Review on “Internal Logic of Causal Sets”

I have been mulling over this for quite a while and here’s my brief 2-cents on it:

This crystal-clear and beautifully simple piece of work by Fotini Markopoulou uses the language of category theory to tear down preconceived notions in quantum theory, to dig deep into the fundamentals of causality (potentially revealing deep insights to the horizon problem in cosmology) and to establish basic background-independent or event-dependent structures in order to enable an observer embedded in the universe to make sense of his observations of the universe.

As can be inferred from the title of the work, the gist of it is to define an entirely new algebra and logic, that of evolving sets or rather evolving pasts of events.

The use of category theory is very apt as it is able to provide the structure of a sieve, which is a novelly constructed “time-till-truth value”, to firstly define the notion of an evolving past i.e. to determine whether a certain event p will ever be in the past of another event q and to determine the moment in time when this occurs.

The lattice description of the universe should already be a given since the framework of set theory and consequently sieves in category theory are used to define evolving pasts (subsets of elements, which in this case, are events that happen before a certain event q).

What I still cannot grasp, and naively so, is how one can determine whether the underlying logic of a physical theory is Boolean or not. What are the cues that we look for in a physical theory to determine this?

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~ by musafiremes on June 5, 2007.

One Response to “Review on “Internal Logic of Causal Sets””

  1. Just remembered that Chris Isham and Andreas Doring of the Imperial College have recently written a series of 4 papers “A Topos Foundation for Theories of Physics” available at arxiv.org which shed some light on the question above.

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