Short-Distance Cutoffs in Curved Space

Details Short-Distance Cutoffs in Curved Space Short-Distance Cutoffs in Curved Space

2004-03-30

arxiv.org/abs/gr-qc/0403112v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Talk presented at 10th Marcel Grossmann Meeting, Rio de Janeiro, July 20-26, 2003

Scientific paper

It is shown that space-time may possess the differentiability properties of manifolds as well as the ultraviolet finiteness properties of lattices. Namely, if a field's amplitudes are given on any sufficiently dense set of discrete points this could already determine the field's amplitudes at all other points of the manifold. The criterion for when samples are sufficiently densely spaced could be that they are apart on average not more than at a Planck distance. The underlying mathematics is that of classes of functions that can be reconstructed completely from discrete samples. The discipline is called sampling theory and is at the heart of information theory. Sampling theory establishes the link between continuous and discrete forms of information and is used in ubiquitous applications from scientific data taking to digital audio.

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