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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Causal sets ： ウィキペディア英語版 Causal sets The causal sets programme is an approach to quantum gravity. Its founding principles are that spacetime is fundamentally discrete and that spacetime events are related by a partial order. This partial order has the physical meaning of the causality relations between spacetime events. The programme is based on a theorem〔D. Malament, ''(The class of continuous timelike curves determines the topology of spacetime )'', Journal of Mathematical Physics, July 1977, Volume 18, Issue 7, pp. 1399-1404〕 by David Malament that states that if there is a bijective map between two past and future distinguishing spacetimes that preserves their causal structure then the map is a conformal isomorphism. The conformal factor that is left undetermined is related to the volume of regions in the spacetime. This volume factor can be recovered by specifying a volume element for each spacetime point. The volume of a spacetime region could then be found by counting the number of points in that region. Causal sets was initiated by Rafael Sorkin who continues to be the main proponent of the programme. He has coined the slogan "Order + Number = Geometry" to characterise the above argument. The programme provides a theory in which spacetime is fundamentally discrete while retaining local Lorentz invariance. == Definition == A causal set (or causet) is a set $C$ with a partial order relation $\backslash preceq$ that is * Reflexive: For all $x\; \backslash in\; C$, we have $x\; \backslash preceq\; x$. * Antisymmetric: For all $x,\; y\; \backslash in\; C$, we have $x\; \backslash preceq\; y\; \backslash preceq\; x\; \backslash implies\; x\; =\; y$. * Transitive: For all $x,\; y,\; z\; \backslash in\; C$, we have $x\; \backslash preceq\; y\; \backslash preceq\; z$ implies $x\; \backslash preceq\; z$. * Locally finite: For all $x,\; z\; \backslash in\; C$, we have card. Here card($A$) denotes the cardinality of a set $A$. We'll write $x\; \backslash prec\; y$ if $x\; \backslash preceq\; y$ and $x\; \backslash neq\; y$. The set $C$ represents the set of spacetime events and the order relation $\backslash preceq$ represents the causal relationship between events (see causal structure for the analogous idea in a Lorentzian manifold). Although this definition uses the reflexive convention we could have chosen the irreflexive convention in which the order relation is irreflexive. The causal relation of a Lorentzian manifold (without closed causal curves) satisfies the first three conditions. It is the local finiteness condition that introduces spacetime discreteness. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Causal sets」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.