Minimum Length from First Principles

Details Minimum Length from First Principles Minimum Length from First Principles

2005-05-16

arxiv.org/abs/hep-th/0505144v1

Int.J.Mod.Phys. D14 (2005) 2195-2200

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, Honorable Mention in the 2005 Gravity Research Foundation Essay Competition

Scientific paper

We show that no device or gedanken experiment is capable of measuring a distance less than the Planck length. By "measuring a distance less than the Planck length" we mean, technically, resolve the eigenvalues of the position operator to within that accuracy. The only assumptions in our argument are causality, the uncertainty principle from quantum mechanics and a dynamical criteria for gravitational collapse from classical general relativity called the hoop conjecture. The inability of any gedanken experiment to measure a sub-Planckian distance suggests the existence of a minimal length.

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