Wednesday, February 24, 2010

Hořava-Lifshitz Gravity.

Now that we discussed loop quantum gravity I wanted to point your attention to another quantum gravity theory that has been generating a lot of attention: Hořava-Lifshitz gravity.

About one year ago, Petr Hořava proposed a new theory of gravity with the following attributes:
  1. It is 4 dimensional just like the space we observe is. (4th dimension being time).
  2. It is a "small" theory in that, like loop quantum gravity, it only addresses gravity and doesn't aim to unify all physics.  (Though it may be embeddable in a larger theory like string theory.)
  3. Here is the kicker part 1: It is anisotropic in space and time on small scales meaning the traditional "equivalence" of space and time breaks down. 
  4. Here is the kicker part 2: Because of #3 above, Lorentz invariance only holds on large scales.  On small scales it breaks down.
  5. It is re-normalizable by virtue of #3 and #4 above.
Basically, what I took from the paper is this:

Hořava wanted to work on a "small" gravity theory that didn't have to solve all the worlds problems at once, just quantum gravity in 4 dimensions.  He noticed that the main problem with quantum gravity is that it blows up at high energies. He understood a concept from condensed matter where there is a scaling between space and time producing an anisotropy that can be parametrized by a variable z.  He applies this scaling to spacetime.  If z = 3 Lorentz invariance becomes broken at small scales but quantum gravity doesn't blow up!  Moreover, at large sclaes, like we observe, Lorentz invariance and the equivalence of space and time is recovered making it a viable quantum gravity theory!

So, with that we have a new theory of quantum gravity.  Hořava has this to say:
It is difficult to imagine how Lorentz symmetry can survive as a fundamental symmetry in a framework in which the space itself is viewed as an emergent property of the theory. In string theory, quantum mechanics appears to be more fundamental than the symmetries of special of general relativity. As a result, we adopt the perspective that Lorentz symmetry should appear as an emergent symmetry at long distances, but can be fundamentally absent at high energies.
Does Hořava-Lifshitz gravity have issues?  Of course, but to it's defense its only been around a year.  The issues, however, are too technical for me to understand without really digging deep.  The interested reader with consult here and here for papers describing problems with the theory.

If nothing else, it's a fun theory to think about.

1 comment:

  1. I did read about this theory before and as you write there are some things against it already.


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