Hi, Kevin,
Ever since I saw Sorkin's presentation with his take of how partially ordered sets may lead to emergent spacetime, ever since 2002, it haunted me what should those point events be, so that we get the quantum side of physics. I guess, this is what Ken Wharton asked you about.
Last year Giovanni Amelino-Camelia wrote essay, in which he stated an obvious fact that we have never (highlight never) detected an empty point of space(time). All we have ever detected are particle events, which are collected in experiments like LHC into statistics.
If we take this seriously, then particle events (now vertices in Feynman diagrams) are elements of the set. Partial temporal order is dictated by particle creation happening before its annihilation. Spacial order, specifically its 3D nature, might be related to spin relations (SU2 connection with O3 groups), and/or there may be something which you mentioned in Q&A part of your talk at Perimeter. Types of vertices, places where incoming particles are annihilated and outgoing ones are created, as well as types of fundamental particles are given by Standard Model. So, there are already lots of known-to-work on experiment elements here, i.e. the is a starting ground to recreate a spacetime, which should approximate to Minkowski thing. Let's not forget that with higgs all fundamental particles are simpler, i.e. none has mass.
When there is an event (in QFT), involving an electron, one cannot say for certain in how many self-energy loops were in its past. This incompletness of information at a fundamental level (QFTs) nicely implies relational nature of information at QM level, expressed in Rovelli's current essay.
I put the physical part of above arrangement in http://www.fqxi.org/community/forum/topic/1597 with clear mention of where poset-like math should be applied. By the way, when we say (as is done in QFT class) that electrons are effective particles, and are maid up of many events involving fundamental particles of Standard Model, then, composition of effective particles makes them indistinguishable. This is shorter, than Philip Goyal's arguments in his recent piece.
Please, let me know, what you think about this.
Cheers,
Mikalai.