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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.
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TL;DR: Hilbert as discussed by the authors was the first to discover the correct form of the law of warpage (i.e., the form that obeys his relativity principle) in space-time.
Abstract: Remarkably, Einstein was not the first to discover the correct form of the law of warpage [of space-time, i.e. the gravitational field equations], the form that obeys his relativity principle. Recognition for the first discovery must go to Hilbert. In autumn 1915, even as Einstein was struggling toward the right law, making mathematical mistake after mistake, Hilbert was mulling over the things he had learned from Einstein’s summer visit to Göttingen. While he was on an autumn vacation on the island of Rugen in the Baltic the key idea came to him, and within a few weeks he had the right law–derived not by the arduous trial-and-error path of Einstein, but by an elegant, succinct mathematical route. Hilbert presented his derivation and the resulting law at a meeting of the Royal Academy of Sciences in Göttingen on 20 November 1915, just five days before Einstein’s presentation of the same law at the Prussian Academy meeting in Berlin. 2
48 citations
TL;DR: In this paper, the impossibility of formulating a modal interpretation of the type proposed by Bub that exhibits serious Lorentz invariance at the fundamental level is proved. But this is not the case for modal interpretations of the types proposed by the authors of this paper.
Abstract: A proof is given, at a greater level of generality than previous “no-go” theorems, of the impossibility of formulating a modal interpretation that exhibits “serious” Lorentz invariance at the fundamental level. Particular attention is given to modal interpretations of the type proposed by Bub.
48 citations
TL;DR: In this paper, the Marzke-Wheeler construction, an extension of the Einstein synchronization convention, produces accelerated systems of coordinates with desirable properties: (a) they reduce to Lorentz coordinates in a neighborhood of the observers' world-lines; (b) they index continuously and completely the causal envelope of the world-line (that is, the intersection of its causal past and its causal future).
Abstract: In special relativity, the definition of coordinate systems adapted to generic accelerated observers is a long-standing problem, which has found unequivocal solutions only for the simplest motions. We show that the Marzke-Wheeler construction, an extension of the Einstein synchronization convention, produces accelerated systems of coordinates with desirable properties: (a) they reduce to Lorentz coordinates in a neighborhood of the observers' world-lines; (b) they index continuously and completely the causal envelope of the world-line (that is, the intersection of its causal past and its causal future: for well-behaved world-lines, the entire space-time). In particular, Marzke-Wheeler coordinates provide a smooth and consistent foliation of the causal envelope of any accelerated observer into space-like surfaces. We compare the Marzke-Wheeler procedure with other definitions of accelerated coordinates; we examine it in the special case of stationary motions, and we provide explicit coordinate transformations for uniformly accelerated and uniformly rotating observers. Finally, we employ the notion of Marzke-Wheeler simultaneity to clarify the relativistic paradox of the twins, by pinpointing the local origin of differential aging.
48 citations
Book•
01 Jan 1977
TL;DR: The rotation group spinor representation of the Lorentz group spinors has been studied in general relativity theory as discussed by the authors, and it has been shown that spinors can be represented by a principal series of representations of SL(2,C) spinors.
Abstract: The rotation group the Lorentz group spinor representation of the Lorentz group principal series of representations of SL(2,C) complementary series of representations of SL(2,C) complete series of representations of SL(2,C) elements of general relativity theory spinors in general relativity SL(2,C) gauge theory of the gravitational field - the Newman-Penrose equations analysis of the gravitational field some exact solutions of the gravitational field equations the Bondi-Metzner-Sachs Group
47 citations