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arXiv · 0709.0898

Space-time uncertainty relation and operational definition of dimension

Michael Maziashvili
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Abstract

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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Michael Maziashvili. 2007-09-06. Space-time uncertainty relation and operational definition of dimension. https://doi.org/10.1142/s0217751x08039827

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