Planck length

Planck length

unit of length
name=Planck length
The Planck length, denoted by scriptstyleell_P , is the unit of length approximately 1.6 × 10−35 meters, 6.3 × 10−34 inches, or about 10−20 times the diameter of a proton. It is in the system of units known as Planck units. The Planck length is deemed "natural" because it can be defined from three fundamental physical constants: the speed of light, Planck's constant, and the gravitational constant.


The Planck length equals [NIST, " [|search_for=universal_in! Planck's Length] ", [ NIST's published] CODATA constants] [NIST's [ 2006] CODATA values]

: ell_P =sqrtfrac{hbar G}{c^3} hickapprox 1.616 252 (81) imes 10^{-35} mbox{ meters}

*c is the speed of light in vacuum;
*G is the gravitational constant;
*hbar (pronounced h-bar) is Dirac's constant, Planck's constant divided by 2π .

The two digits between the parentheses denote the uncertainty in the last two digits of the value.

The Planck length is found by inserting the Planck mass into the equation for the Schwarzchild radius.

In SI units, the Planck length is approximately 1.6 × 10−35 meters. The estimated radius of the observable universe (4.4 × 1026 m or 46 billion light-years) is 2.7 × 1061 Planck lengths.

Physical significance

The physical significance of the Planck length is somewhat abstract. Because it is the only length (up to a constant factor) obtainable from the constants "c", "G", and hbar , it is expected to play some role in a theory of quantum gravity. 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 in other theories of quantum gravity there are no such effects predicted. If there are large extra dimensions (such as those implied by string theory), 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.

The Planck mass is the mass for which the Schwarzschild radius is equal to the Compton length divided by π. The radius of such a black hole would be, roughly, the Planck length. The following thought experiment illuminates this fact. The task is to measure an object's position by bouncing electromagnetic radiation, namely photons, off it. The shorter the wavelength of the photons, and hence the higher their energy, the more accurate the measurement. If the photons are sufficiently energetic to make possible a measurement more precise than a Planck length, their collision with the object would, in theory, create a minuscule black hole. This black hole would "swallow" the photon and thereby make it impossible to obtain a measurement. A simple calculation using dimensional analysis suggests that this problem arises if we attempt to measure an object's position with a precision to within a Planck length.

This thought experiment draws on both general relativity and the Heisenberg uncertainty principle of quantum mechanics. Combined, these two theories imply that it is impossible to measure position to a precision shorter than the Planck length, or duration to a precision to a shorter time interval than a Planck time. These limits may apply to a theory of quantum gravity as well. [John Baez, " [ Length Scales in Physics: The Planck length.] ] [John Baez, " [ Higher-Dimensional Algebra and Planck-Scale Physics: The Planck Length.] "]


Max Planck was the first to propose the Planck length, a base unit in a system of measurement he called natural units. By design, the Planck length, Planck time, and Planck mass are such that the physical constants "c", "G", and hbar all equal 1 and thus disappear from the equations of physics. Although quantum mechanics and general relativity were unknown when Planck proposed his natural units, it later became clear that at a distance equal to the Planck length, gravity begins to display quantum effects, whose understanding would seem to require a theory of quantum gravity. Note that at such a distance scale, the uncertainty principle begins to intrude on one's ability to make any useful statements about what is actually happening.

ee also

* Planck units
* Planck scale
* Orders of magnitude (length)


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Planck length —    a unit of distance representing the scale at which gravity, and perhaps space itself, becomes quantized (discrete) rather than continuous. This is the shortest distance that is meaningful in our understanding of the laws of physics. The Planck …   Dictionary of units of measurement

  • Planck length — noun A unit of length, believed to be the smallest length that has physical meaning, that is defined in terms of the speed of light, the gravitational constant and the reduced Plancks constant viz …   Wiktionary

  • Planck units — are units of measurement named after the German physicist Max Planck, who first proposed them in 1899. They are an example of natural units, i.e. units of measurement designed so that certain fundamental physical constants are normalized to 1. In …   Wikipedia

  • Planck force — is the derived unit of force resulting from the definition of the base Planck units for time, length, and mass. It is equal to the natural unit of momentum divided by the natural unit of time.:F P = frac{m P c}{t P} = frac{c^4}{G} = 1.21027 imes… …   Wikipedia

  • Planck momentum — is the unit of momentum, denoted by m P c, in the system of natural units known as Planck units.m P c = frac{hbar}{l P} = sqrt{frac{hbar c^3}{G approx 6.52485 kg m/swhere*{l P} is the Planck length *hbar is the reduced Planck s constant *c is the …   Wikipedia

  • Planck scale — In particle physics and physical cosmology, the Planck scale is an energy scale around 1.22 × 1028 eV (which corresponds by the mass–energy equivalence to the Planck mass 2.17645 × 10−8 kg) at which quantum effects of gravity become strong. At… …   Wikipedia

  • Length scale — In physics, length scale is a particular length or distance determined with the precision of one order (or a few orders) of magnitude. The concept of length scale is particularly important because physical phenomena of different length scales… …   Wikipedia

  • Planck current — The Planck current is the unit of electric current, denoted by Ip, in the system of natural units known as Planck units. I p = q p/t p = (c^6 4 pi varepsilon 0 / G )^ frac{1}{2} ≈ 3.479 times; 1025 Awhere:q p = (c hbar 4 pi varepsilon 0 )^… …   Wikipedia

  • Planck time — In physics, the Planck time ( tP ), is the unit of time in the system of natural units known as Planck units. It is the time it would take a photon travelling at the speed of light in a vacuum to cross a distance equal to the Planck length.cite… …   Wikipedia

  • Planck energy — In physics, the unit of energy in the system of natural units known as Planck units is called the Planck energy, denoted by E P.:E p = sqrt{frac{hbar c^5}{G approx 1.956 times; 109 J approx 1.22 times; 1019 GeV approx 0.5433 MWhwhere c is the… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.