The Universe from a Single Particle II

TL;DR

This paper investigates a toy quantum model where spontaneous symmetry breaking at the level of probability distributions leads to the emergence of tensor structures, potentially explaining the origins of interactions in the universe.

Contribution

It demonstrates how tensor decompositions can spontaneously arise in simple quantum systems, offering a novel perspective on the emergence of interactions.

Findings

Emergence of tensor structures in quantum state spaces.

Spontaneous decomposition of complex vector spaces into tensor products.

Supports the hypothesis that nature favors tensor decompositions.

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 [7] we saw qubit structure emerge spontaneously on $\mathbb{C}^4$ and $\mathbb{C}^8$, and in this work we see $\mathbb{C}^6$ spontaneously decomposing as $\mathbb{C}^2\otimes \mathbb{C}^3$ and very curiously $\mathbb{C}^5$ (and $\mathbb{C}^7$) 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.