- Planck length
unit of length

name=Planck length

m=0.00000000000000000000000000000000001616252

accuracy=5 The**Planck length**, denoted by $scriptstyleell\_P$, is the unit oflength 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 asPlanck units . The Planck length is deemed "natural" because it can be defined from threefundamental physical constant s: thespeed of light ,Planck's constant , and thegravitational constant .**Value**The

**Planck length**equals [] [NIST , " [*http://physics.nist.gov/cgi-bin/cuu/Value?plkl|search_for=universal_in! Planck's Length*] ", [*http://physics.nist.gov/cuu/Constants/index.html NIST's published*]CODATA constants*NIST's [*]*http://physics.nist.gov/cuu/Constants/index.html 2006*]CODATA values:$ell\_P\; =sqrtfrac\{hbar\; G\}\{c^3\}\; hickapprox\; 1.616\; 252\; (81)\; imes\; 10^\{-35\}\; mbox\{\; meters\}$

where:

*$c$ is thespeed of light in vacuum;

*$G$ is thegravitational constant ;

*$hbar$ (pronounced h-bar) isDirac'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 theSchwarzchild radius .In

SI units , the Planck length is approximately 1.6 × 10^{−35}meters. The estimated radius of theobservable universe (4.4 × 10^{26}m or 46 billion light-years) is 2.7 × 10^{61}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 arelarge extra dimension s (such as those implied bystring 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 theCompton length divided by π. The radius of such a black hole would be, roughly, the Planck length. The followingthought experiment illuminates this fact. The task is to measure an object's position by bouncingelectromagnetic radiation , namelyphoton s, off it. The shorter thewavelength 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 usingdimensional 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 Heisenberguncertainty principle ofquantum 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 aPlanck time . These limits may apply to a theory ofquantum gravity as well. [] [John Baez , " [*http://math.ucr.edu/home/baez/lengths.html#planck_length Length Scales in Physics: The Planck length.*]]John Baez , " [*http://math.ucr.edu/home/baez/planck/node2.html Higher-Dimensional Algebra and Planck-Scale Physics: The Planck Length.*] "**History**Max Planck was the first to propose the Planck length, a base unit in a system of measurement he callednatural units . By design, the Planck length,Planck time , andPlanck mass are such that thephysical constant s "c", "G", and $hbar$ all equal 1 and thus disappear from the equations of physics. Althoughquantum mechanics andgeneral 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 ofquantum gravity . Note that at such a distance scale, theuncertainty 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) **Notes**

*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