Laurenz, Hudetz (2015) Linear structures, causal sets and topology. [Preprint]

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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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Item Type:	Preprint
Creators:	Creators Email ORCID Laurenz, Hudetz laurenz.hudetz@sbg.ac.at
Additional Information:	Forthcoming in Studies in History and Philosophy of Modern Physics.
Keywords:	Linear structures, causal sets, topology, category theory, Alexandrov spaces
Subjects:	Specific Sciences > Mathematics Specific Sciences > Physics > Quantum Gravity Specific Sciences > Physics > Relativity Theory General Issues > Structure of Theories
Depositing User:	Mr. Laurenz Hudetz
Date Deposited:	10 Sep 2015 18:11
Last Modified:	17 Sep 2015 11:48
Item ID:	11667
Subjects:	Specific Sciences > Mathematics Specific Sciences > Physics > Quantum Gravity Specific Sciences > Physics > Relativity Theory General Issues > Structure of Theories
Date:	August 2015
URI:	https://philsci-archive.pitt.edu/id/eprint/11667

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  • Linear structures, causal sets and topology. (deposited 17 Sep 2015 11:48)

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