## Wednesday, October 6, 2010

### Quark Gluon Plasma

Much of the confidence exhibited by today's stringers, against the tsunami of evidence against their stringy foundations, comes from one or two successes of stringy methods. The most notable of these is the stringy black hole description of the quark gluon plasma observed in collisions at RHIC. This is supposed to be so complicated that nobody but a string theorist could possibly even be aware of the results, but the papers are widely available. See, for instance, here.

In this paper, the great machine of stringy physics concludes that the viscosity of the new state of matter behaves as

$\eta = \frac{\pi}{8} N^2 T^3$

where we need not worry for now about the numerical constant. Here $T$ is a Hawking temperature for a $5D$ black hole, and $N$ is the index for the gauge group, which is taken to be large. The perfectness of a fluid is thus characterised by the ratio of a shear viscosity to entropy density. A 2004 paper finds a universal lower bound for this physical quantity, given by the heinously complicated equation

$\frac{\eta}{s} = \frac{\hbar}{ 4 \pi k} = 6.08 \times 10^{-13}$ Ks

with $k$ the Boltzmann constant $8.617343 x 10^{-5}$ eV/K.

1. I have nothing against string like objects. The idealization of these objects as strings is probably excellent approximation in many occasions but the assumption that strings are fundamental leads to a completely wrong track as far as physical interpretation is considered as should be clear after these 40 years. In TGD framework string like objects emerge in practically all applications and have direct physical correlates: in cosmology, in hadron and nuclear physics, in biochemistry, in elementary particle mass calculations, ...

String like objects identified as long and entangled color magnetic flux tubes containing QCD plasma like phase in the critical transition region from plasma phase to hadronic phase could provide a nice explanation for the deviations from QCD observed already at RHIC.

These deviations include much longer duration of the plasma phase than expected, its density which is by a factor of 50 higher than it should be, the low viscosity and liquid like behavior meaning long range correlations characteristic of criticality at which viscosity has minimum.

One can consider also values of Planck constants larger than the standard value (the hierarchy of Planck constants can now be understood as a consequence rather than basic assumption in TGD framework).

It seems that it takes one century for super stringers to realize that the conformal invariance of string models generalizes to 3 dimensions in an elegant manner when one takes basic dynamical objects to be light-like 3-surfaces. This leads to holography, explains why the dimension of space-time must be four, allows to get rid of landscape, explains standard model symmetries number theoretically, etc., etc.. : I wonder how many times I have typed these words in the hope that they could stimulate some activity in some brains;-).

2. The equation for eta/s = hbar/4pik_B for the minimum viscosity is interesting from the point of Planck constant hierarchy. Viscosity is reported to be near the minimum. Does this mean that hbar must be equal to
its standard value in the plasma phase?

This does not seem to be the case if the Planck constant hierarchy is effective hierarchy following from basic TGD as I almost-believe now. The extreme non-linearity and vacuum degeneracy of Kahler action imply that the correspondence between canonical momentum densities and time derivatives of imbedding space coordinates is 1-to-many: for vacuum extremals themselves 1-to-infinite.

A convenient technical manner to treat the situation is to replace imbedding space with its n-fold singular covering. Canonical momentum densities to which conserved quantities are proportional would be same at the sheets corresponding to different values of the time derivatives. At each sheet of the covering Planck constant is effectively hbar=nhbar_0. This splitting to multisheeted structure can be seen as a phase transition reducing densitie of various charges making it possible to get to perturbative phase at each sheet (gauge coupling strengths are proportional to 1/hbar and scaled down). The connection with fractional quantum Hall effect is almost obvious.

Various additive quantities at the sheets of the covering scale down like 1/n. In particular, entropy is proportional to 1/n for each sheet but total entropy defined as sum has the ordinary value corresponding to 1/hbar_0. For instance, black hole entropy would have the same value as in GRT contrary to what I believed for some time although black hole itself would have enormous number of sheets of order GM^2/hbar_0. This is natural since the density is extremely high so that perturbative phase requires really large value of hbar at each sheet of covering.

This would mean that eta/s has same minimum value irrespective of the value of hbar. Therefore the finding that eta/s is near to the lower limit would not pose bounds on the value of hbar = nhbar_0 at the sheets of the covering possibly formed in quark gluon plasma phase.