Showing papers on "Four-force published in 1988"

Flat and curved space-times

Abstract: Preface to second edition Preface Introduction 1. Space-time diagrams and the foundation of special relativity 2. Fundamentals of measurement 3. Measurements in flat space-time 4. The Lorentz transformation and the invariant interval 5. Curved space-times 6. Spherical and stellar collapse 7. Simple cosmological models Afterword APPENDICES A. Line integrals B. Four-vectors and relativistic dynamics C. Four-tensors, electromagnetism, and energy-momentum conservation INDEX

Hendrik Antoon Lorentz, the ether, and the general theory of relativity.

Abstract: From the early days of the development of the general theory of relativity the Dutch physicist Hendrik Antoon Lorentz showed a lively and active interest in this theory of gravitation. He devoted much time and energy to understanding the theory and made several important contributions himself. In this paper I will discuss Lorentz's work in the field of general relativity; in addition I will address the question of the apparent discrepancy between Lorentz's enthusiasm for the general theory of relativity and his belief in the existence of an ether. It is well known that until his death in 1928 Lorentz kept insisting on the usefulness of an ether. In spite of his often-expressed admiration for Einstein's special theory of relativity, he preferred his own ether-based 'theory of electrons'. Lorentz admitted that his theory and the special theory of relativity had the same empirical consequences and that the ether could not be experimentally detected, but he maintained that some kind of ether was needed as carrier of the electromagnetic field. As he said in his Theory of Electrons: "I cannot but regard the ether, which can be the seat of an electromagnetic field with its energy and its vibrations, as endowed with a certain degree of substantiality, however different it may be from all ordinary matter."1 In the light of this and many similar statements it seems remarkable that Lorentz occupied himself with the general theory of relativity, in which the ether played no role whatsoever. I will show that, in fact, Lorentz's point of view was not inconsistent, and that he had the same objections against the general theory as against the special theory.

Curvature structure in general relativity

Abstract: This paper investigates the extent to which the curvature structure of space‐time determines the metric stucture. It continues the work of earlier papers by prescribing the curvature structure and the curvature covariant derivatives up to certain orders. It is shown that, with the exception of the so‐called generalized pp waves, the curvature and its first and second covariant derivatives essentially determine the metric up to coordinate transformations.

Special relativity and the flow of time

Abstract: N. Maxwell (1985) has claimed that special relativity and "probabilism" are incompatible; "probabilism" he defines as the doctrine that "the universe is such that, at any instant, there is only one past but many alternative possible futures". Thus defined, the doctrine is evidently prerelativistic as it depends on the notion of a universal instant of the universe. In this note I show, however, that there is a straightforward relativistic generalization, and that therefore Maxwell's conclusion that the special theory of relativity should be amended is unwarranted. I leave open the question whether or not probabilism (or the related doctrine of the flow of time) is true, but argue that the special theory of relativity has no fundamental significance for this question.

A vortex-line model for a system of cosmic strings in equilibrium

Abstract: We show that the field equations of a scalar-gauge theory in general relativity can admit vortex-type solutions describingN parallel vortex lines that we interpret asN infinite straight cosmic strings remaining in equilibrium.

General relativity: A guide to its consequences for gravity and cosmology

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Curvature of generic space‐times in general relativity

Abstract: Transversality theory is used to study the curvature of generic space‐times in general relativity and some applications to unique determination of the metric by the curvature are given.

Gravomagnetism in special relativity

Abstract: The existence of a gravomagnetic field from a uniformly moving mass is predicted from special relativity and gravitational time dilation. Except for a factor of one‐half, the field is identical to the field following from the linearized theory of gravitation.

Aberration and Doppler shift: An uncommon way to relativity

Abstract: Aberration, as well as the Doppler shift, are phenomena close to everyday experience. Special aspects of relativity are derived from axioms concerning the conformal celestial spheres of coinciding observers and are presented with elementary geometrical tools. One way of linking the mathematical hypotheses to physical quantities related to space‐time is demonstrated. The classical formulas for aberration and Doppler shift are used as starting points for deriving the relativistic counterparts.

Nonequivalence of ether theories and special relativity. Comment on recent interpretation of Lorentz' ether theory

Abstract: The role of synchronization procedure is reanalysed in relation to a recent formulation of Lorentz' ether theory. While special relativity and ether theories turn out to be nonequivalent, the results of ether wind measurements from the Earth indicate that the hypothetical ether may, at most, be at rest with respect to the Sun.

A modified Lorentz theory as a test theory of special relativity

Abstract: A modified Lorentz theory (MLT) based on the generalized Galilean transformation has recently received attention. In the framework of MLT, some explicit formulas dealing with the one-way velocity of light, slow-clock transport and the Doppler effect are derived in this paper. Several typical experiments are analyzed on this basis. The results show that the empirical equivalence between MLT and special relativity is still maintained to second order terms. We confirm recent findings of other works that predict the MLT might be distinguished from special relativity at the third order by Doppler centrifuge experiments capable of a fractional frequency detection threshold of 10−15.

Lorentz Noninvariance and the Universality of Free Fall in Quasi-Riemannian Gravity

Abstract: The possibility of deviations from geodesical motion is discussed in the hypothesis that the Lorentz gauge symmetry of general relativity is broken. In particular it is stressed that, in the limit of a weak static field, an eventual correction to the Newtonian acceleration is independent from the distance of the source, and should affect then the experimental tests of the equivalence principle both in the terrestrial and in the solar gravitational field.

On the action and reaction principle in special relativity

Abstract: Two forces, due to internal action and reaction, with points of application in relative motion are shown to be different even if they are applied to material points in contact. The action and reaction principle holds, in the case of steady-state, relative motion, if the resultants of the forces acting on each of the two interacting bodies are considered. For a nonsteadystate problem the principle does not hold even for the resultants of the forces.

The definition of special relativity

Abstract: Two different definitions of special relativity are currently in use; this situation is discussed, with examples.

Mach's principle and the reciprocal symmetry of nature

Abstract: This article develops the postulate that spacetime-charge inversion invariance reflects a fundamental reciprocal symmetry in nature between the two long range forces, from which the derivation of Mach's principle (i.e., the principle that the fundamental parameters of the electromagnetically elementary charged particle are related to those describing the electromagnetically observable universe) follows quite easily. Interpreting this result, it is argued that relativity and quantum mechanics can be made conceptually compatible and mathematically consistent by this reciprocal symmetry if one realizes that relativity isboth a macroscopic, semiclassical theory (i.e., the “global half of relativity,” described by Eq. (1.1), including special and general relativity) and a microscopic theory (i.e., the “local half of relativity,” described by Eq. (2.1), including relativistic quantum mechanics and field theory). The reciprocal symmetry of nature, then, promises unique (differential and/or integral) relationships between the coordinate variables of the “observers” of these tworeciprocally related theories, which implies unique, consistent numerical values for the scalar curvatureR, the massM, and the critical density for “closure,”ρ c, of the observable universe [derived from the elementary particle parameters (i.e., the electron mass and Coulomb radius)]. With this symmetry we also postulate a plausible mechanism for spontaneous generation of matter from the ubiquitous (zero-mass ether) “nothingness” of the “Dirac sea” of “filled negative energy states,” and can consistently interpret both the positive and negative-energy state solutions of Dirac's equation for massive, spin-1/2 (i.e., fermion) particles and both the advanced and retarded potential solutions of electromagnetic field equations. It is pointed out that, with this interpretation of the “advanced potential solutions” from electromagnetic field theory, one can actuallyderive causality from electromagnetic theory.

Solar-System Tests of General Relativity, the Transition to Second Order

Abstract: The solar system is the traditional laboratory for gravity research. In this laboratory, experiments of heretofore undreamed of accuracy are made possible by modern technologies. Among these are atomic clocks, planetary radar, interplanetary spacecraft, and laser ranging. The results of these experiments are consistent with the predictions of general relativity. The differences between the predictions of general relativity and of classical physics are confirmed to accuracies as great as one part in a thousand. However, the solar system tests examine these differences only to first order in post-Newtonian effects.

On the inertial mass concept in special and general relativity

Abstract: Inertial mass in relativity theory is discussed from a conceptual view It is shown that though relativistic dynamics implies a particular dependence of the momentum of a free particle on its velocityin special relativity, which diverges as v approaches c, the inertial mass itself of a moving body remains constant, from any frame of observation However, extension to general relativity does conceptually introduce variability of the inertial mass of a body, through a necessarily generally covariant field theory of inertia, when the Mach principle is incorporated into the theory of general relativity, as a theory of matter

Theorie der Lorentztransformationen

Abstract: By way of mathematical demonstration proof is given that the Lorentz transformations can completely be based upon the theory of absolute time, i. e. upon the Galilei transformations (without neglecting quantities of higher order). Thus, it becomes evident that the theory of special relativity does not imply a revolution of classical kinematics, let alone of idealistic theory of knowledge.

Knowledge and Belief: The Impact of Einstein's Relativity Theory

Abstract: Einstein's theory of the Brownian motion, his introduc tion of the light quantum, but above all his theories of special and general relativity have profoundly changed the way modern men and women think about the phenomena of inanimate nature It would actually be better to say "modern scientists" than "modern men and women" Indeed, in order to appreciate the contribu tions by Einstein in their fullness one needs to be schooled in the physicist's style of thinking and in mathematical techniques, not that difficult for special relativity but quite advanced for the case of general rela tivity It is an optimistic guess that only one in every hundred thousand people alive today has any insight into what Einstein's relativity is really all about It is of course by no means un common that only a tiny fraction of humanity has a genuine grasp of advances in science of any kind whatsoever, or even knows who made them It is therefore all the -