Planck length
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| SI units | |
|---|---|
| 16.163×10−36 m | 16.163×10−27 nm |
| Natural units | |
| 11.706 lS | 305.43×10−27 a0 |
| US customary / Imperial units | |
| 53.027×10−36 ft | 636.32×10−36 in |
In physics, the Planck length, denoted ℓP, is a unit of length, equal to 1.616252(81)×10−35 meters. It is a base unit in the system of Planck units. The Planck length can be defined from three fundamental physical constants: the speed of light in a vacuum, Planck's constant, and the gravitational constant.
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[edit] Value
The Planck length is defined to be:
where 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.
[edit] Physical significance
The physical significance of the Planck length, if any, is not yet known. Because the Planck length is the only length that can be formed from the constants c, G, and ħ, dimensional analysis suggests that lengths of special significance in quantum gravity are likely to be small multiples of the Planck length. Contrary to statements sometimes found in the popular press, there is no evidence to suggest that distances in space are quantized in units of the Planck length. In some theories or forms of quantum gravity, it is the length scale at which the structure of spacetime becomes dominated by quantum effects, giving it a discrete or foamy structure, but other theories of quantum gravity predict no such effects. If there are large extra dimensions, the measured strength of gravity may be much smaller than its true (small-scale) value. In this case the Planck length would have no physical significance, and quantum gravitational effects would appear at much larger scales. Because of the tininess of the Planck length (about 1020 times smaller than the diameter of a proton) there is no hope of directly probing this length scale in the foreseeable future.
The Planck area, equal to the square of the Planck length, has a clearer role in quantum gravity. Black hole entropy is known to be given by 
where A is the area of the event horizon. The action in string theory is proportional to the area of the string worldsheet, and area may be quantized in loop quantum gravity.
[edit] See also
- Doubly special relativity
- Orders of magnitude (length)
- Planck scale
- Planck units
- Quantum gravity
- Planck epoch
- Fock-Lorentz symmetry
[edit] Notes
- ^ John Baez, The Planck Length
- ^ NIST, "Planck's Length", NIST's published CODATA constants
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