Early last year a tentative hypothesis was proposed to unify quantum mechanics and general relativity, at the cost of Lorentz invariance. Much research was done over the following months and the interest in this framework appears to have changed since then. In this discussion, if there are any physicists out there I would be interested in your thoughts on this framework. Some material related:
Or just search horava:
As a layman I'm interested in following the discussions of those more educated on the subject than I am.
There are some inconsistencies in the Horava-Lifshitz theory of quantum gravity. It relies on the theory of foliations, but the introduction of the preferred foliation breaks the gauge group of general relativity down to the group of spacetime diffeomorphisms explicity preserving this foliation. This requires the introduction of extra degrees of freedom.
A normal degree of freedom corresponds to a 2-dimensional phase space, while the phase space of Horava gravity is five-dimensional. This leaves an obscure extra "half-mode" which lacks a physical interpretation (i.e. it is unclear whether it corresponds to a real degree of freedom). The model also seems to suffer from a strong coupling problem. That is, the strong coupling scale is dependent on background curvature.
It has also been criticized that the Harava model can only be trusted in the realm of very small energies far below the Planck scale. Nevertheless, despite its criticisms it has some clear advantages, such as solving the problem of different concepts of time in quantum field theory and general relativity.
My understanding is that the degrees of freedom come from reduced symmetry as per a report "Strong coupling in Horava gravity." Am I correct in assuming that the preferred foliation's introduction is what is responsible for the reduced symmetry?
Also in the aforementioned strong coupling report, I read that Horava theory lacks a perturbative General Relativity limit, can you elucidate this point? What exactly are perturbative General Relativity limits?
"My understanding is that the degrees of freedom come from reduced symmetry as per a report 'Strong coupling in Horava gravity'. Am I correct in assuming that the preferred foliation's introduction is what is responsible for the reduced symmetry?"
It is assumed that the spacetime diffeomorphism group can be broken down into a subgroup and the correct long-distance limit can be reproduced in Horava quantum gravity. This assumption is what is meant by reduced symmetry. So yes.
"Also in the aforementioned strong coupling report, I read that Horava theory lacks a perturbative General Relativity limit, can you elucidate this point? What exactly are perturbative General Relativity limits?"
The paper you are referring to ("Strong coupling in Horava gravity") talks a bit about perturbative gravitational waves in General Relativity. In this paper I believe when they use that term they are talking about the limit of General Relativity as approximated by perturbation methods (because of the assumption of different distance scales).
It's an advanced topic, certainly, I can understand it being over some people's heads. I heard about it six months ago, and in order to have merely a superficial understanding of it I had to stay up all night reading theoretical physics journals and cross-referencing their jargon with dictionaries. That's practically unheard of for me because I assimilate information very readily in most cases.
However I do believe that if you're smart, you can follow it, you just have to spend the time on it. I only wish my maths abilities were higher, because knowing only algebra limits your ability to follow these models in depth.
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