Special relativity (alternative formulations)

About: Special relativity (alternative formulations) is a research topic. Over the lifetime, 3102 publications have been published within this topic receiving 55015 citations.

Toposes in General Theory of Relativity

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.

Henri Poincaré's Mathematical Contributions to Relativity and the Poincaré Stresses

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 ...