Showing papers on "Special relativity (alternative formulations) published in 1990"

An introduction to general relativity

Abstract: This textbook provides an introduction to general relativity for mathematics undergraduates or graduate physicists. After a review of Cartesian tensor notation and special relativity the concepts of Riemannian differential geometry are introducted. More emphasis is placed on an intuitive grasp of the subject and a calculational facility than on a rigorous mathematical exposition. General relativity is then presented as a relativistic theory of gravity reducing in the appropriate limits to Newtonian gravity or special relativity. The Schwarzchild solution is derived and the gravitational red-shift, time dilation and classic tests of general relativity are discussed. There is a brief account of gravitational collapse and black holes based on the extended Schwarzchild solution. Other vacuum solutions are described, motivated by their counterparts in linearised general relativity. The book ends with chapters on cosmological solutions to the field equations. There are exercises attached to each chapter, some of which extend the development given in the text.

Weakly Associative Groups

Abstract: The space ℝ 3 of 3-dimensional relativistically admissible velocities possesses (i) a binary operation which represents the relativistic velocity composition law; and (ii) a mapping from the cartesian product ℝ 3 ×ℝ 3 into a subgroup of its automorphism group, Aut(ℝ 3 ), representing the Thomas precession of special relativity These binary operation and mapping are studied in special relativity as two isolated phenomena It was recently discovered, however, that they are linked by an algebraic structure which gives rise to a theory of weakly associative and weakly associative-commutative groups The axioms of these groups are presented in this paper and employed to obtain various interesting results The algebraic structure underlying these nonstandard groups has been discovered and studied in a totally different context by Karzel (1965), Kerby and Wefelscheid

Physical holonomy, Thomas precession, and Clifford algebra

Abstract: After a general discussion of the physical significance of holonomy group transformations, a relation between the transports of Fermi–Walker and Levi–Civita in special relativity is pointed out. A well‐known example—the Thomas–Wigner angle—is rederived in a completely frame‐independent manner using Clifford algebra.

Causal Paradoxes in Special Relativity

Abstract: It has been argued that the existence of faster than light particles in the context of special relativity would imply the possibility to influence the past, and that this would lead to paradox. In this paper I argue that such conclusions cannot safely be drawn without consideration of the equations of motion of such particles. I show that such equations must be non-local, that they can be deterministic, and that they can avoid the suggested paradoxes. I also discuss conservation of energymomentum, and how instantaneous action at a distance can avoid similar paradoxes.

Notes on applications of general relativity in free space

Abstract: Varying the step, at which Lorentz signature is introduced in the scheme of applications of general relativity outside the material distribution, new solutions can be obtained. The interpretations of these solutions can be achieved if the field equations Rμv = 0 are written in a wider space than the Riemannian one. A counter example is given in favour of this claim.

Lorentz action on the space of relative velocities and relativity on a three-manifold

Abstract: The space of relative velocities in special relativity has a three‐dimensional hyperbolic structure. This provides not only a geometric interpretation of the Einstein velocity addition law, but also a purely three‐dimensional reformulation of both special and general relativity on a three‐manifold whose tangent bundle is endowed with a hyperbolic distance function on each fiber. Here the basic concepts are that of local physical observers and local time in terms of nonsingular vector fields and their local flows. The hyperbolic structure on the tangent space enables one to define a relative velocity function between two physical observers, as well as space and time measurements and inertial physical observers. It is possible to rederive Lorentz time dilation and gravitational and cosmological redshifts and reformulate Maxwell (or Yang–Mills) equations in a purely three‐dimensional framework instead of the traditional four‐dimensional space‐time approach.

Einstein equations in numerical relativity

Abstract: Rapid progress in modern computer industries now enables us to solve the Einstein equations numerically. In the first part of this paper we briefly review how to deal with those equations in relativistic astrophysics and cosmology. In the second part we introduce two examples-the Centrella and Wilson's cosmology and the Shapiro and Teukolsky's relativistic stellar cluster.

The Einstein Podolsky Rosen paradox: might nature be more imaginative than us?

Abstract: We present arguments against the existence of the EPR state using only elementary fundamental properties of quantum mechanics. The popular arguments in favor of the EPR, such as the example given by Einstein et al, the superposition principle, and the conservation of angular momentum are discussed and found not compelling. With particular emphasis we argue that an action at a distance which would justify the EPR must be a message violating special relativity.