Dear Ben, I liked your idea of casual metric very much. You said in my thread that "you and I have perhaps different ideas on the nature of time" but I don't think so. In my mind, time is the expression of changes in energy state, and what can be more causative than that?
Our major difference lies in you regarding matter and space as a single structure --like a true mathematician!-- and on a certain scale and at certain energies this is right. But there is also an intermediate scale, at low everyday energies, where this approach is not well suited, imo.
Here are the quotes from your essay that especially resonated with me:
Re : "These phenomena suggest the promise of physical models that naturally incorporate scale-dependence,.."
Agree with you: scale is everything.
Re : "The first few assumptions I reject are that spacetime is a manifold, that systems evolve with respect to an independent time parameter, and that the universe has a static background structure."
Agree again: time as an independent parameter is suitable only on macro scales, while on the quantum scale, I believe, the micro-processes themselves (not 'particles'!) define spacetime volumes they trace, which can be mapped into time and distances at different scales. As for the universe having a static structure -- who actually thinks so? I can't even fathom it.
Re : "Dimension becomes an emergent property, and is no longer assumed to be constant, nondynamical, or an integer."
I see it exactly the same way.
Re : "If spacetime has a sufficiently simple structure, "...
Yeah, what is spacetime?
Re : "Finally, the dimension of space as well as its curvature might vary with energy density, "...
Just my thoughts. See, we have more in common than it seemed at first.