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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, the authors developed an approach to the theory of Riemannian manifolds which avoids the use of co-ordinates, by approximating curved spaces by higher-dimensional analogs of polyhedra.
Abstract: In this paper we develop an approach to the theory of Riemannian manifolds which avoids the use of co-ordinates. Curved spaces are approximated by higher-dimensional analogs of polyhedra. Among the advantages of this procedure we may list the possibility of condensing into a simplified model the essential features of topologies like Wheeler’s wormhole and a deeper geometrical insight.
1,363 citations
TL;DR: A modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies is proposed.
Abstract: We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a nonlinear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.
1,194 citations
TL;DR: In this article, a method for the derivation of the equations of motion of test particles in a given gravitational field is developed, where the transformation properties are discussed and the equation of motion is written in a covariant form.
Abstract: A method for the derivation of the equations of motion of test particles in a given gravitational field is developed. The equations of motion of spinning test particles are derived. The transformation properties are discussed and the equations of motion are written in a covariant form.
985 citations
Book•
01 Jan 1924
TL;DR: In this article, the tensor calculus and the law of gravitation have been studied in a tensor tensor geometry setting, and the authors present a review of the literature.
Abstract: Introduction 1. Elementary principles 2. The tensor calculus 3. The law of gravitation 4. Relativity mechanics 5. Curvature of space and time 6. Electricity 7. World geometry Supplementary notes Bibliography Index.
917 citations