The quantum of area?

John Baez

November 28, 2003

One of the key predictions of loop quantum gravity is that the area of a surface can only take on a discrete spectrum of values. In particular, there is a smallest nonzero area that a surface can have. We could call this the "quantum of area".

So far, calculations working strictly within the framework of loop quantum gravity have been unable to determine the quantum of area. But in 2002, thanks to work of Olaf Dreyer and Lubos Motl, two very different methods of calculating the quantum of area have been shown to give the same answer: 4 ln(3) times the Planck area. Both use information about classical black holes. It is still completely mysterious why they give the same answer. It could be a misleading coincidence, or it could be an important clue. Either way, the story is worth telling.

Here's a quick, nontechnical version of the story:

And here's a somewhat longer version with a few equations:

Both versions cite a bunch of papers available online; here are links to those, in alphabetical order by author. They make a good way to learn about the subject!

Warning: in the summer of 2004, Domagala and Lewandowski found a mistake in the Ashtekar-Baez-Corichi-Krasnov paper. Their corrected calculations, done with the help of Meissner, give a new value of the quantum of area! This casts the work of Dreyer in doubt:

So, the mystery continues....

© 2004 John Baez