Linear structures, causal sets and topology

Studies in the History and Philosophy of Modern Physics (2015)
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Abstract

Causal set theory and the theory of linear structures (which has recently been developed by Tim Maudlin as an alternative to standard topology) share some of their main motivations. In view of that, I raise and answer the question how these two theories are related to each other and to standard topology. I show that causal set theory can be embedded into Maudlin’s more general framework and I characterise what Maudlin’s topological concepts boil down to when applied to discrete linear structures that correspond to causal sets. Moreover, I show that all topological aspects of causal sets that can be described in Maudlin’s theory can also be described in the framework of standard topology. Finally, I discuss why these results are relevant for evaluating Maudlin’s theory. The value of this theory depends crucially on whether it is true that (a) its conceptual framework is as expressive as that of standard topology when it comes to describing well-known continuous as well as discrete models of spacetime and (b) it is even more expressive or fruitful when it comes to analysing topological aspects of discrete structures that are intended as models of spacetime. On the one hand, my theorems support (a): the theory is rich enough to incorporate causal set theory and its definitions of topological notions yield a plausible outcome in the case of causal sets. On the other hand, the results undermine (b): standard topology, too, has the conceptual resources to capture those topological aspects of causal sets that are analysable within Maudlin’s framework. This fact poses a challenge for the proponents of Maudlin’s theory to prove it fruitful.

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edition Laurenz, Hudetz (2015) "Linear structures, causal sets and topology". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52(Part B):294-308

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Laurenz Hudetz
London School of Economics

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References found in this work

Category Theory.[author unknown] - 2007 - Studia Logica 86 (1):133-135.
A Theory of Time and Space.Alfred A. Robb - 1915 - Mind 24 (96):555-561.
Geometry of time and space.Alfred Arthur Robb - 1936 - Cambridge [Eng.]: University Press.

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