Modeling Quantum Mechanical Observers via Neural-Glial Networks

We investigate the theory of observers in the quantum mechanical world by using a novel model of the human brain which incorporates the glial network into the Hopfield model of the neural network. Our model is based on a microscopic construction of a quantum Hamiltonian of the synaptic junctions. Using the Eguchi-Kawai large N reduction, we show that, when the number of neurons and astrocytes is exponentially large, the degrees of freedom of the dynamics of the neural and glial networks can be completely removed and, consequently, that the retention time of the superposition of the wave functions in the brain is as long as that of the microscopic quantum system of pre-synaptics sites. Based on this model, the classical information entropy of the neural-glial network is introduced. Using this quantity, we propose a criterion for the brain to be a quantum mechanical observer.Comment: 24 pages, published versio

Dynamical Gauged S-duality Spontaneous Breakdown

Inspired by Yoneya's recent work on D-brane field theory, we present the constructive definition of this theory as a new dual model based on the quantization of non-perturbative string gauged S-dualities and its spontaneous breakdown. Our model is determined by one BRST quantization condition. Here, we provide some testable conjectures, for example, that the partition function of bosonic part of IIB matrix model and string partition functions of various interactions including gravity are realized by the physical state and its Goldstone modes.Comment: latex, 8 page

Holographic Interpretation of Shannon Entropy of Coherence of Quantum Pure States

For a quantum pure state in conformal field theory, we generate the Shannon entropy of its coherence, that is, the von Neumann entropy obtained by introducing quantum measurement errors. We give a holographic interpretation of this Shannon entropy, based on Swingle's interpretation of anti-de Sitter space/conformal field theory (AdS/CFT) correspondence in the context of AdS$_3$/CFT$_2$. As a result of this interpretation, we conjecture a differential geometrical formula for the Shannon entropy of the coherence of a quantum pure or purified state in CFT$_2$ at thermal and momentum equilibrium as the sum of the holographic complexity and the abbreviated action, divided by $\pi\hbar$, in the bulk domain enclosed by the Ryu--Takayanagi curve. This result offers a definition of the action of a bulk model of qubits dual to the boundary CFT$_2$ at this equilibrium.Comment: 9+2 pages, revtex, v6: published version, bundled with the addendu