Hi Tom,
Well I've read through a good bit of the fracton paper. I get some things, but I definitely need to get more background in the basics of TQFT to fully understand it. Nevertheless, I do suspect a deep connection. Even just the idea of fractional charge suggests to me a set-based underpinning. In my terms, the fermionic state, X, of a corpuscle is a set of Q active fermion-planckons. Suppose X corresponds to the presence of one particle in some config. The corpuscle's universal set of fermion-planckons is >> Q. Suppose there is some subset, C, of the corpuscle's fermion-planckons that represent charge. Let C be of size 1000. Then the X can have intersection size of from 0 to 1000. The overall dynamics (physical law) governing the evolution of the corpuscle (and of any corpuscle) might be such that only intersections of certain sizes are possible. Some of them might correspond to integer charges and some to fractional charges.
Yes, I noticed the quote you cite too. In my model, the the initial electron-positron pair, at T, is just one set of Q active fermion-planckons; the remaining, displaced electron, at T+1, is just another set, though (as described in Fig. 4 of the essay), the two sets would have some significant intersection. And, as the article suggests, the two instances of the electron are only thought of as being the *same* electron because the two positions are along a line of travel (e.g., from T-2, T-1) and delta T is small. A key question then is: is the corpuscle's codespace (number of unique sets of size Q) large enough to represent any arbitrary path of movement through the corpuscle? More generally, is the codespace large enough to represent a very large set of quantum state sequences, where (I'm assuming) the vast majority of those states will actually be ensembles of multiple particles. While this might seem like a tall order, note that I'm assuming the corpuscle is very small, e.g., 10^12 planck lengths on a side. In that case, maybe only ensembles of quite limited size might actually need to be modeled (in order to explain all known larger scale (though still quantum) phenomena. In particular, while I said above, the codespace needs to be large enough to represent *any* possible path through a corpuscle, maybe the actual number of possible paths that need to be represented in such a tiny portion of space doesn't actually need to be that large. That is, even if only 6 paths were represented (one for each face of the cube directed inward across the corpuscle), looking from our much higher scale, we'd see all particle paths that span multiple corpuscles, as essentially straight lines. That is, at our high observational scale relative to the actual mechanics, we don't see antialiasing. BTW, the same principles apply with respect to a particle "moving" from one corpuscle to the next as well. The first state in which the particle appears in the next corpuscle is such another set of Q active fermion-planckons, just chosen from that next corpuscle's universal set of fermion-planckons.
Regarding your quote from your paper, I think I agree with you and Einstein and Minkowski about not seeing space or time as physical quantities. But what do you mean by "..grows and decays locally as a function of its global topology"? I realize the answer might be long. But maybe you can point me to an appropriate tutorial for that, or I'd be happy to vchat some time if you want.
What do you mean by the "crank" thing?
I'm happy that you have put time in to understand my theory. As you can see by now then, it is really extremely simple. The big thing I figured out (in my thesis) is that all you need to do, in order to statistically preserve similarity (of all orders, not just pairwise) when learning an input space, is organize the coding field as a set of WTA modules, and bias the distributions from which winners are chosen (one in each WTA module) based on a global measure of the familiarity of the input (my G measure). The great thing is that computing G is trivial and the whole algorithm runs in fixed time (does not grow as the number of stored items increases). And, then the one other, crucial thing, is that once the items have been stored in this way, retrieving the closest-matching item is also trivial (in fact, in simpler than the learning algorithm). I know that this is a better way of achieving the functionality of locality-sensitive hashing. I've reached out to many of the leaders of that field, but never gotten them to listen. Not giving up.
Anyway, it gives me a big boost that a person with your knowledge of QT sees some value in what I've done.
Rod
