Space-time uncertainty relation and operational definition of dimension

Details Space-time uncertainty relation and operational definition of dimension Space-time uncertainty relation and operational definition of dimension

2007-09-06

arxiv.org/abs/0709.0898v1

Int.J.Mod.Phys.A23:1747-1756,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

5 pages

Scientific paper

10.1142/S0217751X08039827

Operational definition of space-time in light of quantum mechanics and general relativity inevitably indicates an intrinsic imprecision in space-time structure which has to do with space-time dimension as well. The operational dimension of space-time turns out to be a scale dependent quantity slightly smaller than four at distances $\gg l_P$. Close to the Planck length the deviation of space-time dimension from four becomes appreciable. The experimental bounds on the deviation of space-time dimension from four coming from the electron ${\tt g} - 2$ factor, Lamb shift in hydrogen atom and the perihelion shift in the planetary motion are still far from the theoretical predictions.

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