Information-theoretic natural ultraviolet cutoff for spacetime Export

@article{citeulike:5636852, abstract = {Fields in spacetime could be simultaneously discrete and continuous, in the same way that information can: it has been shown that the amplitudes, \phi(x\_n), that a field takes at a generic discrete set of points, x\_n, can be sufficient to reconstruct the field \phi(x) for all x, namely if there exists a certain type of natural ultraviolet (UV) cutoff in nature, and if the average spacing of the sample points is at the UV cutoff scale. Here, we generalize this information-theoretic framework to spacetimes themselves. We show that samples taken at a generic discrete set of points of a Euclidean-signature spacetime can allow one to reconstruct the shape of that spacetime everywhere, down to the cutoff scale. The resulting methods could be useful in various approaches to quantum gravity.}, archivePrefix = {arXiv}, author = {Kempf, Achim}, citeulike-article-id = {5636852}, citeulike-linkout-0 = {http://arxiv.org/abs/0908.3061}, citeulike-linkout-1 = {http://arxiv.org/pdf/0908.3061}, day = {25}, eprint = {0908.3061}, keywords = {information-theory, mathematics, physics, quantum, quantum-gravity}, month = {Aug}, posted-at = {2009-08-28 19:10:31}, priority = {2}, title = {Information-theoretic natural ultraviolet cutoff for spacetime}, url = {http://arxiv.org/abs/0908.3061}, year = {2009} }

TY - JOUR ID - citeulike:5636852 L3 - citeulike-article-id:5636852 N2 - Fields in spacetime could be simultaneously discrete and continuous, in the same way that information can: it has been shown that the amplitudes, \phi(x_n), that a field takes at a generic discrete set of points, x_n, can be sufficient to reconstruct the field \phi(x) for all x, namely if there exists a certain type of natural ultraviolet (UV) cutoff in nature, and if the average spacing of the sample points is at the UV cutoff scale. Here, we generalize this information-theoretic framework to spacetimes themselves. We show that samples taken at a generic discrete set of points of a Euclidean-signature spacetime can allow one to reconstruct the shape of that spacetime everywhere, down to the cutoff scale. The resulting methods could be useful in various approaches to quantum gravity. TI - Information-theoretic natural ultraviolet cutoff for spacetime KW - information-theory KW - mathematics KW - physics KW - quantum KW - quantum-gravity AU - Kempf, Achim PY - 2009/Aug/25/ UR - http://arxiv.org/abs/0908.3061 ER -