Four-force

About: Four-force is a research topic. Over the lifetime, 3459 publications have been published within this topic receiving 87308 citations.

Polarizable-Vacuum Approach to General Relativity

Abstract: Topics in general relativity (GR) are routinely treated in terms of tensor formulations in curved spacetime. An alternative approach is presented here, based on treating the vacuum as a polarizable medium. Beyond simply reproducing the standard weak-field predictions of GR, the polarizable vacuum (PV) approach provides additional insight into what is meant by a curved metric. For the strong field case, a divergence of predictions in the two formalisms (GR vs. PV) provides fertile ground for both laboratory and astrophysical tests.

On Connes' new principle of general relativity. Can spinors hear the forces of spacetime?

Abstract: Connes has extended Einstein's principle of general relativity to noncommutative geometry. The new principle implies that the Dirac operator is covariant with respect to Lorentz and internal gauge transformations and the Dirac operator must include Yukawa couplings. It further implies that the action for the metric, the gauge potentials and the Higgs scalar is coded in the spectrum of the covariant Dirac operator. This ``universal'' action has been computed by Chamseddine & Connes, it is the coupled Einstein-Hilbert and Yang-Mills-Higgs action. This result is rederived and we discuss the physical consequences.

The Principle of Equivalence

Abstract: start from John Norton's analysis (1985) of the reach of Einstein's version of the principle of equivalence which is not a local principle but an extension of the relativity principle to reference frames in constant acceleration on the background of Minkowski spacetime. We examine how such a point of view implies a profound, and not generally recognised, reconsideration of the concepts of inertial system and field in physics. We then reevaluate the role that the infinitesimal principle, if adequately formulated, can legitimately be claimed to play in general relativity. We show that what we call the 'punctual equivalence principle' has significant physical content and that it permits the derivation of the geodesic law. (C) 2001 Elsevier Science Ltd. All rights reserved.

Signature change, mixed problems and numerical relativity

Abstract: Classical general relativity takes place on a manifold with a metric of fixed, Lorentzian, signature However, attempts to amalgamate general relativity with quantum theory frequently involve manifolds with metrics whose signatures are Lorentzian in some regions and Euclidean in others (Indeed even more exotic possibilities are discussed frequently) Most theoretical calculations rely on analyticity arguments to continue variables from the Euclidean to the Lorentzian regime and vice versa This paper examines models of signature change It looks at a single second-order quasi-linear partial differential equation on a fixed background, whose principal part is elliptic in one regime and hyperbolic in another, ie a mixed problem It introduces some examples, explains heuristically the concept of a well-posed problem and then discusses the issues involved in constructing a robust numerical algorithm to solve well-posed problems The paper includes a worked example illustrating the proposed techniques, and a discussion of the role of the potential curvature singularity on the transition hypersurface