Every article on quantum gravity begins the same way. On the one hand we have quantum mechanics—excellent at describing the very small and intrinsic lumpiness of the universe—and on the other hand we have general relativity—excellent at describing gravity, but it relies on a smooth universe. At some point the two meet, and just like Manchester United supporters and Liverpool fans, they just don't get along. Luckily for the universe, tire irons haven't been deployed to settle this incompatibility.

A pair of unrelated papers, which appeared in Physical Review Letters, and a News and Views article in Nature Physics all indicate that progress is occurring, but it is coming at the expense of a long-cherished tenet of physics, called the Lorentz Invariance.

Progress in uniting quantum mechanics with general relativity has typically proceeded along two lines. Option one is to generate seemingly outlandish ideas, such as string theory, loop quantum gravity, and their brethren, which resolve the problem by positing the existence of things as yet unobserved. The more sedate approach is the rapid-fire production of grand unified theories, which are neither "grand" nor "unified" and, completing the trifecta, may not warrant the moniker "theory" either, since they simply don't work.

Until recently, the general consensus was that string theory was the great hope, but physicists have been rocked by the discovery that string theory still requires a bunch of fine-tuned values to get to the universe we observe.

This depressing state of affairs has led to reappearance of the anthropic principle, which, while being very deep and meaningful, also finds itself in the embarrassing position of stating the bleeding obvious. Which leads us nicely to a paper by one Petr Ho?ava, brought to my attention and nicely explained in the Nature Physics News and Views article. Ho?ava takes advantage of a recent finding that, in quantum mechanics, the universe behaves as if it has four dimensions at larger scales, but this can be reduced to two dimensions as the scale is reduced. This implies that space and time may be fractal in nature—not a new idea, but it's always nice to have evidence to support the idea.

To summarize the reduction procedure, space and time are treated separately, which would normally cause all sorts of problems in quantum mechanics. However, by treating space and time differently as well as separately, the infinities in the quantum mechanics equations vanish, and gravity behaves as it should.

Interestingly, space remains the same in all directions, while time does not. This appeals to me, because it points to fabric of the universe supplying time with a preferred direction. One of the downsides, though, is the failure of Lorentz invariance.

To understand why physicists might be loath to give up Lorentz invariance, let's take a quick look at it. A key idea, going way back to Galileo is that all accurate observations are equally valid and must agree. A simple example of this is cars on a motorway. I am cruising along at 120km/h but, to me, my car appears to be standing still. An overtaking car appears to me to be traveling at 20km/h, while a person on the side of the road will see speeds of 120km/h and 140km/h. Now, although we all disagree on the speed of each car, we can, given some information, understand each other's results and reach an agreement. These sorts of transformations, based on Lorentz invariance, are a key part of physics and are founded on a certain conception of space and time.

Ho?ava's work is pretty exciting, and has been followed by a paper from Daniela Klammer and Harold Steinacker, which proceeds in a similar vein. In their work, Klammer and Steinacker posit that space and time do not commute, which is a more sophisticated version of space being the same in every direction, while time is not.

They show that this sort of universe would naturally have an early inflationary period, and that the universe slips out of inflation nicely into the universe we observe. Furthermore, unlike other explanations of the universe's previous and current epochs of inflation, no additional fields are required—inflation falls out naturally as a consequence of the geometry. The final win is only mentioned in passing: the stability of the mathematics depends on the existence of vacuum fluctuations, which are the signature of quantum mechanics.

Now, I must admit that these papers are nigh on unreadable to us plebs—the second paper is much easier than the first, though—and I cannot speak with any sort of authority on this. But it appears to me that the two approaches are fairly similar and may even be compatible with each other. If this is the case, we may find that quantum mechanics, gravity, and inflation end up sharing a house and supporting the same football teams. In doing so, we will be eliminating at least one troublesome finely tuned constant and the anthropic principle would resume its rightful place as a forgotten statement of the bleeding obvious.

Nature Physics, 2009, DOI: 10.1038/nphys1298

Physical Review Letters, 2009, DOI: 10.1103/PhysRevLett.102.161301

Physical Review Letters, 2009, DOI: 10.1103/PhysRevLett.102.221301

Listing image by Kevin Wolfe