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New Foundations for Branching Space-Times
Studia Logica ( IF 0.7 ) Pub Date : 2020-03-06 , DOI: 10.1007/s11225-020-09905-2
N. Belnap , T. Müller , T. Placek

The theory of branching space-times, put forward by Belnap ( Synthese 92, 1992), considers indeterminism as local in space and time. In the axiomatic foundations of that theory, so-called choice points mark the points at which the (local) possible future can turn out in different ways. Working under the assumption of choice points is suitable for many applications, but has an unwelcome topological consequence that makes it difficult to employ branching space-times to represent a range of possible physical space-times. Therefore it is interesting to develop a branching space-times theory without choice points. This is what we set out to do in this paper, providing new foundations for branching space-times in terms of choice sets rather than choice points. After motivating and developing the resulting theory in formal detail, we show that it is possible to translate structures of one style into structures of the other style and vice versa. This result shows that the underlying idea of indeterminism as the branching of spatio-temporal histories is robust with respect to different implementations, making a choice between them a matter of expediency rather than of principle.

中文翻译:

分支时空的新基础

由 Belnap (Synthese 92, 1992) 提出的时空分支理论将不确定性视为空间和时间的局部性。在该理论的公理基础中,所谓的选择点标志着(局部)可能的未来可以以不同方式出现的点。在选择点的假设下工作适用于许多应用,但有一个不受欢迎的拓扑结果,这使得很难使用分支时空来表示一系列可能的物理时空。因此,开发一个没有选择点的分支时空理论是很有趣的。这就是我们在本文中着手做的事情,为在选择集而不是选择点方面对时空进行分支提供了新的基础。在正式详细地激发和发展由此产生的理论之后,我们表明可以将一种风格的结构转换为另一种风格的结构,反之亦然。这个结果表明,作为时空历史分支的不确定性的基本思想对于不同的实现是稳健的,在它们之间做出选择是权宜之计而不是原则问题。
更新日期:2020-03-06
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