravitation (P A M Dirac) # New General Relativity (K Hayashi & T Shirafuji) # Relativistic Theory of Gravitation (A A Logunov & M A Mestvirishvili) # Yang-Mills Gravity: A Union of Einstein-Grossmann Metric with Yang-Mills Tensor Fields in Flat Spacetime with Translation Symmetry (J P Hsu) # Experimental Tests of Gravitational Theories: # Empirical Foundations of the Relativistic Gravity (W T Ni) # Binary Pulsars and Relativistic Gravity (J H Taylor, Jr.) # Other Perspectives: # Concept of Nonintegrable Phase Factors and Global Formulation of Gauge Fields (T T Wu & C N Yang) # Gauge Theory: Historical Origins and Some Recent Developments (L O'Raifeartaigh & N Straumann) # The Cosmological Constant and Dark Energy (P J E Peebles & B Ratra) # and other papers

Weber’s gravitational force (WGF) is one of gravitational model that can accommodate a non-static system because it depends not only on the distance but also on the velocity and the acceleration. Unlike Newton’s law of gravitation, WGF can predict the anomalous of Mercury and gravitational bending of light near massive object very well. Then, some researchers use WGF as an alternative model of gravitation and propose a new mechanics theory namely the relational mechanics theory. However, currently we have known that the theory of general relativity which proposed by Einstein can explain gravity with very accurate. Through the static weak field approximation for the non-relativistic object, we also have known that the theory of general relativity will reduce to Newton’s law of gravity. In this work, we expand the static weak field approximation that compatible with relativistic object and we obtain a force equation which correspond to WGF. Therefore, WGF is more precise than Newton’s gravitational law. The static-weak gravitational field that we used is a solution of the Einstein’s equation in the vacuum that satisfy the linear field approximation. The expression of WGF with ξ = 1 and satisfy the requirement of energy conservation are obtained after resolving the geodesic equation. By this result, we can conclude that WGF can be derived from the general relativity.

The physics of gravity is inextricably connected to the geometry of space and time. In Einstein’s theory of general relativity—the best theory of classical gravity that we have—the geometry (curvature) of spacetime, as encoded in the metric tensor g μν, is identified with the gravitational field. But the metric field is also responsible for the characteristic structures of space and time too (causal structure, notions of distance, and so on). Hence, the metric plays a dual role in general relativity: it serves to generate both the gravitational field structures and the chronometric, spatio-temporal structures (cf. Stachel 1993). In the context of general relativistic physics, of course, the metric—and, therefore, the geometry of space—is dynamical : the metric on spacetime is not fixed across the physically admissible models of the theory (as it is in, for example, Newtonian and specially relativistic theories). The geometry of spacetime is affected by matter in such a way that different distributions of matter yield different geometries—the coupling and the dynamics is described by Einstein’s field equation. In other words, general relativity does not depend on the fixed metrical structure of spacetime; rather, the metric itself, and hence the geometry, comes only once a matter distribution has been specified (and the dynamical equation has been solved). Classically, this feature, called background independence,1 is rather

By using purely geometric forces on a noncommutative spacetime, noncommutative spectral geometry (NCSG) was proposed as a possible way to unify gravitation with the other known fundamental forces. The correction of the NCSG solution to Einstein's general relativity (GR) in the four-dimensional spacetime can be characterized by a parameter \(\beta\sim 1/\sqrt{f_{0}}\), where \( f_{0}\) denotes the coupling constants at the unification. The parameter \( \beta\) contributes a Yukawa-type correction \(\mathrm{exp}(-\beta r)/r\) to the Newtonian gravitational potential at the leading order, which can be interpreted as either the massive component of the gravitational field or the typical range of interactions carried by that component of the field. As an extension of previous works, we mainly focus on the Solar System and stellar tests of the theory, and the constraints on \(\beta\) obtained by the present work is independent of the previous ones. In the Solar System, we investigate the effects of the NCSG on the perihelion shift of a planet, deflection of light, time delay at superior conjunction (SC) and inferior conjunction (IC), and the Cassini experiment by modeling new observational results and adopting new datasets. In the binary pulsars system, based on the observational data sets of four systems of binary pulsars, PSR B1913+16, PSR B1534+12, PSR J0737-3039, and PSR B2127+11C, the secular periastron precessions are used to constrain this theory. These effects in the scale of the Solar System and binary pulsars were not considered in previous works. We find that the lower bounds given by these experiments are \(\beta \simeq 10^{-9} \sim 10^{-10}\) m-1, considerably smaller than those obtained in laboratory experiments. This confirms that experiments and observations at smaller scales are more favorable for testing the NCSG theory.

An analytic solution methodology for general relativity (GR) equations describing the hypothetical phenomenon of wormholes is presented and the analysis of wormholes in terms of their physical properties is discussed. An analytic solution of the GR equations for static and dynamic spherically symmetric wormholes is given. The dynamic solution generally describes a 'traversable' wormhole, i.e., one allowing matter, energy, and information to pass through it. It is shown how the energy–momentum tensor of matter in a wormhole can be represented in a form allowing the GR equations to be solved analytically, which has a crucial methodological importance for analyzing the properties of the solution obtained. The energy–momentum tensor of wormhole matter is represented as a superposition of a spherically symmetric magnetic (or electric) field and negative-density dust matter, serving as exotic matter necessary for a 'traversable' wormhole to exist. The dynamics of the model are investigated. A similar model is considered (and analyzed in terms of inflation) for the Einstein equations with a Λ term. Superposing enough dust matter, a magnetic field, and a Λ term can produce a static solution, which turns out to be a spherical Multiverse model with an infinite number of wormhole-connected spherical universes. This Multiverse can have its total energy positive everywhere in space, and in addition can be out of equilibrium (i.e., dynamic).

Many Dimensions in Gravity Theory