## Friday, January 20, 2006

### Weak gravity developments

There are several developments that are based on similar reasoning as the paper by Mahmoud Ahmadinejad et al.

Shamit Kachru, John McGreevy, and Peter Svrček present evidence that string theory compactified on manifolds of radius "R" always has particles that are parametrically lighter than "1/R". This is a new development in the line of reasoning that the existence of multiple scales is inevitable in quantum gravity unless everything occurs at the Planck scale. Note that their preprint number is pretty good, too: 0601111 instead of Ayatollah Khomeini's 0601001.

In a remotely related research, Cremonini and Watson argue that "beauty is beautiful" and the self-dual couplings are preferred.

Tonight, Li, So, and Wang argue that in 2+1 dimensions and probably also 1+1 dimensions, the principle of weak gravity can be proved without special arguments based on quantum gravity such as the remnants. I have not yet understood how it works. I suspect that they essentially prove more reliably the relation between the monopoles and the black holes.

1. Lubos:

That paper by Li et al is nonsense. Just look at equation (3), the term -8*PI*G*M is used as exponent.

Anything that appears to be an exponent has got to be evaluated to be a dimensionless term. But there is no way you can make -8*PI*G*M a dimensionless term. I am fully aware that they use natural unit where hbar and C are presumed to be one and thus not occuring in the expression. But you can feel free to insert any combination of hbar and C into the expression -8*PI*G*M, you could never get something that is dimensionless. That is, unless M is not refered to as mass, or G is not refered to as the Newton gravitational constant.

The rest of the paper is crap if such low level error occurs.

Quantoken

2. Dear Quantoken,

I assure you that the validity of your comment is equal to the validity of most of your comments.

In three dimensions, G newton has a dimension of length, which is why GM is dimensionless, as required.

Be sure that you can't judge papers just by trying to find an error in one equation. With your perforated reasoning, there is 80% probability that you will find an error in every correct equation, and a 55% probability that you will find an error in a wrong equation - but not the true error.

Best
Lubos

3. Lubos:

Let me ask you what shall the formula for the radius of a blackhole in 3D spacetime look like?

Gravity in 3D is very problematic. If you integrate from infinite distance away, the gravitational potential at any finit distance is always negative infinity. This may not be a problem for the classical Newtonian gravity, but is a big trouble for General Relativity, because GR is based on the equivalence principle, and gravity energy itself also gravitates. So if you have negative infinite gravitational energy, then even point becomes a blackhole, and any circle you draw becomes an event horizon. There is no meaningful metric equation you can write down. So GR is in big trouble if the spacetime is 3D.

One has to realize, like Einstein did, that gravitation is NOT a force. But rather, gravitation is a pure geometric effect. As such, gravity is something related to some unique geometric things that exists only in 4D spacetime.