On A- and B-theoretic elements of branching spacetimes

Synthese 188 (1):85-116 (2012)
This paper assesses branching spacetime theories in light of metaphysical considerations concerning time. I present the A, B, and C series in terms of the temporal structure they impose on sets of events, and raise problems for two elements of extant branching spacetime theories—McCall’s ‘branch attrition’, and the ‘no backward branching’ feature of Belnap’s ‘branching space-time’—in terms of their respective A- and B-theoretic nature. I argue that McCall’s presentation of branch attrition can only be coherently formulated on a model with at least two temporal dimensions, and that this results in severing the link between branch attrition and the flow of time. I argue that ‘no backward branching’ prohibits Belnap’s theory from capturing the modal content of indeterministic physical theories, and results in it ascribing to the world a time-asymmetric modal structure that lacks physical justification.
Keywords Branching time  A series  B series  C series  Indeterminism  Open future  Passage of time  Supertime  Direction of time
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DOI 10.1007/s11229-011-0046-y
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Oliver Pooley (2013). Relativity, the Open Future, and the Passage of Time. Proceedings of the Aristotelian Society 113 (3pt3):321-363.

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