Thursday, March 15, 2012

Caustics in quantum gravity

Following up on the toy model post part 1. In part one, I consider a world that is essentially a large elastic 3D ball that is initially compressed and starts expanding. It is still expanding and the elastic compression potential is akin to dark energy (aka repulsive). This simple toy model is of type "ether". While ether theories are widely recognized to be wrong due to the evidence from Michelson Morley, I use the mental model to think about questions like E=mc2, gravity, the cosmological constant, the de Sitter universe and some cosmological questions. The link is here.

The next question is where do the stable waveforms come from? There exists many naturally occurring and stable patterns out there in nature. Light for example is focused in swimming pools or coffee cups. If you pay attention to the video the lines never really disappear even though the surface of the pool can be rather agitated. If you mentally project what is going on in the tank from the intersection on the wall you will see the surfaces, this is better done with the still 2D pictures.

There is a language, a math and a science behind these objects. For the optical ones it is called "geometrical optics". The mathematics behind it tells you that these are "folds" and "cusps". The folds are 2D planes, the cusps are 1D strings. It further tells you that they appear as soon as you have any fluctuation in the density of the media and leads to focusing in your media. And they always will be of seven types in 3D (catastrophe theory by Thom). The first two forms will be folds and cusps and there will be everywhere in your geometry. It happens all time, everywhere, as soon as the space compresses randomly out of fluctuations. Nye, stresses the 'genericity' and "structural stability" of these wave foldings in his book. I am using these caustics to think about the "naturally occurring and stable" waves of nature.

If the elastic universe is awash in 'waves' since it started expanding after the big bang, the waves will start focusing in the media as soon as they encounter any fluctuation in density (such as another wave) and they will automatically form these strings and branes. String theory says most matter comes from vibrating strings (albeit in 9 dimensions in the current form). You can grasp that the folds represent "matter" as well however of a lower density than the cusps(3 to 2 in density). Since what we observe from them is electromagnetic and supposedly emanates from the vibration of the string, then the fold is not "visible" and we do not measure enough mass, since the whole fold is not counted. Fold would be dark matter.

Also you can see that the folds and cusps will vibrate. You can see a string of light wiggling about. One can envision a path formalism on these fluctuating geometries as an averaged out behavior. A very similar quantum gravity formalism has been developed by R.Loll. By using computation she shows that a classic path integral formalism needs a highly non-smooth geometry in order to even make sense. The geometries she generates are full of caustics. She further shows that at short distance the space looks 2D. Intriguing.

1 comment:

Marcf said...

Thanks to R.Loll for the private feedback. Fixed.