The generalized uncertainty principle in the presence of extra dimensions

Details The generalized uncertainty principle in the presence of extra dimensions The generalized uncertainty principle in the presence of extra dimensions

2009-09-20

arxiv.org/abs/0909.3635v2

Physics

High Energy Physics

High Energy Physics - Theory

4 pages, REVTeX; updated version; Corrected typos; Added references

Scientific paper

We argue that in the Generalized Uncertainty Principle (GUP) model, the parameter $\beta_0$ whose square root, multiplied by Planck length $\ell_p$, approximates the minimum measurable distance, varies with energy scales. Since minimal measurable length and extra dimensions are both suggested by quantum gravity theories, we investigate models based on GUP and one extra dimension, compactified with radius $\rho$. We obtain an inspiring relation $\sqrt{\beta_0} \ell_p/\rho \sim {\cal O}(1)$. This relation is also consistent with predictions at Planck scale and usual quantum mechanics scale. We also make estimations on the application range of the GUP model. It turns out that the minimum measurable length is exactly the compactification radius of the extra dimension.

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