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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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01 Oct 1981
TL;DR: In this paper, the development of the structure of space-time from the theory of Aristotle to the present day is analyzed, and the present work attempts to sketch a science of relativistic mechanics.
Abstract: Analyzing the development of the structure of space-time from the theory of Aristotle to the present day, the present work attempts to sketch a science of relativistic mechanics. The concept of relativity is discussed in relation to the way in which space-time splits up into space and time, and in relation to Mach's principle concerning the relativity of inertia. Particular attention is given to the following topics: Aristotelian dynamics Copernican kinematics Newtonian dynamics the space-time of classical dynamics classical space-time in the presence of gravity the space-time of special relativity the space-time of general relativity solutions and problems in general relativity Mach's principle and the dynamics of space-time theories of inertial mass the integral formation of general relativity and the frontiers of relativity (e.g., unified field theories and quantum gravity).
17 citations
17 citations
TL;DR: The Lagrangian method to generate conserved currents in field theories starting from the so-called Poincare-Cartan form is reviewed in this article, with examples of application to general relativity.
Abstract: The general 'Lagrangian' method to generate conserved currents in field theories starting from the so-called Poincare-Cartan form is reviewed, with examples of application to general relativity.
17 citations
TL;DR: In this paper, the uniqueness result due to David Malament concerning simultaneity relative to an inertial worldline and an extension of it due to Mark Hogarth for simultaneity in time-oriented spacetimes is discussed.
Abstract: In this note I briefly discuss some aspects of relative geometric-simultaneity in special relativity. After saying a. few words about the status and nature of Minkowski spacetime in special relativity I recall a uniqueness result due to David Malament concerning simultaneity relative to an inertial worldline and an extension of it due to Mark Hogarth and I prove an extension of it for simultaneity relative to an inertial frame in time-oriented spacetimes. Then I point out that the uniqueness results do not generalise to definitions of simultaneity relative to the rotating disk. Finally, I evaluate some recent claims of Selleri in the light of the results. Whilst some of his claims are supported by the approach taken here, the conclusion he draws from these claims, that special relativity harbours a discontinuity and so stands in need of replacement, does not follow and is rejected.
17 citations
TL;DR: In this paper, the authors discuss the definition of velocity as $dE/d|\mathbf{p}|, where E is the energy and p is the momentum of a particle in doubly special relativity.
Abstract: We discuss the definition of velocity as $dE/d|\mathbf{p}|$, where $E$, $\mathbf{p}$ are the energy and momentum of a particle, in doubly special relativity (DSR). If this definition matches $dx/dt$ appropriate for the space-time sector, then space-time can in principle be built consistently with the existence of an invariant length scale. We show that, within different possible velocity definitions, a space-time compatible with momentum-space DSR principles cannot be derived.
17 citations