Monday, April 13, 2009

Horava´s quantum gravity

I have mentioned many approaches to quantum gravity, other than string theory, in this blog.

Besides LQG none of them has had major success in attracting people to do research in it. Now, at least it seems so, there is a new option, the so called Quantum Gravity at a Lifshitz Point initiated by Peter Horava, a well known string theorist (remember the Horawa-Witten model of heterotic string theory). I had the first new about it in the Lubos blog, but since them a few other papers have appeared. As far as another string theory minirevolution is going on (F-theory GUTs) which is leading to , seemengly, actual predictions testable in the LHC, as well as, maybe, in cosmology, I have had not time to read these articles, beyond an slight overview. I will use this entry mainly to keep track of the actual papers and also to encourage possible readers of this blog to investigate about them.

I will limit, so, to link some of the papers and paste the abstracts. Just to say that the theory will probably be of the liking of the people who likes condensed matter and critical phenomena.

This was the firs paper, Quantum Gravity at a Lifshitz Point. This is the abstract:

We present a candidate quantum field theory of gravity with dynamical critical
exponent equal to z = 3 in the UV. (As in condensed matter systems, z measures the degree
of anisotropy between space and time.) This theory, which at short distances describes
interacting nonrelativistic gravitons, is power-counting renormalizable in 3 + 1 dimensions.
When restricted to satisfy the condition of detailed balance, this theory is intimately related
to topologically massive gravity in three dimensions, and the geometry of the Cotton tensor.
At long distances, this theory flows naturally to the relativistic value z = 1, and could
therefore serve as a possible candidate for a UV completion of Einstein’s general relativity
or an infrared modification thereof. The effective speed of light, the Newton constant and
the cosmological constant all emerge from relevant deformations of the deeply nonrelativistic
z = 3 theory at short distances


This is the second one: Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point, and this is the abstract:

We extend the definition of “spectral dimension” (usually defined for fractal and
lattice geometries) to theories on smooth spacetimes with anisotropic scaling. We show that
in quantum gravity dominated by a Lifshitz point with dynamical critical exponent z in D+1
spacetime dimensions, the spectral dimension of spacetime is equal to

ds = 1 + D/z

In the case of gravity in 3 + 1 dimensions presented in arXiv:0901.3775, which is dominated
by z = 3 in the UV and flows to z = 1 in the IR, the spectral dimension of spacetime flows
from ds = 4 at large scales, to ds = 2 at short distances. Remarkably, this is the qualitative
behavior of ds found numerically by Ambjørn, Jurkiewicz and Loll in their causal dynamical
triangulations approach to quantum gravity


The next article is not written by Horova, the authors are Tomohiro Takahashi and Jiro Soda. The paper is this:Chiral Primordial Gravitational Waves from a Lifshitz Point. This is the abstract:

We study primordial gravitational waves produced during inflation in quantum gravity at a Lifshitz
point proposed by Hoˇrava. Assuming power-counting renormalizability, foliation preserving
diffeomorphism invariance, and the condition of detailed balance, we show that primordial gravitational
waves are circularly polarized due to parity violation. The chirality of primordial gravitational
waves is a quite robust prediction of quantum gravity at a Lifshitz point which can be tested through
observations of cosmic microwave background radiation and stochastic gravitational waves.


I find this one particularly important because it claims that it has a measurable prediction that could falsify (or give credit to) the theory.

The last one is neither written by Horava, the authors are H. L¨u †⋆, Jianwei Mei † and C.N. Pope. The paper is: Solutions to Horava Gravity

And the abstract is:

Recently Horava proposed a non-relativistic renormalisable theory of gravitation, which
reduces to Einstein’s general relativity at large distances, and that may provide a candidate
for a UV completion of Einstein’s theory. In this paper, we derive the full set of equations
of motion, and then we obtain spherically symmetric solutions and discuss their properties.
We also obtain the Friedman-Lemaitre-Robertson-Walker cosmological metric.


I would advise the readers of this blog to read the entries in the other blogs that I have linked in this page because the last month there have been many many interesting things that are worth reading. Maybe I will make a post resuming them.

3 comments:

Dale B. Ritter, B.A. said...

Gravitation theory is seeking a quantized formula to express the physics of masses' interactions that will fit the essential equations for electromagnetic wave propagation at velocity c, unified with the relativistic transform functions for time, mass, and energy.
That set of physical relationships must have a model for the gravitational field as a force field composed of discrete forcon particles, the gravital quanta.
One way to decipher quantum gravity in a mode that agrees closely with ferromagnetism is to solve the wavefunction of an atom, psi (Z), through combination of the quantum functions for frequency and wavelength with the relativistic transforms.
That model enumerates nuclear emissions of gravity and positrons by the GT integral atomic topofunc, with psi pulsating at the frequency [ Nhu = e/h ] by
[ e = m(c^2) ] transform of massive nucleoplasm to radiation of force fieldons. The series differential expansion of psi's possible rates of output gives a spectrum of gravitalons which have five quantum states of decay from the ground state of nuclear surface contact g(0)s. These diffuse outward and interact with electric and magnetic fields of the electron shells as part of the process of atomic conservation of symmetry and momentum. The gravitalon (5) is clearly the synchronous particle giving iron it's metallic and magnetic qualities, by it's topology.
When the psi's internal momentum function is written, rearranged to give the photon gain rule, and integrated for GT [ Gravity <--> Time ] boundaries the series of 26 resulting functions may be solved for the picoyoctometric topologies of the energy intermedons of the 5/2 kT J heat capacity energy cloud.
That is true because quantum symmetry numbers are included along the nuclear differential series, building RQT (Relative Quantum Topological) physics topofuncs. The resultant intermedon joule sizes intersect the values for the fundamental physical constants: h, h-bar, delta, nuclear magneton, beta magneton.
Unified field RQT discussions, essays, graphics, calculations, and commercial infotools for MAVCAM (Molecular or Material Animated Video Computer Assisted Modeling) build projects are available online at | http://www.symmecon.com |. Images of the h-bar magneparticle of ~175 picoyoctometers are on display there.

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cristi dumitrescu said...

there during and outside the movement, alteration, but not relevant.
time is relevant only if the motion is taken into account,
to have the motion must have energy, that energy must have a manifest imbalance, if you have a balance, that it contains a potential level of imbalance, as long as you have or generate mass interaction energy as you hold steady relative or unbalanced approx.

thus we have infinite time.

and have the time to explain each system and infinite universes
Each element generates a point matching enrgie a myriad of choices.
both theories are right, only that they have treated time after each concept's existence
return time is but illusion,
who could manage the movement would have its own uniqueness as compared to others and should remain.