Trans-Planckian Redshifts and the Substance of the Space-Time River

Trans-Planckian redshifts in cosmology and outside black holes may providewindows on a hypothetical short distance cutoff on the fundamental degrees offreedom. In cosmology, such a cutoff seems to require a growing Hilbert space,but for black holes, Unruh's sonic analogy has given rise to both fieldtheoretic and lattice models demonstrating how such a cutoff in a fixed Hilbertspace might be compatible with a low energy effective quantum field theory ofthe Hawking effect. In the lattice case, the outgoing modes arise via a Blochoscillation from ingoing modes. A short distance cutoff on degrees of freedomis incompatible with local Lorentz invariance, but may nevertheless becompatible with general covariance if the preferred frame is definednon-locally by the cosmological background. Pursuing these ideas in a differentdirection, condensed matter analogs may eventually allow for laboratoryobservations of the Hawking effect. This paper introduces and gives a fairlycomplete but brief review of the work that has been done in these areas, andtries to point the way to some future directions.Comment: 18 pages, to appear in Progress of Theoretical Physics Supplement, Proceedings of Yukawa International Seminar 1999; typos correcte