Quantum mechanics and general relativity are fundamentally incompatible for reasons that relate to views of the world that simply cannot be reconciled. In general relativity, space and time are regarded as continuous objects, while quantum mechanics requires that, at some level, space and time be discrete.

Now, although we know that quantum mechanics will have to be modified to include gravity, which will allow it to incorporate the behaviors ascribed to general relativity, it should be noted that general relativity needs to be replaced for other reasons as well. For example, the continuous nature of space allows black holes to collapse to point-like objects. Likewise, using just general relativity, the universe began with an infinitely dense point. Physicists don't like infinity, and we tend to object to theories that distill down to it.

Among the many contenders for combining gravity and quantum mechanics is loop quantum gravity. As with all proposals of this sort, this one has its detractors. One of the most serious failings of the theory is that it was thought that it might not be possible to perform what are called gauge transformations using it. This would have been a significant problem, because gauge transformations are fundamental to quantum mechanics and it would be unlikely that loop quantum gravity would be able to encompass all of quantum mechanics without them—a major failing for a theory aiming to replace the standard model. A recent publication, by scientists at the University of Rome, shows that gauge transformations generally do work in loop quantum gravity.

Loop quantum gravity might be thought of as the dark horse in the race for a quantum gravity. Nevertheless, it has some remarkable features. For instance, gravity becomes repulsive at high densities, preventing the formation of singularities. This naturally prevents black holes from collapsing to a point-like object. Similarly, the big bang becomes a big bounce, and questions like "what happened before the big bang?" become physically meaningful. Importantly, space and time quantization occurs naturally with loop quantum gravity.

Its biggest problem lies not in its ability to encompass gravity but in its ability to retain the properties of the standard model. The standard model relies heavily on something called a gauge transformation. The point to gauge transformations is that, when this mathematical trick is played, certain parts of the physics remains the same, while others change. The way these changes and invariants crop up tells us about the symmetry that's observed in nature and explain a huge variety of results.

This is such a powerful tool in physics that it will take a significant amount of evidence to convince physicists to give up gauge transformations. That makes it a really important that any theory that replaces the standard model is compliant with gauge transformations as well. This latest work shows that gauge transformations work in loop quantum gravity for systems which don't change with time—everything traveling at constant speed and in straight lines. Furthermore, the way it is constructed shows that time varying systems should work as well—they'll just be much more difficult to work on.

This is great hurdle that loop quantum gravity has overcome. It should still be considered an outside contender, at least as far as most of the quantum gravity community is concerned. Its very existence, however, shows that physicists will look under any mathematical rock to acquire a unified theory of quantum mechanics and gravity.

Physical Review Letters, 2009, DOI: 10.1103/PhysRevLett.102.091301