Frequently asked questions:

• Q: Why should we pursue yet another approach to quantizing gravity?
  
  A: Simply because none of the other approaches is at present really satisafctory. This may be due to technical difficulties, or because the present approach(es) are fundamentally flawed, or both. The matrix model approach is rather new and needs more time to grow up, but it has major advantages over more conventional approaches concerning its quantization. Roughly speaking it preserves the strength of string theory – which appears to contain some sort of quantum gravity along with many other degrees of freedom – while avoiding its main problem, notably its vast landscape and lack of predictivity.

• Q: Why should the matrix model allow to quantize gravity?
  
  A: because it can equivalently be viewed as maximally supersymmetric N=4 noncommutative Yang-Mills theory on the Moyal-Weyl quantum plane \R^4_\theta. This means that there is very good reason to expect that it is at least perturbatively finite, just like its commutative cousin. „Noncommutative“ is crucial however: it implies – and this is really the new insight – that it contains also gravity, as opposed to „ordinary“ N=4 super-Yang Mills. Hence the quantization of this gauge theory, which goes along the well-established lines of quantizing Yang-Mills gauge theory, gives automatically at least some quantum theory of gravity. Since it comes along with all the other ingredients for the description of fundamental interactions such as nonabelian gauge fields, it should be physically very interesting.
  
  All this is in fact closely related to string theory, and as such perhaps not too surprising. However as opposed to „standard“ string theory it does not come with a phletora of 10-dimensional geometries, and it reallly is a non-perturbative model which allows to ask questions about its vacuum or ground state.
  
  
  

• Q: General relativity is the correct description of gravity, so why „emergent gravity“?
  
  A: Surely GR is the best available description of gravity, and very well tested at least at the solar system level. On the other hand, on cosmological scales much less is really known about gravity. This is manifested in the big open questions concerning dark matter (galactic rotation curves etc.) and dark energy (cosmic acceleration ...?). Most seriously, the cosmological constant problem remains to be the „biggest failure in theoretical physics“, and we don't have any sound proposal how to solve it. The point is that that any combination of quantum mechanics with GR seems to lead quite unavoidably to a huge cosmological constant, in conflict with observation.

  Given that state of affairs, it seems wise to think also about alternative approaches to gravity, in particular for its quantization. GR „just“ has to be recovered at length scales relevant to gravity, i.e. in the far infrared. String theory is one such approach. Indeed string theory does not really give GR, it just seems (or is hoped to be) close enough. Matrix models provide another very promising approach.
  
  Another point is that there are good reasons to expect some sort of „fuzzyness“ of space-time at the Planck scale. This is „automatic“ in the matrix model framework, although other approaches may also lead to a similar fuzzy space-time.

• Q: So what's the problem?
  
  A: The main open question is whether the matrix model – and which version of it – really leads to a gravity theory which is close enough to GR at least for solar system scales. This is not evident and not yet proved. The difficulty is that in order to reliably answer this question, one needs to compute first the quantum effective action at least at one-loop. This is so because the (analog of the) Einstein Hilbert action, plus additional terms, are induced only at one loop (or beyond). This is a lot of work, which is in progress. Contributions towards this goal are highly welcome.