Hi Fred,
Ditto what Joy said.
I think that any classical program comes up against a built-in prejudice in favor of discontinuous particle reality. A continuous measurement function, however, is time dependent; i.e., continuous from the initial condition, such that one thinks of points of spacetime as particle manifestations after a measurement event is recorded. As Professor Bel in Joy's link of this thread concluded, "A bricklayer does not need a time-keeper as much as he needs a plumb line and a T-square, therefore we shall end this paper with some notes about the space geometry of space-time models."
The "bricks" of topology, IOW, are not what the wall is built of; continuous measurement results recorded by "the plumb line and the T-square" which reveal how the contours of the wall change over time, depend on where in the continuum the tools are applied. What Joy's simulation shows is that no matter what local configuration of the wall one chooses to plumb and square, the global state corresponds to it in a deterministic way. Conventional quantum theory says the local measurement *creates* the corresponding global state, without having to show or prove anything about it -- it's simply "nonlocal" and in a state of linear superposition before the measurement tools create the "reality."
Topology, though, is all about the global properties of spacetime -- which is where the torsion issue comes in, because non-vanishing torsion forces a self-similarity of quantum correlations independent of scale. As Prof. Kiehn explains:
"The mathematical ideas of torsion can be put into two general categories:
1. The category of geometric torsion produced by continuous deformation of a metric. The mathematical description has been called fiber bundle theory.
2. The category of topological torsion which does not depend upon metric. The mathematical description has been called twisted fiber bundle theory."
This obviously ties into Joy's explanation. Something that most find hard to understand about topology when first introduced to it, is that conventional ideas of distance, of metric measure, don't apply.
Sorry this is getting so long. Forgive me if I am distracting from the main message. However, I just want to add one more thing -- I have thought (and written) for a long time, that topological quantum field theory would be the next big thing in particle physics, because it takes the pressure off the notion of "particle" in favor of the continuous functions (albeit nonlocal) that string theory promises. Never until I was introduced to Joy Christian's measurement framework had I even conceived that a classical schema -- manifestly local -- would converge on these globally continuous functions.
In my Email today, I find a paper uploaded to academia.edu by Nathan Seiberg giving the strongest hint that local symmetries are dependent on global configuration space; i.e., local gauge symmetries whose curvature is everywhere zero, may be driven by a nonzero torsion in the global sysmmetry. This would account, I think, for the teleparalellism in Joy's framework, i.e., we might get a higher dimensional gauge theory in strictly *classical* terms. Manifestly local. Seiberg et al write in their introduction:
"The correlation functions of local operators in R4 depend only on the choice of the Lie algebra g of the gauge group G. They are independent of the global structure of G and the different choices of line operators. So naively these subtleties are of no interest for a four-dimensional physicist. However, we will argue that they have several important consequences. First, these subtleties affect the correlation functions of line operators in the theory. Therefore, they affect the phase structure of the theory on R4. Second, these subtleties become more dramatic when we compactify the theory. For example, we will see that the choices of G and of these parameters have important consequences even for local dynamics on R3 テ--S1. In particular, these different theories can have a different number of vacua (and, in supersymmetric theories, different Witten indices) on R3 テ-- S1. The simple reason for the difference between R4 and R3 テ-- S1 is that wrapping a line operator around the S1 leads to a local operator in R3. These issues play an important role in the relation between IR dualities of four dimensional gauge theories and those of three dimensional gauge theories."
I'm just thinking out loud here. At the least, 2014 is shaping up as a big year for theoretical physics, and I am betting that Joy's classical framework will play a central role.
All best,
Tom