Covariant Information-Density Cutoff in Curved Space-Time
- 1 June 2004
- journal article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 92 (22), 221301
- https://doi.org/10.1103/physrevlett.92.221301
Abstract
In information theory, the link between continuous information and discrete information is established through well-known sampling theorems. Sampling theory explains, for example, how frequency-filtered music signals are reconstructible perfectly from discrete samples. In this Letter, sampling theory is generalized to pseudo-Riemannian manifolds. This provides a new set of mathematical tools for the study of space-time at the Planck scale: theories formulated on a differentiable space-time manifold can be equivalent to lattice theories. There is a close connection to generalized uncertainty relations which have appeared in string theory and other studies of quantum gravity.Keywords
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