- 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 × 10−34inches , 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 × 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 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.