A geometric formulation of the gravitation theory in the spacetime R × S 3 is given. A linear connection is introduced on the tangent bundle T(R × S 3 ) and then the connection coefficients and the Riemann curvature tensor are calculated. It is shown that their expressions differ from those of Carmeli and Malin [Found. Phys.17, 407 (1987)] by supplementary terms due to the noncommutativity of derivatives used on the spacetime R × S 3 . The Einstein field equations (...) are written as usually and a comparison with other results is given. Finally, some observations about a possible gauge theory of gravitation in the spacetime R × S 3 are made. (shrink)

The story of Einstein's struggle to create a general theory of relativity, and his early discontentment with the final form of the theory , is well known in broad outline. Thanks to the work of John Norton and others, much of the fine detail of the story is also now known. One aspect of Einstein's work in this period has, however, been relatively neglected: Einstein's commitment to Mach's ideas on inertia, and the influence this commitment had on Einstein's work on (...) general relativity from 1907 to 1918. In this paper published writings and archival material are examined, to try to reconstruct the details of Einstein's thinking about inertia and gravitation, and the role that Mach's ideas played in Einstein's crucial work on the general theory. By the end, a clear picture of Einstein's conceptions of Mach's ideas on inertia, and their philosophical motivations, will emerge. Several surprising conclusions also emerge: Einstein's desire for a Machian gravitation theory was the central force driving his work from 1912 to 1915, keeping him going despite numerous frustrating setbacks; Einstein's continued commitment to Mach's ideas in 1916–1917 kept him at work trying various strategies of modification of the field equations, in order to exclude anti-Machian solutions ; and as late as early 1918, Einstein was ready to call the whole General Theory a failure if no way of squaring it with Mach's ideas on inertia could be found. But by 1920 Einstein advocated a view that granted spacetime independent existence with physical qualities of its own, a complete break with his earlier Machian views. (shrink)

Four empirically equivalent versions of general relativity, namely standard GR, Lorentz-invariant gravitational theory,and the gravitational gauge theories of the Lorentz and translation groups, are investigated in the form of a case study for theory underdetermination. The various ontological indeterminacies (both underdetermination and inscrutability of reference) inherent in gravitational theories are analyzed in a detailed comparative study. The concept of practical underdetermination is proposed, followed by a discussion of its adequacy to describe scientific progress.

Newtonian cosmology is logically inconsistent. I show its inconsistency in a rigorous but simple and qualitative demonstration. "Logic driven" and "content driven" methods of controlling logical anarchy are distinguished.

1.1 Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Tangent Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (...) . . . . . . . . . . . 7 1.3 Vector Fields, Integral Curves, and Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4 Tensors and Tensor Fields on Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.5 The Action of Smooth Maps on Tensor Fields . . . . . . . . . . . . . . . . . . . . . . . . . 31 1.6 Lie Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1.7 Derivative Operators and Geodesics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 1.8 Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 1.9 Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 1.10 Hypersurfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 1.11 Volume Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96.. (shrink)

Classical and quantum field theory provide not only realistic examples of extant notions of empirical equivalence, but also new notions of empirical equivalence, both modal and occurrent. A simple but modern gravitational case goes back to the 1890s, but there has been apparently total neglect of the simplest relativistic analog, with the result that an erroneous claim has taken root that Special Relativity could not have accommodated gravity even if there were no bending of light. The fairly recent acceptance (...) of nonzero neutrino masses shows that widely neglected possibilities for nonzero particle masses have sometimes been vindicated. In the electromagnetic case, there is permanent underdetermination at the classical and quantum levels between Maxwell's theory and the one-parameter family of Proca's electromagnetisms with massive photons, which approximate Maxwell's theory in the limit of zero photon mass. While Yang–Mills theories display similar approximate equivalence classically, quantization typically breaks this equivalence. A possible exception, including unified electroweak theory, might permit a mass term for the photons but not the Yang–Mills vector bosons. Underdetermination between massive and massless (Einstein) gravity even at the classical level is subject to contemporary controversy. (shrink)

We consider a quadratic Lagrangian, in both curvature and torsion, with the aim of exploring the possibility that torsion and curvature behave as conjugate variables satisfying the commutation relations. For that proposal we first show that torsion represents a quantum correction to the classical equations of motion. We then observe that we have to introduce the spin in the Einstein theory with two spaces: a real space-time where we describe the curvature with tensors; and a complex space-time, where we describe (...) torsion with spinors. This is not satisfactory, and to overcome this contradiction we describe both mass and spin in a unique manifold, the real space-time, with the use of geometric algebra and geometric product. In that manner we are able to introduce a torsion trivector and curvature trivector that satisfy the commutation relations, opening the road for a quantum description of gravity theory. (shrink)

The concepts underlying our present theoretical understanding of the radiative two-condensed-body problem in general relativity and in bimetric gravitation theory are critically reviewed. The relevance of the 1935 Einstein-Rosen “bridge” article is emphasized. The possibility (first suggested by N. Rosen, for the linearized approximation) of extending to gravity the Wheeler-Feynman time-symmetric approach is questioned.

David Malament, now emeritus at the University of California, Irvine, where since 1999 he served as a Distinguished Professor of Logic and Philosophy of Science after having spent twenty-three years as a faculty member at the University of Chicago , is well known as the author of numerous articles on the mathematical and philosophical foundations of modern physics with an emphasis on problems of space-time structure and the foundations of relativity theory. Malament’s Topics in the foundations of general relativity and (...) Newtonian gravitation theory has grown out of a set of lecture notes on the foundations of general relativity that he has taught for many years. In full agreement with Manchak , it should be pointed out from the beginning that the book neither is and was never intended to be a graduate general relativity a .. (shrink)

: This paper first discusses the current historical and philosophical framework forged during the last century to account for both the history and the epistemic status of Newton's theory of general gravitation. It then examines the conflict surrounding this theory at the close of the seventeenth century and the first steps towards the revolutionary shift in rational mechanics in the eighteenth century. From a historical point of view, it shows the crucial contribution of the Cartesian mechanistic philosophy and Leibnizian analytic (...) methods to the emergence of so-called Newtonian mechanics which can also be fairly characterized as a synthetic theory of attraction. From a philosophical standpoint, the paper suggests that the reworking of Newton's theory in the 18th century is better understood in a theoretical framework that reconciles Kuhn's notion of "invisible revolution" rather than his notion of "normal science" with Whewell's ascription of the completion of dynamical studies to the post Newtonian period. (shrink)

Weinberg's 1972 work, in his description, had two purposes. The first was practical to bring together and assess the wealth of data provided over the previous decade while realizing that newer data would come in even as the book was being printed. He hoped the comprehensive picture would prepare the reader and himself to that new data as it emerged. The second was to produce a textbook about general relativity in which geometric ideas were not given a starring role for (...) (in his words) too great an emphasis on geometry can only obscure the deep connections between gravitation and the rest of physics. (shrink)

The theory of quantum gravitation, which is designed to unite the general relativity with the quantum field theory into one consistent theory, raises several major problems. The paper examines the limitations posed by general relativity on the efforts to create an ontological basis of the quantum theory of gravitation, which the latter ought to accept. It concerns mainly problems arising from relating the new field theory with the gravitational field in the general theory of relativity, the problems of the (...) autonomy of the space-time with its gravitational masses, as well as the problems of the covariance of the physical equations in the theory of quantum gravitation equations, the former being the consequence of the principle of a general covariance of the general relativity equations. (shrink)

There are well-known problems associated with the idea of gravitational energy in general relativity. We offer a new perspective on those problems by comparison with Newtonian gravitation, and particularly geometrized Newtonian gravitation. We show that there is a natural candidate for the energy density of a Newtonian gravitational field. But we observe that this quantity is gauge dependent, and that it cannot be defined in the geometrized theory without introducing further structure. We then address a potential response by (...) showing that there is an analogue to the Weyl tensor in geometrized Newtonian gravitation. (shrink)

L'éternalisme, la thèse selon laquelle les entités que nous catégorisons comme étant passées, présentes et futures existent tout autant, est la meilleure approche ontologique de l'existence temporelle qui soit en accord avec les théories de la relativité restreinte et de la relativité générale. Cependant, les théories de la relativité restreinte et générale ne sont pas fondamentales si bien que plusieurs programmes de recherche tentent de trouver une théorie plus fondamentale de la gravité quantique rassemblant tous les enseignements de la physique (...) relativiste et de la physique quantique. Certaines de ces approches soutiennent que le temps n'est pas fondamental. Toutefois, si le temps n'est pas fondamental, quelles en sont les conséquences pour l'éternalisme et les débats sur l'existence dans le temps ? Premièrement, je soutiendrai que la non-fondamentalité du temps que l'on rencontre dans la théorie des cordes mène à l'éternalisme standard. Deuxièmement, je soutiendrai que la non-fondamentalité du temps rencontrée dans la gravité quantique à boucles implique l'éternalisme atemporel, à savoir une nouvelle position qui demeure fidèle à l'esprit de l'éternalisme standard. (shrink)

The Weyl-Dirac theory of gravitation and electromagnetism is modified by the introduction of a background metric characterized by a scale constant related to the size of the universe. One is led to a natural gauge giving ${{\dot G} \mathord{\left/ {\vphantom {{\dot G} G}} \right. \kern-0em} G} = - 5.5 \times 10^{ - 12} y^{ - 1} $ . This is smaller by about a factor of ten than the value obtained on the basis of Dirac's large number hypothesis.

The foundations of a theory of nonminimal coupling of matter and the gravitational field in the framework of Riemannian (or Riemann-Cartan) geometry are presented. In the absence of matter, the Einstein vacuum field equations hold. In order to allow for a Newtonian limit, the theory contains a new parameter l0 of dimension length. For systems with finite total mass, l0 is set equal to the Schwarzschild radius.

In the present paper a relativistic theory of gravitation (RTG) is unambiguously constructed on the basis of the special relativity and geometrization principle. In this a gravitational field is treated as the Faraday-Maxwell spin-2 and spin-0 physical field possessing energy and momentum. The source of a gravitational field is the total conserved energy-momentum tensor of matter and of a gravitational field in Minkowski space. In the RTG the conservation laws are strictly filfilled for the energy-momentum and for (...) the angular momentum of matter and a gravitational field. The theory explains the whole available set of experiments on gravity. By virtue of the geometrization principle, the Riemannian space in our theory is of field origin, since it appears as an effective force space due to the action of a gravitational field on matter. The RTG leads to an exceptionally strong prediction: The universe is not closed but just “flat.” This suggests that in the universe a “missing mass” should exist in a form of matter. (shrink)

Proceeding from our absolute space-time conceptions, we obtain the formula for the gravitational frequency shift in an extremely simple way. Using our “burst” model for photons, we show that the different rates of clocks placed in spatial regions with different gravitational potentials appear as a direct result of the gravitational frequency shift and the axiomatic assumption that at any space point the time unit is to be defined by light clocks with equal “arms,” i.e., that at any (...) space point the light velocity (in moving frames the “there-and-back” velocity) has the same numerical valuec. Considering the principle of equivalence, we come to the logical conclusion that the kinematic (Einstein-Lorentz) time dilation is an absolute phenomenon. (shrink)

The LIGO-Virgo Collaboration achieved the first ‘direct detection’ of gravitational waves in 2015, opening a new “window” for observing the universe. Since this first detection (‘GW150914’), dozens of detections have followed, mostly produced by binary black hole mergers. However, the theory-ladenness of the LIGO-Virgo methods for observing these events leads to a potentially-vicious circularity, where general relativistic assumptions may serve to mask phenomena that are inconsistent with general relativity (GR). Under such circumstances, the fact that GR can ‘save the (...) phenomena’ may be an artifact of theory-laden methodology.This paper examines several ways that the LIGO-Virgo observations are used in theory and hypothesis testing, despite this circularity problem. First, despite the threat of vicious circularity, these experiments succeed in testing GR. Indeed, early tests of GR using GW150914 are best understood as a response to the threat of theory-ladenness and circularity. Each test searches for evidence that LIGO-Virgo’s theory-laden methods are biasing their overall conclusions. The failure to find evidence of this places constraints on deviations from the predictions of GR. Second, these observations provide a basis for studying astrophysical and cosmological processes, especially through analyses of populations of events. As gravitational-wave astrophysics transitions into mature science, constraints from early tests of GR provide a scaffolding for these population-based studies. I further characterize this transition in terms of its increasing connectedness to other parts of astrophysics and the prominence of reasoning about selection effects and other systematics in drawing inferences from observations.Overall, this paper analyses the ways that theory and hypothesis testing operate in gravitational-wave astrophysics as it gains maturity. In particular, I show how these tests build on one another in order to mitigate a circularity problem at the heart of the observations. (shrink)

The paper sheds light from philosophical and methodological points of view on limitations, imposed on the building of the ontological basis of the theory of quantum gravitation by the quantum field theory: 1. this basis necessarily has to be a constantly fluctuating global dynamic field; 2. the field has to be locally excited and of quantum character, i.e, with local excitations subordinated to the principle of indeterminacy and the principle of canonic relationship between commutativeness and noncommutativeness; 3. sufficient theoretical grounds (...) are needed so that quantum theory of gravitation could justify the basic concepts of the structure of the quantum field theory. The analysis of these limitations should show which fundamental concepts and categories of the quantum field theory could in their transformed forms become a part of the ontological basis of the theory of quantum gravitation. (shrink)

Unifying physics by describing a variety of interactions – or even all interactions – within a common framework has long been an alluring goal for physicists. One of the most ambitious attempts at unification was made in the 1910s by Gustav Mie. Mie aimed to derive electromagnetism, gravitation, and aspects of the emerging quantum theory from a single variational principle and a well-chosen Lagrangian. Mie’s main innovation was to consider nonlinear field equations to allow for stable particle-like solutions (now called (...) solitons), and he clarified the use of variational principles in the context of special relativity. The following brief introduction to Mie’s work has three main objectives. The first is to explain how Mie’s project fit into the contemporary development of the electromagnetic world view. Part of Mie’s project was to develop a relativistic theory of gravitation as a consequence of his generalized electromagnetic theory, and our second goal is to briefly assess this work, which reflects the conceptual resources available for developing a new account of gravitation by analogy with electromagnetism. Finally, Mie was a vocal critic of other approaches to the problem of gravitation. Mie’s criticisms of Einstein, in particular, bring out the subtlety and novelty of the ideas that Einstein used to guide his development of general relativity. (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Excerpt from Relativity: The Electron Theory and Gravitation The first edition of this book was published while the General Principle of Relativity was being worked out, before it seemed possible to arrive at any confirmation from observation. Shortly after, however, it was shown that the new theory explained the motion of the perihelion of Mercury, and now the result of the Solar Eclipse expedition has clinched matters. It seemed best to leave practically untouched the account of the special principle as (...) the natural avenue of approach to the broader view, which is described at length in Part II. Acknowledgment is due to the authors friends, Prof. H. F. Baker and Mr. E. V. Appleton, who kindly read through the proofs of the new matter. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

This article gives an explicit presentation of Newtonian gravitation on the backdrop of Maxwell space-time, giving a sense in which acceleration is relative in gravitational theory. However, caution is needed: assessing whether this is a robust or interesting sense of the relativity of acceleration depends on some subtle technical issues and on substantive philosophical questions over how to identify the space-time structure of a theory.

In the present paper, these authors argue on actual reasons why Hilbert’s axiomatic program to unify gravitation theory and electromagnetism failed completely. An outline of plausible resolution of this problem is given here, based on: a) Gödel’s incompleteness theorem, b) Newton’s aether stream model. And in another paper we will present our calculation of receding Moon from Earth based on such a matter creation hypothesis. More experiments and observations are called to verify this new hypothesis, albeit it is inspired from (...) Newton’s theory himself. (shrink)

The advent of the general theory of relativity was so entirely the work of just one person - Albert Einstein - that we cannot but wonder how long it would have taken without him for the connection between gravitation and spacetime curvature to be discovered. What would have happened if there were no Einstein? Few doubt that a theory much like special relativity would have emerged one way or another from the researchers of Lorentz, Poincaré and others. But where would (...) the problem of relativizing gravitation have led? The saga told here shows how even the most conservative approach to relativizing gravitation theory still did lead out of Minkowski spacetime to connect gravitation to a curved spacetime. Unfortunately we still cannot know if this conclusion would have been drawn rapidly without Einstein's contribution. For what led Nordström to the gravitational field dependence of lengths and times was a very Einsteinian insistence on just the right version of the equality of inertial and gravitational mass. Unceasingly in Nordström's ear was the persistent and uncompromising voice of Einstein himself demanding that Nordström see the most distant consequences of his own theory. © 1992 Springer-Verlag. (shrink)

We present a gravitational quantum dynamics theory that combines quantum field theory for particle dynamics in space-time with classical Einstein’s general relativity in a non-Riemannian Finsler space. This approach is based on the geometrization of quantum mechanics proposed in Tavernelli and combines quantum and gravitational effects into a global curvature of the Finsler space induced by the quantum potential associated to the matter quantum fields. In order to make this theory compatible with general relativity, the quantum effects are (...) described in the framework of quantum field theory, where a covariant definition of ‘simultaneity’ for many-body systems is introduced through the definition of a suited foliation of space-time. As in Einstein’s gravitation theory, the particle dynamics is finally described by means of a geodesic equation in a curved space-time manifold. (shrink)

The Weyl theory of gravitation and electromagnetism, as modified by Dirac, contains a gauge-covariant scalar β which has no geometric significance. This is a flaw if one is looking for a geometric description of gravitation and electromagnetism. A bimetric formalism is therefore introduced which enables one to replace β by a geometric quantity. The formalism can be simplified by the use of a gauge-invariant physical metric. The resulting theory agrees with the general relativity for phenomena in the solar system.

The aim of this book is to give an account of Einstein's work without introducing anything very technical in the way of mathematics, physics, or philosophy.

A class of metric theories of gravitation on Minkowski spacetime is considered, which is—provided that certain assumptions (staying close to the original ideas of Einstein) are made—the almost most general one that can be considered. In addition to the Minkowskian metric G a dynamical metric H (called the Einstein metric)is defined by means of a second-rank tensor field S (referred to as gravitational potential).The theory is defined by a Lagrangian ℒ, from which the field equations as well as, (...) e.g., the energy-momentum tensor field for the gravitational field follow. The case of weak fields is considered explicitly. The static, spherically and time-inversal symmetric field is calculated, and as a first step to investigate the theory's viability the parameters are fitted to the experimental data of the perihelion advance and the deflection of light at the Sun. Finally the question of gauge freedoms in the gravitational potential is briefly discussed. (shrink)