# What categorical mathematical structure(s) best describe the space of “localized events” in “relational quantum mechanics”?

In a recent (and to me, very beautiful) paper, entitled "Relational EPR", Smerlak and Rovelli present a way of thinking about EPR which relies upon Rovelli's previously published work on relational quantum mechanics (at see arxiv.org/abs/quant-ph/9609002 ). In relational quantum mechanics, there is no non-locality, but the definition of when an event occurs is weakened from Einstein's strict definition and instead is localized to each observer-measurement apparatus, including subsequent observers. There are (informal) coherence assumptions to ensure the consistency of reports from different subsequent observers.

All of this seems very similar to various results in modern categorical mathematics. Is there a standard mathematical structure which well describes the structure of the space of localized measurements which Rovelli has envisioned? I know of Isham's work on topos theory and quantum mechanics, but I think he is aiming at something a little different.

I am asking the question here because I am only an interested amateur.

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I think this is an interesting question, but I also think all of the people here who could answer it here are on MO anyway and that this question wouldn't be out of place there. –  Qiaochu Yuan Aug 29 '10 at 18:22
Ok, I reposted the same question as question 37081 at Mathoverflow. –  sigoldberg1 Aug 29 '10 at 20:07
Here's the link in case anyone wants to see it there: mathoverflow.net/questions/37081/… –  Jason DeVito Aug 30 '10 at 1:21