This continuum limit might be a way that Wigner, Wigner’s friend and the cat might form tripartite entanglement. This is (|00〉 + |11〉)|W〉 → |000〉 + |111〉 where |W〉 is Wigner’s state that couples to the bipartite Bell state |00〉 + |11〉 to form the GHZ entangled state. The process is removed by a form of topological obstruction, where this coupling is some local operation that transfers “quantum phase” to the bipartite entangled state so it is now entangled with Wigner’s state. The following diagram illustrates this
[image: wormhole 3-way.png] The original Bell state is the red and green, where starting from c we then unwrap this into the diagram at the left. We can then refold it again so either red or green are on the outside and blue/green or blue/red are inside. The middle diagram can be collapsed so the colored openings squash to a point and this is a diagram for the tripartite. This is a topological map of an entanglement into something that is cobordant. We may think of this as a map of the tripartite entanglement into a spacetime configuration of a wormhole. The bipartite entanglement is mapped to a simple wormhole and the formation of this entanglement is equivalent to the formation of a three-way wormhole. This three-way tubular construction can be the fundamental joints for nontrivial graphs. I can imagine well enough a 4-way entanglement where I topologically move the new colored ring, say colored yellow. Way out near blue. I then slice the diagram into two so we have two 3-way diagrams. The boundary that is produced “constructs” two states. This means we have two tripartite states of the form |000_〉 + |111_〉 and |00_0〉 + |11_1〉, here _ mean “blank” or unknown. We then have a sort of fusion rule that would produce the entanglement |0000〉 + |1111〉 + |0010〉 + |1101〉. This again requires a local operation of the LOCC variety to work. We now put these tinker toys together to generate a large graph. The actual nodes of the graphs are not the quantum states, but more the internal branching region. A large N-graph corresponding to an N-tangle can be fused with others and indeed even closed so the quantum states are in effect hidden away. They are no longer available to experimentation. The more I think about this there are some interesting prospects. We might have by this a means to construct in a large N limit N → ∞ a continuum that is classical spacetime. On Thursday, August 6, 2020 at 7:06:55 AM UTC-5 [email protected] wrote: > > > What is really going on here is that a* language of hypergraphs* (not > well specified) is what is assumed to be defined. All of fundamental > physics is to be rewritten in this language, replacing the others. > > > > https://writings.stephenwolfram.com/2020/04/finally-we-may-have-a-path-to-the-fundamental-theory-of-physics-and-its-beautiful/ > > By the way, when it comes to mathematics, even the setup that we have is > interesting. Calculus has been built to work in ordinary continuous spaces > (manifolds that locally approximate Euclidean space). But what we have here > is something different: in the limit of an infinitely large hypergraph, > it’s like a continuous space, but ordinary calculus doesn’t work on it (not > least because it isn’t necessarily integer-dimensional). So to really talk > about it well, we have to invent something that’s kind of a generalization > of calculus, that’s for example capable of dealing with curvature in > fractional-dimensional space. (Probably the closest current mathematics to > this is what’s been coming out of the very active field of geometric group > theory.) > > @philipthrift > > On Thursday, August 6, 2020 at 6:54:33 AM UTC-5 Lawrence Crowell wrote: > >> In reading the first of these I run into the usual sense or difficulty >> with Wolfram of understanding how to compute or calculate things. >> >> This does get into HoTT (homotopy type theory) which I see as a sort of >> quantum of homotopy or index that represents the obstruction to >> diffeomorphisms on paths. A hole or "horn you can't pull the reins over" >> that prevents any diffeomorphism that moves a curve past the hole or horn, >> defines a first fundamental form π_1(M) = ℤ. The HoTT is a binary set of >> paths that wrap around the obstruction and those which do not. In a quantum >> mechanical form this can be a form of quantum bit. >> >> The role of topology with quantum mechanics is not fully understood. An >> elementary particle is really a set of quantum states or numbers, and these >> may have topological definition. The charge, spin, etc are topological >> quantum numbers, and the Cheshire Cat experiments illustrate how these are >> in a form of entanglement. Elementary particles are really not that >> different from quasiparticles in condensed matter physics' >> >> LC >> >> On Wednesday, August 5, 2020 at 1:17:48 PM UTC-5 [email protected] >> wrote: >> >>> >>> (HyPE = Hypergraph Programming Engine ?) >>> >>> >>> https://www.wolframphysics.org/bulletins/2020/08/a-candidate-geometrical-formalism-for-the-foundations-of-mathematics-and-physics/ >>> Formal Correspondences between Homotopy Type Theory and the Wolfram Model >>> >>> cf. >>> >>> https://writings.stephenwolfram.com/2020/07/a-burst-of-physics-progress-at-the-2020-wolfram-summer-school/ >>> >>> @philipthrift >>> >> -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/df4b91d2-b5ac-483c-9692-3bd8d9af0d45n%40googlegroups.com.
