Planck units
Planck length

The Planck length, denoted ℓ, is a unit of length defined as: ℓ P = ℏ G c 3 {\displaystyle \ell _{\mathrm {P} }={\sqrt {\frac {\hbar G}{c^{3}}}}}

It is equal to 1.616 255 (18) × 10 m (the two digits enclosed by parentheses are the estimated standard error associated with the reported numerical value) or about 10 times the diameter of a proton. It can be motivated in various ways, such as considering a particle whose reduced Compton wavelength is comparable to its Schwarzschild radius, though whether those concepts are in fact simultaneously applicable is open to debate. (The same heuristic argument simultaneously motivates the Planck mass.)

The Planck length is a distance scale of interest in speculations about quantum gravity. The Bekenstein–Hawking entropy of a black hole is one-fourth the area of its event horizon in units of Planck length squared. Since the 1950s, it has been conjectured that quantum fluctuations of the spacetime metric might make the familiar notion of distance inapplicable below the Planck length. This is sometimes expressed by saying that "spacetime becomes a foam at the Planck scale ". It is possible that the Planck length is the shortest physically measurable distance, since any attempt to investigate the possible existence of shorter distances, by performing higher-energy collisions, would result in black hole production. Higher-energy collisions, rather than splitting matter into finer pieces, would simply produce bigger black holes.

The strings of string theory are modeled to be on the order of the Planck length. In theories with large extra dimensions, the Planck length calculated from the observed value of G {\displaystyle G} can be smaller than the true, fundamental Planck length.
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