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http://arxiv.org/abs/hep-th/0505144

Minimum Length from First Principles

Xavier Calmet, Michael Graesser, Stephen D. H. Hsu

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

"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."

if they happened to be right, this would not mean that space is necessarily discrete, only that you can't MEASURE a length smaller than such and such.

quantum theories tend to be about measurement, about what one system can know or not know about another system, about observation of one thing by another, they tend to shy away from a notion of some absolute reality (that is "there" regardless of who is measuring or observing what).

so? so you can't measure any length finer than planck length accuracy? it does not mean that smaller lengths do not exist, only that measurment fails. well if you cant measure it shouldnt we say it doesnt exist

anyway CDT and LQG are based on topological continuums, LQG is even based on a (smooth) differentiable manifold of definite preselected dimension (usually 4D). CDT is a continuum limit and the main authors say they have found no indication that spacetime is discrete.

so maybe spacetime really is a continuum, but some mechanism we do not understand yet puts a limit on the precision of measurement

have fun

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# Minimum Length from First Principles

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