Abstract
We continue to explore, in the context of a toy model, the hypothesis that the interacting universe we see around us could result from single particle (undergraduate) quantum mechanics via a novel spontaneous symmetry breaking (SSB) acting at the level of probability distributions on Hamiltonians (rather than on states as is familiar from both Ginzburg-Landau superconductivity and the Higgs mechanism). In an earlier paper [1] we saw qubit structure emerge spontaneously on ℂ4 and ℂ8, and in this work we see ℂ6 spontaneously decomposing as ℂ2 ⊗ ℂ3 and very curiously ℂ5 (and ℂ7) splitting off one (one or three) directions and then factoring. This evidence provides additional support for the broad hypothesis: Nature will seek out tensor decompositions where none are present. We consider how this finding may form a basis for the origins of interaction and ask if it can be related to established foundational discussions such as string theory.
Highlights
Using the concept GUE, we obtain one toy model for this Hamiltonian of the universe, drawn from the Gaussian ensemble:
We continue to explore, in the context of a toy model, the hypothesis that the interacting universe we see around us could result from single particle quantum mechanics via a novel spontaneous symmetry breaking (SSB) acting at the level of probability distributions on Hamiltonians
We consider how this finding may form a basis for the origins of interaction and ask if it can be related to established foundational discussions such as string theory
Summary
To specify each Hs,k requires 4 parameters for a total of 4N , but since scalars pass through the tensor factors 4N becomes 3N + 1 for each value of k of which there are 4N − 1 This makes a total of (4N − 1) + (3N + 1)(4N − 1) = (3N + 2)(4N − 1) parameters to determine a kaq metric (not normalizing so that det(gij) = 1), whereas the space of metrics gij on su(2N ) has dimension. To show that even when N = 2 kaq is a proper subvariety we estimate its local dimension around a generic, normalized metric gij which is diagonal in the so-called Pauli-word basis PBn defined below. We suspect that 21 is the maximum kaq strata dimension in Her0(4)
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