Four-force

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

Substance and Function and Einstein's Theory of Relativity

Abstract: THE translators of Prof. Ernst Cassirer's most important contributions to mathematico-Jogical theory have done well to issue his “Substanz-begriff und Fonktionsbegriff” and his “Zur Einstein-schen Relativitatstheorie” together in one volume, although a considerable time interval separates the two works. The first appeared in 1910, the second in 1921, and the interval covers the formulation by Einstein of the new theory of gravitation. By pre-senting the two together, the philosophical significance of the principle of relativity and the intimate connexion of its mathematico-physical form with the logico-epistemological form of the philosophical problem are clearly brought out. The translation has succeeded in reproducing the clear scientific expression of the German and reads like an original English work. For an American publication there are singularly few Americanisms in the text. It is very unfortunate, however, that the word “Begriff” is not retained in the English title. The book is not about substance and function but about the concept; substance and function are meant to be adjectival, not substantival terms. Substance and Function and Einstein's Theory of Relativity. By Ernst Cassirer. Authorised translation by Dr. William Curtis Swabey and Dr. Marie Collins Swabey. Pp. xii + 465. (Chicago and London: The Open Court Publishing Co., 1923.) 3.75 dollars.

Construction of a Complete Set of Independent Observables in the General Theory of Relativity

Abstract: The construction of a complete set of quantities in general relativity, whose functional form is invariant under coordinate transformations, is indicated. The set obtained is highly redundant. The Cauchy problem for obtaining an independent complete set of such quantities ("observables") is therefore discussed. It is also pointed out that the observables obtained may alternatively be viewed as the metric tensor in a special "gauge" (i.e., with a special coordinate condition). This latter viewpoint may facilitate the quantization of general relativity.

A left-handed simplicial action for Euclidean general relativity

Abstract: An action for simplicial Euclidean general relativity involving only left-handed fields is presented. The simplicial theory is shown to converge to continuum general relativity in the Plebanski formulation as the simplicial complex is refined. This contrasts with the Regge model for which Miller and Brewin have shown that the full field equations are much more restrictive than Einstein's in the continuum limit. The action and field equations of the proposed model are also significantly simpler than those of the Regge model when written directly in terms of their fundamental variables. An entirely analogous hypercubic lattice theory, which approximates Plebanski's form of general relativity, is also presented.

The General Theory of Relativity

Abstract: The general theory of relativity grew out of Einstein’s attempts to apply his earlier theory, the special theory of relativity, to the gravitational field. These efforts came to fruition in 1916, eleven years after the first publication of the fundamentals of the special theory. As it turned out, the inclusion of gravitation into the scope of the newly developed space-time concepts was by no means straight-forward but required a further modification of these concepts away from the Galileo-Newtonian ideas. As we shall see later, because the general theory of relativity enriches the geometric structure of Minkowski still further, it requires a new revision of all physical theories so as to achieve consistency with the underlying space-time continuum. This revision is still proceeding. In particular we do not possess today a fully worked-out general relativistical quantum theory.