Showing papers on "Four-force published in 1989"
TL;DR: In this paper, the integrability conditions for the embedding of a d-dimensional world manifold generated by a (d-1)-dimensional extended object in a flat space are examined.
Abstract: The integrability conditions for the embedding of a d-dimensional world manifold generated by a (d-1)-dimensional extended object in a flat space are examined. It is shown that, for the case of non-minimal world manifolds with d>2, these conditions contain the Einstein and Yang-Mills equations as an independent set of equations, where the first and third fundamental forms act as gravitation and gauge fields respectively, while the second fundamental form plays the role of the source field. Using these results the string model of relativity is shown to be compatible with general relativity.
62 citations
TL;DR: In this paper, a variation on the twin paradox of special relativity is presented where twins undergo the same acceleration for the same length of time, yet they age differently, and it is shown that the acceleration experienced by a relativistic traveler is directly related to the rate at which that traveler ages.
Abstract: A variation on the ‘‘twin paradox’’ of special relativity is presented wherein twins undergo the same acceleration for the same length of time, yet they age differently. Although this problem is simple to solve, it gets to the heart of the behavior of clocks in special relativity and, hopefully, will help to dispel the notion students develop that the acceleration experienced by a relativistic traveler is directly related to the rate at which that traveler ages.
40 citations
34 citations
TL;DR: The variational theory of an ideal fluid with spin is formulated in Riemannian spacetime within the framework of general relativity theory in this article, and applied in cosmology, showing the very weak influence of spin on gravity.
Abstract: The variational theory of an ideal fluid with spin is formulated in Riemannian spacetime within the framework of general relativity theory. It is applied in cosmology, showing the very weak influence of spin on gravity.
28 citations
TL;DR: In this article, a more acceptable alternative, consistent with the relativity principle and with some other textbooks, is discussed, and counterfactual consequences from such an assumption are deduced.
Abstract: Certain physics textbooks convey a false impression that the stellar aberration angle depends on the relative velocity of the light source and observer. Counterfactual consequences are deduced from such an assumption and a more acceptable alternative, consistent with the relativity principle and with some other textbooks, is discussed.
23 citations
01 Aug 1989
TL;DR: In this paper, important relativistic effects and issues must be considered in the interpretation of current measurements such as ranging measurements to LAGEOS and to the moon, in the implementation of the Global Positioning System, and in the synchronization of clocks near the earth's surface, for the communication of scientific results.
Abstract: Important relativistic effects and issues are discussed which must be considered in the interpretation of current measurements such as ranging measurements to LAGEOS and to the moon, in the implementation of the Global Positioning System, in the synchronization of clocks near the earth's surface, and in the adoption of appropriate scales of time and length for the communication of scientific results.
21 citations
TL;DR: In this paper, it was shown that longitudinal Ampere forces between current elements can be interpreted as the overall average integrated effect of conducting electrons within the frame of Maxwell's theory.
19 citations
TL;DR: In this paper, it was shown that no static nonsingular solution of the general relativity equations exists for the gravitational field of an uniformly planar matter distribution under very general assumptions.
Abstract: It is shown that, under very general assumptions, no static nonsingular solution of the general relativity equations exists for the gravitational field of an uniformly planar matter distribution.
17 citations
TL;DR: In this article, a two-way moving sidewalk is used to illustrate relative velocity, time dilation, and length contraction of the theory of special relativity on a rotating disc model.
Abstract: Some classical thought experiments in special relativity are performed on a two-way moving sidewalk. Since each of the two sides moves at constant speed, this device provides a simple, intuitive way to illustrate relative velocity, time dilation, and length contraction. It should therefore allow for a better understanding of the basic concepts of the theory. Furthermore, being a closed system the two-way sidewalk exhibits some of the characteristics of a rotating disc, and might therefore be helpful in an introduction to general relativity.
17 citations
TL;DR: In this paper, it was shown that the universe is expanding during the evolutionary phase with the limit velocity of the signal propagation, and the discovery of this fact throws a new light on a number of cosmological questions.
Abstract: From the special theory of relativity it follows that the Universe is expanding during the expansive evolutionary phase with the limit velocity of the signal propagationc. The discovery of this fact throws a new light on a number of cosmological questions.
15 citations
01 Mar 1989
TL;DR: In this article, it was shown that the principles of the special relativity can be realized not only on the Minkowskian spacetime but also on the spacetimes of non-zero constant curvature.
Abstract: We show that Einstein's principles of the special relativity can be realized not only on the Minkowskian spacetime but also on the spacetimes of non-zero constant curvature.
01 Mar 1989
TL;DR: The Pauli algebra as mentioned in this paper is an associative, invertible multiplication of vectors in 3D Euclidean space, which gives a compact, covariant formulation for problems in special relativity.
Abstract: The Pauli algebra introduces an associative, invertible multiplication of vectors in 3-dimensional Euclidean space. Some elements of the algebra may be interpreted as 4-vectors, the Minkowski metric for which appears naturally. The algebra gives a compact, covariant formulation for problems in special relativity.
TL;DR: In this article, a metrosphere, a theoretical device which incorporates the functions of clock, rod, nonrotating platform, and accelerometer, and whose operation depends on the properties of light rays and free particles, is defined.
Abstract: A theoretical device, which incorporates the functions of clock, rod, nonrotating platform, and accelerometer, and whose operation depends on the properties of light rays and free particles, is defined. The device, which we call a metrosphere, is simple enough that it can be introduced at the starting point of relativity theory and versatile enough that it can serve as an aid in the development and conceptualization of the theory. Relative to an inertial frame, a moving metrosphere undergoes a Lorentz-Fitzgerald contraction and the associated clock exhibits a Lorentz-Larmor rate retardation. From this fact and the assumption that there exists one inertial frame, it is possible to generate the kinematical results of special relativity. A metrosphere provides an observer with a local frame of reference, hence it is well adapted to the needs of general relativity, allows the equivalence principle to be introduced in a straightforward manner, and permits a smooth transition from special relativity to general relativity.
Book•
01 Jan 1989
TL;DR: In this article, the authors developed Relativity as a modern theory of motion, starting by placing it in historical perspective and proceeding to show its logical necessity using only one assumption rather than two.
Abstract: The most important feature in this book is the simple presentation with details of calculations. It is very easy to follow. Fairly sophisticated calculations are developed very rapidly. The presentation is logical and the detailed coverage makes this book very readable and useful. The contents develop Relativity as a modern theory of motion, starting by placing it in historical perspective and proceeding to show its logical necessity. The development of the Lorentz transformation is given using only one assumption rather than two. Right away in Chapter 3, geometry as required in Special Relativity for extension to General Relativity is introduced. This enables the use of the four-vector formalism of Minkowski. By the end of Chapter 4, the general Lorentz transformations for three-dimensional motion and their relation to four-dimensional boosts have already been explained. In Chapter 5 applications of relevance in Physics are provided. After a brief introduction to elementary electromagnetic theory, it is reformulated as a theory in four-dimensions using tensors in Chapter 6. Finally in Chapter 7, the theory is extended to deal with accelerated motion as “corrections” to Special Relativity.
TL;DR: In this article, the relationship among the metric, the connection, the curvature, and the covariant curvature derivatives in general relativity is investigated, and some topological aspects of the problem are included and some applications to holonomy and symmetry groups are given.
Abstract: This essay investigates the relationships among the metric, the connection, the curvature, and the covariant curvature derivatives in general relativity. The extent to which the connection or the curvature together, possibly with certain curvature derivatives, determines the metric is considered, as well as other related problems. Some topological aspects of the problem are included and some applications to holonomy and symmetry groups are given.
TL;DR: Experiments with rotating systems are examined from the point of view of a test theory of the Lorentz transformations (LTs), permitting, in principle, the verification of the simultaneity relation.
Abstract: Experiments with rotating systems are examined from the point of view of a test theory of the Lorentz transformations (LTs), permitting, in principle, the verification of the simultaneity relation The significance of the experiments involved in the testing of the LTs can be determined using Robertson's test theory (RTT) A revised RTT is discussed, and attention is given to the Ehrenfest paradox in connection with the testing of the LTs
TL;DR: In this article, it was shown that the corresponding active coordinate transformations are not equal in general to the passive ones and that the composite active-passive transformations act on a space whose number of dimensions is ten (one-particle case) or larger (more than one particle).
Abstract: It has recently been shown by Vargas,(4) that the passive coordinate transformations that enter the Robertson test theory of special relativity have to be considered as coordinate transformations in a seven-dimensional space with degenerate metric. It has also been shown by Vargas that the corresponding active coordinate transformations are not equal in general to the passive ones and that the composite active-passive transformations act on a space whose number of dimensions is ten (one-particle case) or larger (more than one particle).
TL;DR: In this article, a formulation of general relativity on a three-dimensional space with a fixed volume element is presented, which is obtained by fixing part of the gauge freedom of the theory.
Abstract: The author presents a formulation of general relativity on a three-dimensional space with a fixed volume element. This formulation is obtained by fixing part of the gauge freedom of the theory.
TL;DR: In this article, a generalised test theory of special relativity, using a non-inertial frame, is presented, which contains a term which depends on the angular velocity of the rotating system, and hence measures an absolute effect.
Abstract: The authors present a generalised test theory of special relativity, using a non-inertial frame. Within the framework of the special theory of relativity the transport and Einstein synchronisations are equivalent on a rigidly rotating disc. But in any theory with a preferred frame, such an equivalence does not hold. The time difference resulting from the two synchronisation procedures is a measurable quantity within the reach of existing clock systems on the Earth. The final result contains a term which depends on the angular velocity of the rotating system, and hence measures an absolute effect. This term is of crucial importance in this test theory of special relativity.
TL;DR: In this paper, a method has been derived which enables one to obtain solutions to the stationary, axially symmetric vacuum fields in general projective relativity developed by Arcidiacono from known solutions of the vacuum field in Einstein's theory.
Abstract: A method has been derived which enables one to obtain solutions to the stationary, axially symmetric vacuum fields in general projective relativity developed by Arcidiacono from known solutions of the vacuum field in Einstein's theory. The analogue of the Kerr solution in general projective relativity has been obtained as an example. Finally, a relation between the stationary and static axially symmetric vacuum fields in general projective relativity has been derived.
TL;DR: The role played by coordinates in the formulation of an absolute spacetime theory is assessed in this paper, where it is shown that recent criticism on previous work of ours is wrong and the role of coordinates in spacetime theories is shown to be important.
Abstract: The role played by coordinates in the formulation of an absolute spacetime theory is assessed. It is shown that recent criticism on previous work of ours is wrong.
Dissertation•
01 Jan 1989
TL;DR: Bini et al. as discussed by the authors derived a compact analytical parametric approximate solution of Padé type which gives density curves and stellar radii in good accordance with already existing numerical results.
Abstract: The “effective geometry” formalism is used to study the perturbations of a white dwarf described as a self-gravitating fermion gas with a completely degenerate relativistic equation of state of barotropic type. The quantum nature of the system causes an absence of homological properties manifested instead by batropic stars and requires a parametric study of the solutions both at numerical and analytical level. We have explicitly derived a compact analytical parametric approximate solution of Padé type which gives density curves and stellar radii in good accordance with already existing numerical results. After validation of this new type of approximate solutions, we use them to construct the effective acoustic metric governing perturbations of any type following Chebsch’s formalism. Even in this quantum and relativistic case the stellar surface exhibits a curvature singularity due to the vanishing of density, as already evidenced in past studies on non relativistic and non quantum self-gravitating polytropic star. The equations of the theory are finally numerically integrated, in the simpler case of irrotational spherical pulsating perturbations including the effect of back-reaction, in order to have a dynamical picture of the process occurring in the acoustic metric. 10. Bini D., de Felice F., Geralico A., Accelerated orbits in black hole fields: the static case Classical and Quantum Gravity, vol. 28 225012, 2011. Abstract We study non-geodesic orbits of test particles endowed with a structure, assuming the Schwarzschild spacetime as background. We develop a formalism which allows one to recognize the geometrical characterization of those orbits in terms of their Frenet-Serret parameters and apply it to explicit cases as those of spatially circular orbits which witness the equilibrium under conflicting types of interactions. In our general analysis we solve the equations of motion offering a detailed picture of the dynamics having in mind a check with a possible astronomical set up. We focus on certain ambiguities which plague the interpretation of the measurements preventing one from identifying the particular structure carried by the particle. 11. Bini D., Geralico A., Jantzen R.T., Semeřák O.,