Showing papers on "Four-force published in 1984"
Book•
14 Nov 1984
TL;DR: In this paper, the authors focus on the physical content of the theory of relativity and provide a reference for the reader unfamiliar with Cartan's co-ordinate-free calculus, which is used throughout the text.
Abstract: This study edition, which concentrates on the physical content of Einstein's theory of relativity, is intended for students of physics, astrophysics and mathematics. The mathematical background of modern differential geometry is kept to a minimum and serves mainly as a reference for the reader unfamiliar with Cartan's co-ordinate-free calculus, which is used throughout the text. The author discusses the equivalence principle and the field equations together with their experimental support by recent observations. The book concludes with an analysis of modern astrophysics. It analyzes the Kerr-Newman solutions, gravitational collapse, the cooling of neutron stars, radio sources and black holes.
381 citations
01 Jan 1984
TL;DR: In this paper, it was shown that it is not reasonable to expect that the principle of relativity can be extended to non-inertial frames, i.e., there should be no way to determine by an experiment which of two frames of reference is in motion relative to the other.
Abstract: THE WORD “SPECIAL” IN “SPECIAL THEORY OF RELATIVITY” means that the theory is restricted to those frames of reference for which the law of inertia holds, that is, inertial frames of reference.* Einstein sometimes referred to them as Galilean frames of reference. At first glance, it does not seem reasonable to expect that the principle of relativity can be extended to non-inertial frames. The reasons are fairly obvious. The principle of relativity that we have been using states that the laws of physics have the same form in all frames of reference to which the principle applies. In other words there should be no way to determine by an experiment which of two frames of reference is in motion relative to the other.
222 citations
164 citations
TL;DR: In this article, the authors derived Regge's action for a discrete lattice from Einstein's continuum formula ǫ √ |g| R d D x in general relativity.
128 citations
TL;DR: The relativistic addition law for parallel velocities is derived directly from the principle of relativity and a few simple assumptions of smoothness and symmetry, without making use of the constancy of the velocity of light as mentioned in this paper.
Abstract: The relativistic addition law for parallel velocities is derived directly from the principle of relativity and a few simple assumptions of smoothness and symmetry, without making use of the principle of the constancy of the velocity of light.
124 citations
TL;DR: In this article, an ansatz is given which reduces the equations of sourceless (n+p)-dimensional general relativity to those of n-dimensional GRS coupled to a repulsive O(p) scalar field.
Abstract: An ansatz is given which reduces the equations of sourceless (n+p)-dimensional general relativity to those ofn-dimensional general relativity coupled to a repulsiveO(p) scalar field. Regular solutions are obtained for (n=2,p=3,n=3,p=2), and (n=3, p=4). All these solutions have the wormhole topology.
85 citations
TL;DR: In this article, various physical covariance groups: SO(3), the Lorentz group, general theory of relativity group, the Clifford algebra SU(2) and the conformal group can easily be related to the quaternion group.
Abstract: The paper shows how various physical covariance groups: SO(3), the Lorentz group, the general theory of relativity group, the Clifford algebra SU(2) and the conformal group can easily be related to the quaternion group. The quaternion calculus is introduced and several physical applications: crystallography the kinematics of rigid body motion, the Thomas precession the special theory of relatively, classical electromagnetism, the equation of motion of the general theory of relativity, and Dirac's relativistic wave equation are discussed.
83 citations
TL;DR: In contrast to electromagnetic theory, in general relativity the elimination of acceleration terms in a lagrangian by substituting into the lagrangians the equations of motion which follow from the Lagrangian is a correct procedure; it corresponds to a gauge transformation.
62 citations
TL;DR: In this paper, an attempt is made to achieve a degree of definitiveness in the results that would enhance their usefulness in ongoing studies on the conceptual foundations of relativistic physics.
Abstract: Since Einstein’s first publication on relativity many papers have been published on the logical derivation of the Lorentz transformations, but apparently without any conclusiveness on the subject having been reached. In this paper, by basing the analysis of this problem on purely kinematic postulates that can be shown to be necessary, an attempt is made to achieve a degree of definitiveness in the results that would enhance their usefulness in ongoing studies on the conceptual foundations of relativistic physics.
37 citations
Book•
01 Jan 1984
TL;DR: The theory of Relativity was introduced by Nikolaos Nikolaos and Nikolaos as mentioned in this paper in the early 19th century, and it has been studied extensively in the literature since then.
Abstract: I. The Creation of The Theory of Relativityl.- 1.Science, Logic, and Objectivity.- The Role of Mathematics and Other Formal Systems in Science.- The Case of Euclidean Geometry.- The Case of Natural Numbers.- The Case of Free Fall.- The Aristotelian Analysis of Motion.- The Galilean Analysis of Free Fall.- Belief as a Cultural Phenomenon.- Objectivity and the Social Institutions of Science.- Science and Technology.- 2. The Rise and Fall of the Mechanical World View.- The Seventeenth Century.- The Evidence.- Newton's Axioms and Definitions.- The Application and Consequences of Newton's Laws.- Newton's Theory of Measurement.- The Galilean Transformation Equations.- The Classical Principle of Relativity.- The Search for the Absolute Frame of Reference.- 3. Einstein's Special Theory of Relativity and Its Consequences.- The Special Theory of Relativity.- The Postulates.- Simultaneity.- The Relativity of Simultaneity.- The Order of Events and Causality.- The Relationship of Einstein's Theory to Lorentz's Theory.- Time Dilation and the Relativity of Simultaneity.- Length Contraction.- Mass.- 4. Further Consequences of the Heuristic Nature of the Special Theory of Relativity.- Mass and Energy.- The Clock Paradox.- Four-Dimensional Analysis.- 5. The General Theory of Relativity.- II. The Early Response to the Special Theory of Relativity, 1905-1911.- 6. When a Hundred Flowers Bloom: The German Response.- The Contributions of Max Planck.- The Rigidity Paradoxes.- Wave and Group Velocity.- 7. As If It Never Happened: The French Response.- Henri Poincare.- The Principle of Relativity.- Poincare and Second Order Theory.- The Theory of Electrons.- Poincare's Vision of a Good Theory.- Simplicity and Induction.- Flexibility and Gradualism.- Naturalness and the Increase of Hypotheses.- Poincare's Silence and Einstein's Theory.- Other French Response.- Aftermath.- 8. Defending the Ether: The British Response.- The Tradition of British Ether Theory.- Oliver Lodge.- The Mechanical Ether.- The Introduction of Relativity Theory.- Conclusions.- 9. Defending the Practical: The American Response.- The American Tradition in Science.- Science and American Technology.- Science and American Universities.- The American Physics Community.- American Silence, 1905 -1907.- The Contributions of Lewis and Tolman.- Reaction to Lewis and Tolman.- The Appeal to Common Sense.- The Popular Response, 1905-1911.- Conclusions.- III. From Response to Assimilation.- 10. Relativity in America, 1912-1980.- 1911-1919: The Lull Before the Storm.- The Assimilation of Special Relativity Within the Scientific Community, 1920-1980.- The Evidence.- Graduate Textbooks, 1920-1945.- Advanced Undergraduate Textbooks, 1920-1945.- Introductory Textbooks, 1920-1945.- Post World War II.- Bridgman's Operationism and Einstein's Relativity.- Bridgman's Early Studies of Relativity Theory.- Being Operational Versus Operationism.- Spreading Time Through Space, 1959-1961.- Philosophy and Physics.- The Popular Response to the Theory of Relativity.- Conclusions.- 11. Relativity and Revolutions in Science.- Scientific Revolutions.- Relativity and Scientific Revolutions.- Appendix 1. Trigonometry.- Appendix 2. Kinematics: The Galilean Description of Motion.- Appendix 3. Newtonian Mechanics.- Appendix 4. The Kinetic Theory of Matter and the Mechanical World View.- Appendix 5. Ether Drift Experiments: The Search for Absolute Frame of Reference.- Appendix 6. Some Relativistic Derivations.- Bibliographic Essay: On Understanding Relativity.- Inde.
30 citations
TL;DR: In this article, the (3 + 1)-formalism of the Einstein equations has been used to determine apparent horizons in general space-times in three-dimensional numerical relativity.
01 Jan 1984
TL;DR: Algebraic Computing i.e. the use of computers to manipulate formulae, has been used in general relativity since about 1965 and a very early example was the program GRAD ASSISTANT (Fletcher, 1965) that could calculate the Ricci tensor from a given not too complicated metric.
Abstract: Algebraic Computing i.e. the use of computers to manipulate formulae, has been used in general relativity since about 1965. A very early example was the program GRAD ASSISTANT (Fletcher, 1965) that could calculate the Ricci tensor from a given not too complicated metric.
TL;DR: In this article, a method for extending general relativity, called the method of algebraic extension, is presented, and it is shown under certain restrictions that only five theories of gravity, one of which is general relativistic, result from such an extension.
Abstract: A new method for extending general relativity, called the method of algebraic extension, is presented. It is shown under certain restrictions that only five theories of gravity, one of which is general relativity, result from such an extension. Lagrangians for the five theories are constructed. The relationship between algebraically extended theories and higher-dimensional theories of Riemannian gravity is outlined.
TL;DR: The only test theory used by workers in the field of testing special relativity to analyze the significance of their experiments is the proof by H. P. Robertson as mentioned in this paper of the Lorentz transformations from the results of the experimental evidence.
Abstract: The only test theory used by workers in the field of testing special relativity to analyze the significance of their experiments is the proof by H. P. Robertson [Rev. Mod. Phys.
21, 378 (1949)] of the Lorentz transformations from the results of the experimental evidence. Some researchers would argue that the proof contains an unwarranted assumption disguised as a convention about synchronization procedures. Others would say that alternative conventions are possible. In the present paper, no convention is used, but the Lorentz transformations are still obtained using only the results of the experiments in Robertson's proof, namely the Michelson-Morley, Kennedy-Thorndike, and Ives-Stilwell experiments. Thus the revised proof is a valid test theory which is independent of any conventions, since one appeals only to the experimental evidence. The analysis of that evidence shows the directions in which efforts to test special relativity should go. Finally it is shown how the resulting test theory still has to be improved for consistency in the analysis of experiments with complicated experimental setups, how it can be simplified for expediency as to what should be tested, and how it should be completed for a missing step not considered by Robertson.
TL;DR: In this paper, it is shown that the same laws of nature which are operative in the Lorentz-FitzGerald contraction also condition the relativistic version of the contraction.
Abstract: A recurrent theme in the philosophical literature on the special theory of relativity is the question as to the “reality” of the Lorentz contraction. It is often suggested that there is a difference between the Lorentz-FitzGerald contraction in the pre-relativistic ether theory and the Lorentz contraction from special relativity in the sense that the former is a real contraction of matter conditioned by dynamical laws, whereas the latter should be compared with the apparent changes in the size of objects when the perspective of the observer changes. It is here shown, however, that the same laws of nature which are operative in the Lorentz-FitzGerald contraction also condition the relativistic Lorentz contraction. The relevant distinction therefore is not between the “reality” of the two contractions. What is at issue is the difference in explanatory structure of the pre-relativistic theory on the one hand and the special theory of relativity on the other. In the course of the argument the question of the “conventionality” of simultaneity is also discussed.
TL;DR: The equivalence principle which states that all forms of mass energy are equivalent in producing gravitational acceleration, which itself is indistinguishable from mechanical acceleration, is the cornerstone of the general theory of relativity, which quantitatively links matter, energy and space-time.
Abstract: Gravitation is the weakest of the four fundamental particle interactions in physics. The equivalence principle which prescribes that all forms of mass energy are equivalent in producing gravitational acceleration, which itself is indistinguishable from mechanical acceleration, is the cornerstone of the general theory of relativity, which quantitatively links matter, energy and space-time. Experiments designed to verify the general theory fall into five categories: those which attempt to prove the invariance of conventional constants; those designed to confirm the predictions of the special theory of relativity for non-accelerating systems; tests of the equivalence principle involving the question of how various forms of energy contribute to mass; those attempting to determine the mathematical relationship between the curvature of space-time and mass energy; and those, which may be possible in future, to test the warping effects of moving mass on space-time by the detection of gravitational radiat...
01 Jan 1984
TL;DR: In this paper, a method of finding axially symmetric stationary vacuum solutions of the equations of general relativity is presented, which is based on the calculation of the elements of a matrix, from an arbitrary function of certain arguments or from a second-order linear partial differential equation.
Abstract: A method of finding axially symmetric stationary vacuum solutions of the equations of general relativity is presented. The method is based on the calculation of the elements of a matrix, from an arbitrary function of certain arguments or from an arbitrary solution of a second-order linear partial differential equation. From this matrix, solutions of the Ernst equation, in the form of which the equations of general relativity are written, are obtained explicitly.
TL;DR: In this paper, the authors exploit the theory of random functions to derive an approximate kinetic equation for the evolution of a self-gravitating system, valid in an "impulse" or "weak coupling" approximation in the limit that radiative effects may be neglected.
Abstract: Recently, Israel and Kandrup have developed a new, manifestly covariant approach to non-equilibrium statistical mechanics in classical general relativity. One by-product of that approach has been the formulation of an approximate kinetic equation for the evolution of a self-gravitating system, valid in an “impulse” or “weak coupling” approximation in the limit that radiative effects may be neglected. This paper exploits the theory of random functions to present a much simpler derivation of that approximate kinetic equation.
TL;DR: In this paper, it was shown that the wave-particle duality implies the extension of special relativity to superluminal frames, and the real one-dimensional superluminant Lorentz transformations are obtained as a special case of the Parker-Antippa transformations.
Abstract: It is shown that the wave-particle duality implies the extension of special relativity to superluminal frames. The real one-dimensional superluminal Lorentz transformations are obtained as a special case of the Parker-Antippa transformations. Some interrelations between extended special relativity and the many-wave hypothesis are discussed.
TL;DR: In this paper, the authors used Landau and Lifschitz from their Classical Fields in the title of a talk to describe the aesthetic appeal of the general theory of general relativity.
Abstract: By common consent, the general theory of relativity has a special aesthetic appeal to those who have studied it. I have chosen to quote Landau and Lifschitz from their Classical Fields in the title of my talk since their magnificent series of volumes, encompassing the whole range of physics, gives to their assessment a special authenticity. Others besides Landau and Lifschitz have applied the epithet ‘beautiful to general relativity. Thus, Pauli, in his well-known article on ‘The Theory of Relativity’ in the Encyclopädie der Mathematischen Wissenschaftien (1921) has written
TL;DR: In this paper, the same authors exhibit theories of gravitation leading to the same set of solutions with algebraically special Ricci tensors as Einstein's equations, but they differ from general relativity.
31 Dec 1984
TL;DR: In this paper, a mass spectrum derived qualitatively from general relativity for the boson fields that play the role of transferring energy-momentum between the spinor matter components in the elementary-particle domain is derived.
Abstract: In this note, a mass spectrum is derived qualitatively from general relativity, for the boson fields that play the role of transferring energy-momentum between the spinor matter components in the elementary-particle domain. The theory is shown to formally relate to the nonzero inertial mass aspect of a fused electromagnetic weak interaction in terms of (previously derived) processes, and to possibly relate to the recently observed W±-particle from p{ie17-1} collisions.
01 Jan 1984
TL;DR: The current use of computers in general relativity was reviewed at GR10. as discussed by the authors, where several groups have working codes which can calculate the coupled general relativity/hydrodynamics equations in two spatial dimensions plus time.
Abstract: The current use of computers in general relativity was reviewed at GR10. Today several groups have working codes which can calculate the coupled general relativity/hydrodynamics equations in two spatial dimensions plus time. These codes are compared and a critical review is made of the areas needing improvement. The potential uses of numerical relativity are discussed. In some situations the gravitational field can be chosen to be an analytically known solution, and hydrodynamics can be done in that background field. Regge calculus is still in its infancy numerically, but interesting new work has been done. Algebraic computing is becoming a mature technology, with the emphasis moving toward making these powerful software tools available to those relativists without previous computer training.
TL;DR: In this paper, exact solutions of isotropic and anisotropic fluid distributions in general relativity have been generated on the basis of the Letelier theory of fluids, and the exact solutions have been shown to be the same as in this paper.
Abstract: Some exact solutions of isotropic and anisotropic fluid distributions in general relativity have been generated in this paper on the basis of the Letelier theory of fluids.