Evidently, some condensed matter models have an exponential factor which represents the degree of anisotropy (a directionally variable divergence) between space and time. Adopting an appropriate exponent, along with some other pragmatic assumptions (including imposing something called a “detailed balance condition”) creates the high energy decoupling of time from space and allows for renormalization. (A Lifshitz point evidently is a special critical point in a model with such a anisotropic continuous phase transition).

At high energies, the model implies a fundamentally non-relativistic theory, where there is a “preferred foliation” consisting of a structure of time slices. This means a directional causal structure is part of the foundation: time is freed from being bound to space.

In a second paper here, Hořava discusses that the theory has a feature in common with the simulated outputs from the model known as Causal Dynamical Triangulations. Both theories imply that the effective dimensionality of space-time changes with the scaling, from d=2 at high energy to the familiar d=4 at low energy. The imposition of a preferred causal structure is common both models.

As always, my summaries could be flawed by my lack of background knowledge -- please see the papers for details. I’m a little late to reading about all this: Hořava’s papers have led to a good burst of activity on Arxiv in recent months. Also, a short mention of his work in SciAm magazine is here.

It’s interesting to me that another physicist (and a string theorist, at that), has taken up this type of approach to the problem. It seems to my amateur eye to be most fertile area of research in quantum gravity. The theories in this genre share the following characteristics (see the end of the post for a full list of my blog entries on these research programs):

**1**. In assessing the incompatibility of quantum mechanics and general relativity, and despite the breathtaking triumph that is Einstein’s theory, QM is assumed to be more fundamental than GR.

**2**. Gravity as we know it from GR, is an emergent phenomenon: it arises as an effective limit from a more fundamental theory (some approaches attempt to show both gravity and matter/energy co-emerge from a fundamental quantum mechanical theory; others just model gravity and assume the theory can be married to matter fields).

**3**. Some notion of time/causality is fundamental.

**4**. Many (but not all) of the approaches utilize concepts and/or mathematics from condensed matter physics.

One key difference running through some of the approaches has to do with the issue of background independence. In the case of some, including Hořava’s, the mathematics is that of quantum field theory and all the action, including gravity, takes place against a fixed space-time background. Some researchers object that this is a conceptually untenable situation, and a truly “background independent” approach is needed. This debate, which figured prominently in the original critique of string theory by those working in loop quantum gravity, continues to lurk as an issue in the emergent gravity genre.

[UPDATE: 3 December 2009 -- Here's another interesting paper which appeared in Arxiv. "A quantum Bose-Hubbard Model with evolving graph as toy model for emergent spacetime"]

Emergent Quantum Gravity Research Series (in chronological order):

What’s New in Quantum Gravity

*A section of Lee Smolin’s recent book discusses new approaches.*

Causality First

*Rafael Sorkin’s Causal Sets and Fotini Markopoulou’s Quantum Causal Histories.*

Emerging From the Noise

*More on Markopoulou’s approach.*

Caution: Universe under Construction

*The Causal Dynamical Triangulation program.*

Geometrogenesis

*More papers from Markopoulou and colleagues.*

In the Beginning was the Qubit

*Seth Lloyd’s quantum computing-inspired take on quantum gravity.*

Dreyer's Internal Relativity

*Olaf Dreyer's approach to finding emergent gravity from a quantum mechanical base.*

The Superfluid Universe

*Grigory Volovik looks for the answers to fundamental physics in the surprising phenomena displayed in condensed matter physics.*

Group Field Theory and Emergent Space-Time

*Daniele Oriti's Group Field Theory.*

CDT in Scientific American

*A bit more on Causal Dynamical Triangulations and how it compares with other research programs.*

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