Planck length

A unit of length in an absolute system of units devised by Max Planck, about 1.616 199 × 10⁻³⁵ meter.¹ Symbol, lP. Algebraically, it is

the square root of a fraction. h-bar G is the numerator. c to the third power is the denominator.

where c = the speed of light, G = Newtonian gravitational constant, and ħ = the reduced Planck's constant.

Though this length is derived from well-known, measured, physical quantities, its meaning, if any, is not known. It often comes up in discussions of whether space is continuous or quantized. In quantized space, for example, only certain distances could exist, and a statement of a distance that fell between those distances would be meaningless. Physicists who think space is quantized often think the Planck length describes it in some way.

To illustrate how the quantization of space might be investigated: Choose a process happening over a very, very long distance, say, the distance to another galaxy. In December 2004 the European Space Agency's Integral Satellite recorded a particularly powerful gamma ray burst (GRB 041219). The distance to the source (about 275 million light years) was determined in 2011. Under some theories, photons from the gamma ray burst should be affected by any graininess of space on their 275-million-year journey, and the higher energy photons should be changed more than the lower energy ones. Researchers² examining Integral's data found there was no difference, and concluded that if space is quantized, its graininess must be smaller than 10⁻⁴⁸ meter, which is much smaller than the Planck length. Other physicists have disagreed with the conclusion.

1. For the most up-to-date value, consult the CODATA page at NIST:|search_for=Planck+length The figure given here is the 2010 CODATA value.

2. P. Laurent, D. Götz, P. Binetruy, S. Covino, A. Fernandez-Soto.
Constraints on Lorentz Invariance Violation using INTEGRAL/IBIS observations of GRB041219A.
Physical Review D, vol. 83, issue 12 (28 June 2011).