On Saturday, November 30, 2019 at 4:30:28 PM UTC-6, John Clark wrote: > > > > On Sat, Nov 30, 2019 at 4:36 PM Lawrence Crowell <goldenfield...@gmail.com > <javascript:>> wrote: > > *> The Planck unit of length and time does not mean space or spacetime is >> discrete. All it means is this is the smallest scale one can localize a >> quantum bit of information. It does not mean that spacetime is somehow >> discrete.* >> > > If discrete spacetime does not mean there is a smallest scale that a Qubit > of information can be localized then what does "discrete spacetime" mean? >
> John K Clark > It is a form of quotient geometry. For 1 → G → H → K → 1 for G = U(1), H = U(N) and K = PSU(N) = SU(N)/Z_N this short exact sequence defines a discrete gauge group. The projective Lie group is a Kleinian and for a manifold associated with SU(N), say AdS_5 = U(2, 2)/O(4,1) the quotient defines an underlying discretization. Of course to do this in greater generality we need to have a discrete system with polytopes that define cells. So G could be the Coxeter group for a polytope. Say for G the Coxeter group for the 4-dim icosian H the group O(3,2) ≈ AdS_4×O(3,1) then K would be this spacetime, with the Lorentz group, in a quotient with a lattice space. LC -- 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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/78f99b59-4a4b-4cdf-8614-d28abdbfdcbc%40googlegroups.com.
