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$l_p= \sqrt{G \hbar/c^3}$

# Planck Length

## Why is it interesting?

There are many indications that in quantum gravity there might exist a minimal observable distance on the order of the Planck length. The emergence of a minimal length is usually considered a dynamical phenomenon, related to the fact that at the Planck scale there are violent fluctuations of the metric and even topology changes, as in Wheeler space-time foam/ from Quantum groups, gravity, and the generalized uncertainty principle by Michele Maggiore

if one wants to probe an event in the length scale of Planck length with a photon, by the uncertainty principle, the particle has to have roughly Planck energy. Now according to general relativity, a photon on such energy scales causes a gravitational collapse and therefore it does not yield any information of the event. The gravitational collapse is caused by the fact that the Schwarzschild radius of a particle with Planck energy is approximately equal to the Planck length. Consequently, due to the uncertainty principle and the Schwarzschild radius, the very measurement of an event in this length scale creates a black hole and no information about this event will emerge. The region with Planck-length of radius, therefore becomes in a sense noncontinuous, i.e. experimentally not accessible.Source

## Layman

Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.

## Researcher

The motto in this section is: the higher the level of abstraction, the better.

Example1
Example2: