exceptional group symmetry breaking as a binary entropy process

*To*: mathgroup at smc.vnet.net*Subject*: [mg75483] exceptional group symmetry breaking as a binary entropy process*From*: Roger Bagula <rlbagula at sbcglobal.net>*Date*: Wed, 2 May 2007 03:56:32 -0400 (EDT)

Continuation of my work on entropy in the early universe and information theory; Thought experiment: Suppose we had a worm hole from the remote past when the universe was E8 symmetry to the present and you could represent the state as a graph: GE8->ME8 ( matrix for the graph) Gpresent-> Mpresent Then you would necessarily have a transform T that would take place in the worm hole as: GE8->Gpresent as Mpresent=T*ME8 For the information to be conserved T would have to be a unitary Jacobian like transform: Information Entropy as H(present)=H(E8)+Log[Measure[T]]/Log[2] I get the the Limit : Limit[Measure[T], t-> Large]=0 This single approach gave me two copies of a group with 98 elements. A symmetry breaking linear approach with two "target" groups also gave an unexpected result: E8-> -37*"7" +39*"13" 507->507 E8*E8 and SO(32) are 496 =507-11 Entropy excess is ( inflation's heating origin?) : 0.003310557481995602 which is less than alpha/2. "7"-> U(1)*SO(4)->(in hyperbolic terms) U(1)*SO(3,1) I'm having trouble getting the {x,y} out of the "a" array. Mathematica: Clear[En,a,b,x,y,n,m] (*Binary Information Entropy for a group with n elements:*) En[n_]=Sum[-(m/n)*Log[m/n]/Log[2],{m,1,n}] a = Flatten[Table[Table[ Flatten[{n, m, x /. NSolve[{x*N[En[n]] + y*N[En[m]] - En[248] == 0, x*n + y*m - 248 == 0}], y /. NSolve[{x*N[En[n]] + y*N[En[m]] - En[248] == 0, x*n + y*m - 248 == 0}]}], {n, 1, m}], {m, 1, 50}], 1] x = 100; y = 100; b = Table[Abs[Round[a[[n, 3]]]*N[En[a[[n, 1]]]] + Round[a[[n, 4]]]*N[ En[a[[n, 2]]]] - N[En[248]]], {n, 1, Length[a]}] Min[b] 0.003310557481995602` Flatten[Table[If[b[[n]] - Min[b] == 0, a[[n]], {}], {n, 1, Length[a]}]] {7, 13, -36.996957416987826`, 38.99836168607037`}