Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-05-16
Phys.Rev.Lett. 85 (2000) 2873
Physics
High Energy Physics
High Energy Physics - Theory
rewritten for readability, 8 pages, LaTeX
Scientific paper
10.1103/PhysRevLett.85.2873
It has been shown that space-time coordinates can exhibit only very few types of short-distance structures, if described by linear operators: they can be continuous, discrete or "unsharp" in one of two ways. In the literature, various quantum gravity models of space-time at short distances point towards one of these two types of unsharpness. Here, we investigate the properties of fields over such unsharp coordinates. We find that these fields are continuous - but possess only a finite density of degrees of freedom, similar to fields on lattices. We observe that this type of unsharpness is technically the same as the aperture induced unsharpness of optical images. It is also of the same type as the unsharpness of the time-resolution of bandlimited electronic signals. Indeed, as a special case we recover the Shannon sampling theorem of information theory.
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