Unit system Planck units Symbol ℓP | Unit of length 1 ℓP in ... ... is equal to ... | |
SI units 6965161622900000000♠1.616229(38)×10 m natural units 11.706 ℓS
6975305419999999999♠3.0542×10 a0 | ||
In physics, the Planck length, denoted ℓP, is a unit of length, equal to 6965161622900000000♠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.
Contents
Value
The Planck length ℓP is defined as
where
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 precise effects of quantum gravity are unknown; it is often guessed that spacetime might have a discrete or foamy structure at a Planck length scale.
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
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. The string scale ls is related to the Planck scale by ℓP = 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.
Visualization
The size of the Planck length can be visualized as follows: if a particle or dot about 0.1 mm in size (which is approximately the smallest the unaided human eye can see) 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 0.1 mm dot. In other words, a 0.1 mm dot is halfway between the Planck length and the size of the observable universe on a logarithmic scale.