Abstract
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.
Highlights
What are the consequences that relativity theory has for the notion of the present, or more generally for our everyday notion of time? Famously, Minkowski said that given the experimental corroboration of relativity theory, “space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the
In this paper we have tried a novel approach to defining an ontologically fundamental notion of co-presentness that does not go against the tenets of relativity theory
Our investigation has focused on providing relativistically tenable formal foundations for presentism, culminating in Theorem 1, which states that given the resources of branching space-times, it is possible to define a non-trivial equivalence relation of co-presentness on relativistic space-time structures
Summary
Foundations of Physics (2020) 50:644–664 two will preserve an independent reality.” A strong formal result appears to vindicate Minkowski’s view that before the background of the space-time physics of special relativity theory, time can only be a derivative, dependent notion: there is no sensible way to define a notion of simultaneity based solely on the resources of the spatiotemporal ordering of events in Minkowski space-time. We hold that it is the latter role that is important for presentism as a doctrine in the metaphysics of time, and we will show that a relativity-proof notion of the present in its dynamical role can be defended by exploiting the idea that dynamic change must be based on the indeterministic realization of possibilities for the future. In this paper we will work within a formal framework that allows for making precise sense of spatio-temporal indeterminism and of the fixedness of the past vs the openness of the future: branching space-times (BST; [4]). The main ideas of branching space-times and the necessary formal definitions are introduced in Sect. 4 we prove our main formal result, Theorem 1, which states that a non-trivial relation of co-presentness can be defined in terms of the resources of BST.
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