Dean:
May I ask you to help me understand your main idea. You wrote:
" ... general relativity leads us to view spacetime geometry as part of a dynamical system, as something that satisfies equations of motion and evolves. But clearly the evolution here cannot be understood in a temporal sense, unless we have at our disposal some external time parameter in which to understand it."
...
"The observables so 'localized' are relational in the sense that they are not defined on a background space but only relative to other dynamical entities (matter fields, spatial volume, etc.). Observables are not of the form A(x; t) (where x and t label an independent manifold) but A(B) (where B is another observable and neither B nor A is privileged in any sense)."
Footnote 5: "I restrict the discussion to classical systems in order to make the presentation easier to follow. For the technically savvy, one can transform to the quantum case, roughly, by thinking of the functional relation or correlation A(B) as representing the expectation values of A relative to the eigenvalues of B."
I am not "technically savvy" (cf. footnote 5), and cannot grasp the line of thought in the three excerpts from your essay, particularly the adverb "roughly" in footnote 5.
To be specific, the relational emergence of time poses a paradox, which may be explained as follows.
Imagine a herd of Buridan donkeys, with two stacks of hey in front of each donkey, such that the distance from any given donkey to its stacks of hey is determined -- relationally -- by 'the rest of the donkeys in the herd'.
Consider a donkey called A, and denote 'the rest of the donkeys in the herd' with B, to match your idea in the second excerpt above.
We end up with totally halted/frozen set of (Buridan) donkeys, because donkey A has to wait until the distance to its stacks of hey is determined by B , but any donkey that belongs to the subset denoted with B has to wait until the distance to its stacks of hey is determined -- relationally -- by A.
And since none of the donkeys is "privileged in any sense" (cf. above), the same halting occurs for all donkeys.
I restrict the discussion to classical donkeys in order to make the presentation of the paradox easier to follow. Hope you can solve this 'classical Buridan donkey paradox', and show that the "relational emergence of time" matches the time read by your wristwatch. Then please proceed to the mystery outlined in your footnote 5 above.
Good luck.
Dimi Chakalov