# Planck length

(Redirected from Planck area)
Planck length
Unit system Planck units
Unit of length
Symbol P
Unit conversions
1 P in ... ... is equal to ...
SI units    1.616229(38)×10−35 m
natural units    11.706 S
3.0542×10−25 a0
imperial/US units    6.3631×10−34 in

In physics, the Planck length, denoted P, is a unit of length, equal to 1.616229(38)×10−35 metres. It is a base unit in the system of Planck units, developed by physicist Max Planck. The Planck length can be defined from three fundamental physical constants: the speed of light in a vacuum, the Planck constant, and the gravitational constant.

## Value

The Planck length P is defined as

${\displaystyle \ell _{\mathrm {P} }={\sqrt {\frac {\hbar G}{c^{3}}}}\approx 1.616\;229(38)\times 10^{-35}\ \mathrm {m} }$

where ${\displaystyle c}$ is the speed of light in a vacuum, G is the gravitational constant, and ħ is the reduced Planck constant. The two digits enclosed by parentheses are the estimated standard error associated with the reported numerical value.[1][2]

The Planck length is about 10−20 times the diameter of a proton.

## Theoretical significance

There is currently no proven physical significance of the Planck length. However, it is theoretically considered to be the quantization of space which makes up the fabric of the universe, also referred to as quantum foam.

In some forms of quantum gravity, the Planck length is the length scale at which the structure of spacetime becomes dominated by quantum effects, and it is impossible to determine the difference between two locations less than one Planck length apart.

The Planck area, equal to the square of the Planck length, plays a role in black hole entropy. The value of this entropy, in units of the Boltzmann constant, is known to be given by ${\displaystyle A/(4\ell _{\mathrm {P} }^{2})}$, where A is the area of the event horizon. The Planck area is the area by which the surface of a spherical black hole increases when the black hole swallows one bit of information, as was proven by Jacob Bekenstein.[3]

If large extra dimensions exist, the measured strength of gravity may be much smaller than its true (small-scale) value. In this case the Planck length would have no fundamental physical significance, and quantum gravitational effects would appear at other scales.

In string theory, the Planck length is the order of magnitude of the oscillating strings that form elementary particles, and shorter lengths do not make physical sense.[4] The string scale ls is related to the Planck scale by P = gs1/4ls, where gs is the string coupling constant. Contrary to what the name suggests, the string coupling constant is not constant, but depends on the value of a scalar field known as the dilaton.

In loop quantum gravity, area is quantized, and the Planck area is, within a factor of 10, the smallest possible area value.

In doubly special relativity, the Planck length is observer-invariant.

The search for the laws of physics valid at the Planck length is a part of the search for the theory of everything.[clarification needed]

## Visualization

The size of the Planck length can be visualized as follows: if a particle or dot about 0.005 mm in size (which is the same size as a small grain of silt) were magnified in size to be as large as the observable universe, then inside that universe-sized "dot", the Planck length would be roughly the size of an actual 0.005 mm dot. In other words, a 0.005 mm dot is halfway between the Planck length and the size of the observable universe on a logarithmic scale.[5] All said, the attempt to visualize to an arbitrary scale of a 0.005 mm dot is only for a hinge point. With no fixed frame of reference for time or space, where the spatial units shrink toward infinitesimally small spatial sections and time stretches toward infinity, scale breaks down. Inverted, where space is stretched and time is shrunk, the scale adjusts the other way according to the ratio V-squared/C-squared (Lorentz transformation).