In this paper we describe a novel approach to defining an ontologically fundamental notion of co-presentness that does not go against the tenets of relativity theory. We survey the possible reactions to the problem of the present in relativity theory, introducing a terminological distinction between a static role of the present, which is served by the relation of simultaneity, and a dynamic role of the present, with the corresponding relation of co-presentness. We argue that both of these relations need to be equivalence relations, but they need not coincide. Simultaneity, the sharing of a temporal coordinate, need not have fundamental ontological import, so that a relativizing strategy with respect to simultaneity seems promising. The notion of co-presentness, on the other hand, does have ontological import, and can therefore not be relativized to an observer or to an arbitrarily chosen frame. We argue that a formal representation of indeterminism can provide the structure needed to anchor the relation of co-presentness, and that this addition is in fact congenial to the notion of dynamic time as requiring real (indeterministic) change. The resulting picture is one of an extended dynamic present, implying a formal distinction between static (coordinate) simultaneity and dynamic co-presentness. After working out the basics of our approach in the simpler framework of branching time, we provide our full analysis in the framework of branching space-times, which allows for a formal definition of modal correlations. The spatial extension of the dynamic present can reach as far as the modal correlations do. In the limit, the dynamic present could extend across a maximal space-like hypersurface.

中文翻译：

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通过时空不确定性定义现在的相对性证明概念

在本文中，我们描述了一种新方法来定义共存性的本体论基本概念，该概念不违背相对论的原则。我们调查了相对论中对现在问题的可能反应，引入了由同时性关系服务的现在的静态角色和现在的动态角色之间的术语区别，其对应关系为 co -在场。我们认为这两种关系都需要是等价关系，但它们不必重合。同时性，时间坐标的共享，不需要具有基本的本体论意义，因此关于同时性的相对化策略似乎是有希望的。另一方面，共存性的概念确实具有本体论意义，因此不能相对于观察者或任意选择的框架。我们认为，不确定性的正式表示可以提供锚定共存关系所需的结构，并且这种添加实际上与动态时间的概念相契合，因为它需要真正的（不确定的）变化。由此产生的画面是一种扩展的动态呈现，暗示了静态（坐标）同时性和动态共存之间的正式区别。在更简单的分支时间框架中确定了我们方法的基础之后，我们在分支时空框架中提供了我们的全面分析，这允许对模态相关性进行正式定义。动态存在的空间扩展可以达到模态相关性。在极限中，