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Four-force
About: Four-force is a research topic. Over the lifetime, 3459 publications have been published within this topic receiving 87308 citations.
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TL;DR: In this article, different topos-theoretical approaches to the problem of construction of General Theory of Relativity (GOR) have been studied, and a new theory of space-time, created in a purely logical manner, has been proposed.
Abstract: We study in this paper different topos-theoretical approaches to the problem of construction of General Theory of Relativity. In general case the resulting space-time theory will be non-classical, different from that of the usual Einstein theory of space-time. This is a new theory of space-time, created in a purely logical manner. Four possibitities are investigated: axiomatic approach to causal theory of space-time, the smooth toposes as a models of Theory of Relativity, Synthetic Theory of Relativity, and space-time as Grothendieck topos.
17 citations
01 Aug 2006
TL;DR: In this paper, a simple hamiltonian formulation of general relativity, derived from the work of Esposito, Gionti and Stornaiolo, is defined over a finite dimensional space.
Abstract: I illustrate a simple hamiltonian formulation of general relativity, derived from the work of Esposito, Gionti and Stornaiolo, which is manifestly 4d generally covariant and is defined over a finite dimensional space. The spacetime coordinates drop out of the formalism, reflecting the fact that they are not related to observability. The formulation can be interpreted in terms of Toller's reference system transformations, and provides a physical interpretation for the spinnetwork to spinnetwork transition amplitudes computable in principle in loop quantum gravity and in the spin foam models.
17 citations
Posted Content•
TL;DR: In this article, the conservation condition is best understood as a consequence of the differential equations governing the evolution of matter in general relativity and many other theories, and the relationship between that geometry and the dynamical properties of matter is discussed.
Abstract: As Harvey Brown emphasizes in his book Physical Relativity, inertial motion in general relativity is best understood as a theorem, and not a postulate. Here I discuss the status of the "conservation condition", which states that the energy-momentum tensor associated with non-interacting matter is covariantly divergence-free, in connection with such theorems. I argue that the conservation condition is best understood as a consequence of the differential equations governing the evolution of matter in general relativity and many other theories. I conclude by discussing what it means to posit a certain spacetime geometry and the relationship between that geometry and the dynamical properties of matter.
17 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: Henri Poincare was the first to introduce four-vectors, the Lorentz group and its invariants (including the space-time metric), "Poincare stresses", as well as making other valuable contributions to relativity theory as mentioned in this paper.
Abstract: Henri Poincare was the first to introduce four-vectors, the Lorentz group and its invariants (including the space-time metric), “Poincare stresses,” as well as making other valuable contributions to relativity theory. We owe to him the names: “Principle of Relativity,” “Lorentz group,” “Lorentz transformation,” and “invariants of the Lorentz group.” It will be shown that his main contributions to relativity were those of a mathematical nature. This has not been sufficiently recognized, although his physical contributions to relativity have been much discussed recently. Frequent misunderstanding of the work of Poincare and Einstein has resulted in controversy tending to obscure the main achievements of Poincare. The Poincare stresses are discussed because of widespread ignorance regarding the theory of classical fundamental charges. The emphasis in this article is on those accomplishments of Poincare by which he should be better known today. In addition, some misconceptions about the history of relativity ...
17 citations