Abstract
The article discusses the relation between two intuitive properties of time, namely its flow and branching. Both properties are introduced first in an informal way and compared. The conclusion of this informal analysis is that the two properties do not entail each other nor are they in contradiction. In order to verify this, we briefly introduced the branching temporal structures called branching space-time, branching continuation and their versions Minkowski branching structure and branching time with Instants. Two possible ways how to formalize flow of time are given, one based on the definition of flow of time from temporal logics and the other based on relativistic physics. The latter is used to define flow of time with the use of linearly ordered points on worldines while respecting the ontological definiteness given by the difference of the past and the future. This is formalized in each of the branching models and it is concluded by comparing the resulting properties that branching and flow, even in the formal sense, do not entail each other. However, notions connected with flow of time represent a useful basis for semantics of the branching models.
Similar content being viewed by others
Notes
This term is borrowed from (Placek 2011) wherein can be found a discussion about the role of “now” in branching theories.
A hypothetical problematic case could be, if events on different branches become time-like related. However, our general idea of flow of time is not perturbed as two events that would be time-like related would still be partially ordered. Although allowing in theory time-like relatedness between branches would significantly increase the complexity of the final structure, it would not disrupt the definition of flow of time. In a less general case, we will see that such structure cannot exist due to conditions imposed on branching.
For example, branching is possible in discrete non-dense structures too. However, the idea of flow of time does not need to be connected to denseness.
We used the unpublished updated version of this paper from 2003 that is available at http://philsci-archive.pitt.edu/1003/.
All referenced material has a bibliography reference number in its title. If the referenced definition is altered in some way, this reference number is accompanied by an apostrophe. We do not repeat proofs from the given articles.
See p. 399 in (Müller 2010).
Seen later in this article as Def. 15.
Emphasis added.
For a more detailed discussion please see later or page 759 in (Placek 2011).
We use \(\Vdash \) instead of Placek’s \({|\!\!\!\!\!\approx }\) purely for technical reasons, the meaning is the same.
A very good observation of the reviewer was that based on this definition there is no unique setting of now-points and thus a unique Flow of Time and it should be therefore “Flows of Time”. However, it is not necessary for the remainder of the article to have a unique setting of now-points.
See the difference in definitions, where we can use simply \(e^{\prime }\in h\) instead of \(e^{\prime }\cup A\in \text {l-events}\). In the case of the replacement of a fan of options, it is sufficient to take all the histories that have a common past with \(h\) at least up to the point of \(e_{C}\). In these histories we choose our evaluation points \(e/h^{\prime }\).
Neither of these was formally introduced, but they are simple placeholders for the originally defined terms of ‘strictly above’ and ‘strictly below’.
An additional observation is that branching models are understood as an eternalism favouring system. The introduction of world-lines, and in a certain sense also observers, means branching can represent observer based presentism. The argument can be that on a given world-line, every choice point is unique by the choices it offers and hence every point is unique by its distance to such a choice point. It remains for future investigation, whether this presentism based on an observer, can be strengthened into an ontological claim.
References
Belnap, N. (1992). Branching space-time. Synthese, 92(3), 385–434.
Belnap, N., & Placek, T. (2012). Indeterminism is a modal notion: branching spacetimes and Earmans pruning. Synthese, 187(2), 441–469.
Dieks, D. (1988). Special relativity and the flow of time. Philosophy of Science, 55, 456–460.
Hodkinson, I., & Reynolds, M. (2006). Temporal Logic. In P. Blackburn, J. F. van Benthem, & F. Wolter (Eds.), Handbook of modal logic (Vol. 3, pp. 655–720). Amsterdam: Elsevier Science.
McTaggart, J. E. (1908). The unreality of time. Mind, 17(68), 457–474.
Müller, T. (2010). Towards a theory of limited indeterminism in branching space-times. Journal of Philosophical Logic, 39, 395–423.
Müller, T. (2014). Alternatives to histories? Employing a local notion of modal consistency in branching theories. Erkenntnis, 79(3), 343–364.
Placek, T. (2011). Locus for now. In D. Dieks, W. J. Gonzales, S. Hartmann, T. Uebel, & M. Weber (Eds.), Explanation, prediction, and confirmation (pp. 395–410). Amsterdam: Springer, Netherlands.
Placek, T. (2011). Possibilities without possible worlds/histories. Journal of Philosophical Logic, 40(6), 737–765.
Placek, T., & Wroński, L. (2009). On infinite EPR-like correlations. Synthese, 167(1), 1–32.
Švarný, P. (2013). Flow of time in BST/BCont models and related semantical observations. In V. Punčochář & P. Švarný (Eds.), The logica yearbook 2012 (pp. 199–218). London: College Publications.
Venema, Y. (2001). Temporal Logic. In L. Goble (Ed.), The blackwell guide to philosophical logic. Wiley-Blackwell: Hoboken.
Acknowledgments
This article is part of the project VG107 supported by the Internal Grant of the Faculty of Arts, Charles University, 2012 (Výstup projektu VG107 Vnitřních Grantů 2012 Filozofické fakulty UK). The author also needs to thank the reviewers for their suggestions and help.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Švarný, P. Does branching explain flow of time or the other way around?. Synthese 192, 2273–2292 (2015). https://doi.org/10.1007/s11229-014-0638-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-014-0638-4