Information loss, and emergent type III1 algebras in time

About

I discuss a key example to demonstrate that the decay of the two-point function (clustering in time) in a black hole background holds important clues to the nature of observable algebras, states, and dynamics in quantum gravity. In the thermodynamic limit of infinite entropy (infinite volume or large N), the operators that cluster in time are expected to form an algebra. I show that this algebra is a unique and very special infinite dimensional algebra called the III_1 factor. I prove a generalization of a conjecture of Leutheusser and Liu to arbitrary out-of-equilibrium states. I explicitly construct the C-algebra and von Neumann subalgebras associated with time bands and more generally, arbitrary open sets of the bulk spacetime in the strict N\to\infty limit. The emergence of time algebras is intimately tied to the second law of thermodynamics and the emergence of an arrow of time. .

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