Dear Roy,good questions, replies below:
a) Do you view the "time" element of your amalgam as *real* or only as an operational convenience, transported from GR & QM?
Time at the level of graphs (the amalgam) is merely the ordering over, and identification of, some subset of the vector J that creates "one" source.
b) Could your "SCC" be formulated with a foundation, one element of which is a 4th dimensional, *spatially* relational, orthogonal vector, rather than "time?"
You might think of the ordering and identification process explained in (a) as creating a vector in the 4th (temporal) dimension. The main point is that there is no "thing" (source in parlance of QFT) without that ordering and identification. Further, you don't have two "things" without space.
c) Could you also explain why you said that Smolin's solution is..."just a multiverse in time rather than space" and..."the first-order laws and other fundamental facts change over time"? I don't see how in this sense (evolution laws) Smolin's dynamical finite space of evolving states would necessarily differ from a "Block World" view.
In a standard multiverse (think eternal inflation or landscapes of string theory) you have possibly infinite spatiotemporally distinct worlds with different initial conditions, laws, values for constants, etc. In Smolin's scheme as we understand it, there is only one world but the fundamental elements such as laws, values of constants and even configuration space change over time. Thus functionally speaking, this is just a multiverse in time rather than space or spacetime. Certainly one could try and tell this story in a BW but again, as we understand him, Smolin wants to make time/change (process as process people like Whitehead would call it) truly fundamental, in part to get out of the dilemma we discussed. He even seems willing to give up or modify relativity with its BW implications; at least he doubts its fundamental or complete truth will survive the true unification of QM and GR. In the language of philosophers he seems to be defending something like presentism. As Smolin says, what "we are all missing" in the
search for unification "involves two things: the foundations of quantum mechanics and the nature of time" (Smolin, 2006). According to Smolin's taxonomy there are only the following possibilities when it comes to explaining time: it's emergent in some limit a la string-theory, it's an illusion a la Barbour/Wheeler-Dewitt or it's fundamental a la Smolin's new Heraclitean evolving laws approach. Our SCC is none of these FYI. In short, Smolin thinks many problems with unification stem from the geometrizing of time, spacetime realism, and Wheeler-Dewitt/Barbour is just a function of a certain interpretation of GR and a certain way of thinking about how to quantize it.
c')I assume you are saying that your "BBP" can describe or at least constrain, let alone *explain*, a final boundary condition simultaneously as per the Tralfamadorians? I admittedly had trouble with the mathematics & would appreciate clarification of how the SCC either guarantees invariance of the physical laws at all points in the BW, or can "self-explain" variation of those laws without dynamical causation?
Not sure where you see a problem here. We take QFT, CFT, relativity, etc., at face-value and try to show how to recover them from the fundamental graph world, so your concern just doesn't arise.
d) It seems to me that if you want a BW, to stay adynamical and retain time, you are necessarily describing an external "God-like" view.
There is no "external view" of a relational blockworld. Any "viewer" is co-defined relationally with the things being "viewed." The relationalism is a rejection of a God's eye view defined as separate from the relational structure of everything else.
e) If you want BW, stay adynamical and remove time, you are still "God-like" but describing a Wheeler-DeWitt type quantum cosmology, basically the same as Julian Barbour's *static* "Platonia". I have trouble with that type of model for Darwinian reasons among others.
RBW is not Platonia, which is configuration space of all spatial hypersurfaces of the spacetime manifold. Barbour claims his is a timeless reality, but he brings time in the back door, as we pointed out to him in the last essay contest. We do not claim to remove time at all. On the contrary, time is as necessary as space and "things," as explained above.
Cheers,
Michael and Mark