I spent the day with Juna Kollmeier (CITA) talking about epistemology, physical cosmology, and project management (especially academic management). I found myself saying to her the following argument (which I have not seen written down anywhere): Imagine that our Universe is hamiltonian (or lagrangian; it doesn't matter for these purposes). And imagine that our Universe is a simulation being run inside some bigger universe, which is also hamiltonian.
If our Universe is being observed in any sense by any system in that bigger universe, then there ought to be a loss of unitarity in our Universe. That is, there should be a violation of Liouville's theorem, or a violation of key conservation laws, or an information sink. And there is! At black hole horizons, there is an information paradox: Information that goes in never comes back (an evaporating black hole evaporates thermally, or so we think). Thoughts?
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