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arXiv:2108.12709 · Journal of High Energy Physics

The universe from a single particle. Part II

Michael Hartley Freedman, Modjtaba Shokrian Zini

Published Oct 1, 2021• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1007/jhep10(2021)102

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•Apr 1, 2026•0 citations
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.
Abstract We study a mechanism by which the most basic structures of quantum physics can emerge from the most meager of starting points, a Hilbert space, lacking any preassigned structure such as a tensor decomposition, and a loss function. In a simple toy model of the universe, we hypothesize a fundamental loss functional for the combined Hamiltonian and quantum state, and then minimize this loss functional by gradient descent. We find that this minimization gives rise to a co-emergence of locality, i.e. a tensor product structure simultaneously respected by both the Hamiltonian and the state, suggesting that locality can emerge by a process analogous to spontaneous symmetry breaking. We discuss the relevance of this program to the arrow of time problem. In our toy model, we interpret the emergence of a tensor factorization as the appearance of individual degrees of freedom within a previously undifferentiated (raw) Hilbert space. Earlier work [5, 6] looked at the emergence of locality in Hamiltonians only, and in that context found strong numerical confirmation of the hypothesis that raw Hilbert spaces of dim = n are unstable and prefer to settle on tensor factorization when n is not prime, expressing, for example, n = pq, and in [6] even primes were seen to “factor” after first shedding a small summand, e.g. 7 = 1 + 2 · 3. This was found in the context of a rather general potential functional F on the space of metrics {gij} on su \mathfrak{su} su su (n), the Lie algebra of symmetries. This emergence of qunits through operator-level spontaneous symmetry breaking (SSB) may help us understand why the world seems to consist of myriad interacting degrees of freedom. But understanding why the universe has an initial Hamiltonian H0 with a many-body structure is of limited conceptual value unless the initial state, ∣ψ0〉, is also structured by this tensor decomposition. Here we adapt F to become a functional on {g, | ψ0〉} = (metrics) × (initial states), and find SSB now produces a conspiracy between g and ∣ψ0〉, where they simultaneously attain low entropy by jointly settling on the same qubit decomposition. Extreme scaling of the computational problem has confined us to studying ℂ4 breaking to ℂ2 ⊗ ℂ2 and ℂ8 breaking to ℂ2 ⊗ ℂ4 or ℂ2 ⊗ ℂ2 ⊗ ℂ2.
Philosophical analysis of spontaneous symmetry breaking (SSB) in particle physics has been hindered by the unavailability of rigorous formulations of models in quantum field theory (QFT). A strategy for addressing this problem is to use the rigorous models that have been constructed for SSB in quantum statistical mechanics (QSM) systems as a basis for drawing analogous conclusions about SSB in QFT. On the basis of an analysis of this strategy as an instance of the application of the same mathematical formalism to different domains and as an instance of drawing analogies between domains, I conclude that certain structural explanations can be exported from QSM to QFT but that causal explanations cannot.
Spontaneous symmetry breaking (SSB) is responsible for structure formation in scenarios ranging from condensed matter to cosmology. SSB is broadly understood in terms of perturbations to the Hamiltonian governing the dynamics or to the state of the system. We study SSB due to quantum monitoring of a system via continuous quantum measurements. The acquisition of information during the measurement process induces a measurement backaction that seeds SSB. In this setting, by monitoring different observables, an observer can tailor the topology of the vacuum manifold, the pattern of symmetry breaking, and the nature of the resulting domains and topological defects.
We consider a pure 3-qubits system interacting through a XY-Hamiltonian with antiferromagnetic constant J. We employ the 3-tangle as an efficient measure of the entanglement between such a 3-qubit system. The time evolution of such a 3-tangle is studied. In order to do the above, the 3-tangle associated to the pure 3-qubits state|ψ(t)⟩ = c0(t)|000⟩+c1(t)|001⟩+c2(t)|010⟩+c3(t)|011⟩+ c4(t)|100⟩+c5(t)|101⟩+c6(t)|110⟩+c7(t)|111⟩ is calculated as a function of the initial coefficients {ci(t = 0)} (i = 0,1,...,7), the time t and the antiferromagnetic constant J. We find that the 3-tangle of the 3-qubits system is periodic with period t = 4π/J. Furthermore, we also find that the 3-tangle as a function of the time t and J has maximal and minimum values. The maximal values of the 3-tangle can be employed in Quantum Information Protocols (QIP) that use entanglement as a basic resource. The pattern found for the 3-tangle of the system of three qubits interacting through a XY Hamiltonian as a function of J and the time t resembles to a quantized physical quantity.
A controlled experimental protocol for testing the von Neumann–Wigner (VNW) interpretation of quantum mechanics, the hypothesis that consciousness plays a role in quantum state reduction, against the prevailing environmental decoherence framework (Zurek, Zeh, Joos). The experimental platform places a single experienced meditator in EEG-verified cognitive states inside a shielded environment. A quantum coherence sensor measures decoherence rates (T₂) across seven consciousness conditions (C1–C7) spanning the full cognitive-excitation axis, against a separate empty-chamber instrumental baseline. The primary pre-registered hypothesis is that T₂ at C7 (Cessation / Objectless Awareness) and T₂ at C6 (Minimal Phenomenal Experience) will both exceed T₂ at the chamber baseline and at conditions C1–C5, and that T₂ at C7 will further exceed T₂ at C6. This is tested via two pre-registered orthogonal planned contrasts: (i) [C6, C7] vs. [baseline, C1–C5], and (ii) C7 vs. C6, both with directional predictions. All other cross-condition comparisons are treated as exploratory. A secondary experiment uses quantum random number generators with improved shielding, blinding, and instrumentation. The protocol is phased: a Phase 0 foundational test using nitrogen-vacancy centers in diamond, and a Phase 1 full protocol using superconducting qubits in an underground laboratory, conditional on Phase 0 results and adoption by an institutional host. The protocol employs blinding when feasible and pre-registered statistical thresholds. Null results establish pre-registered upper bounds; positive results require replication. The theoretical basis for this protocol is detailed in the companion paper, The Silence Paradigm.