Planck length

1 Planck length =
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.

Contents

Value

The Planck length is defined to be:

\ell_P =\sqrt\frac{\hbar G}{c^3} \approx 1.616 252 (81) \times 10^{-35} \mbox{ meters}[1][2]

where c is the speed of light in a vacuum, G is the gravitational constant, and \hbar is the reduced Planck constant.

The two digits enclosed by parentheses are the estimated standard error associated with the reported numerical value.

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. 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 one-1020th of 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 A/4\ell_P^2 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.

See also

Notes

  1. ↑ John Baez, The Planck Length
  2. ↑ NIST, "Planck's Length", NIST's published CODATA constants
Planck's natural units
Base Planck units
Planck time · Planck length · Planck volume · Planck mass · Planck charge · Planck temperature
Derived Planck units
Planck energy · Planck force · Planck power · Planck density · Planck angular frequency · Planck pressure · Planck current · Planck voltage · Planck impedance · Planck momentum