most recent 30 from http://mathoverflow.net 2013-05-25T20:26:15Z http://mathoverflow.net/feeds/question/37081 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/37081/what-categorical-mathematical-structures-best-describe-the-space-of-localized sigoldberg1 2010-08-29T20:04:14Z 2010-12-20T20:22:13Z

<p>In a recent (and to me, very beautiful) paper, entitled "Relational EPR", <a href="http://arxiv.org/abs/quant-ph/0604064" rel="nofollow">Smerlak and Rovelli</a> present a way of thinking about EPR which relies upon Rovelli's previously published work on relational quantum mechanics (see <a href="http://arxiv.org/abs/quant-ph/9609002" rel="nofollow">http://arxiv.org/abs/quant-ph/9609002</a> ). 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 possible friends of Wigner).</p> <p>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.</p> <p>PS I first asked this on <a href="http://math.stackexchange.com/questions/3608/what-categorical-mathematical-structures-best-describe-the-space-of-localized" rel="nofollow">mathunderflow</a>, but was advised to repost here.</p>

http://mathoverflow.net/questions/37081/what-categorical-mathematical-structures-best-describe-the-space-of-localized/48473#48473 Chris Heunen 2010-12-06T19:41:50Z 2010-12-06T19:41:50Z

<p>I wouldn't say it is a standard structure (yet), but Samson Abramsky has recently given a relational/categorical account of a lot of properties like non-locality and no-signaling. Relations between these notions, including no-go theorems, that are surprisingly involved in other formulations, are quite simply derived, indicating that this could be a good way to state things. See <a href="http://arxiv.org/abs/1007.2754" rel="nofollow">arxiv:1007.2754</a>.</p>