A new theoretical model posted onto the ArXiv website by Stephen Hawking and colleagues proposes something very curious: that space may actually reflect a curious structure that has more in common with the artistic style of M.C. Escher than the smooth fabric that is often taken as the cornerstone of general relativity. As described in *New Scientist* (registration required):

The images in question are tessellations, arrangements of repeated shapes, such as the images of interlocking bats and angels seen in Circle Limit IV. Although these are flat, they serve as "projections" of an alternative geometry called hyperbolic space, rather like a flat map of the world is a projection of a globe. For example, although the bats in the flat projection appear to shrink at an exponential rate at the edges, in hyperbolic space they are all the same size. These distortions in the projection arise because hyperbolic space cannot lie flat. Instead, it resembles a twisting, wiggly landscape of saddle-like hills.

Hawking - together with University of California's James Hartle - have been working on an approach to create a quantum picture of cosmology since the 1980's, and the Escher-like structure fell out of that. The problem with their approach was that the expansion of the universe seems to indicate that the universe has a positive cosmological constant, and that makes their equations unstable and fairly useless.

However, the team (also consisting of Thomas Hertog, from the Institute for Theoretical Physics at Catholic University of Leuven in Belgium) has recently realized that when a negative cosmological constant is put into the wave functions of the universe using their models, it turns out that the model can evolve over time to be very similar to a form of string theory developed by Juan Maldacena in 1997. This famous "Maldacena conjecture" stunningly linked the holographic principle to string theory and is seen by many as having the potential to translate string theory into a format that yields more direct insights, because it links a string theory model together with a quantum physics model and helps reduce the complexities arising from the extra dimensions. (Here is a link to the ArXiv copy of Maldacena's 1997 paper, for those interested in the more technical aspects.)

Hawking, Hertog, and Hartle certainly aren't done with their work ... in many ways, it creates more questions than it solves. That is, if the idea even works at all!

Already, physicist Lubos Motl has indicated on his blog that he doesn't have particularly high regard for the possibilities of this work being decisive and, in fact, it looks like possibly the calculations have been negated in his own comment thread! (Although the Hawking paper on ArXiv has been edited since then, so it's possible that the sign error he's talking about has been fixed and the paper is still there.)

The truth is that these models are sometimes introduced and get a bit of fanfare, but usually they don't really end up going anywhere ... or, if they do go somewhere, it takes years for them to get there. This model is so new that there's very little discussion of it yet, and it's through that discussion that scientists will help to determine whether or not it has any value. At present, I'm suspect, though ... and I'd urge caution from anyone before they begin declaring that our universe has some bizarre geometric structure that isn't experimentally verified!

Still, if the model could be extended and refined to match experimental data, and if it then makes predictions that could be further tested, it might represent some true progress at creating a theory that combines quantum physics with general relativity. And, if that works, then we'll have discovered that, once again, the universe really doesn't look the way that we expect it to ... and that would be a pretty neat discovery.

**Related Articles:**

- The Reference Frame - Hartle, Hawking, and Hertog: How Our C.C. Could Be Negative, May 2012
- From our archives - Hawking & Hertog: String Theory Can Explain Dark Energy, June 20, 2006

## Comments

Hello!

Just one question. On what date was that published on Arxiv?

An Escher-like or holographic-like model only works if space/time is discrete i.e. made up of interconnected identical units. Even, if so, it could only describe an empty universe. This is because any additional “stuff” gravitates and interacts with space/time units. This results in General Relativity’s result that mass bends space/time.

One problem is how could the space/time units bond i.e. the bats and angels? We need some crazy glue of some sort. A further problem for any Escher-like model is to explain how and why anything other than the units of space/time came into existence. In other words even if we allow the assumption of space/time unity but the rest of the stuff is outside that assumption. It is the other stuff that breaks down the unity of the bats and angels. the reason is again General Relativity does not allow any mass/energy within space/time that does not pull on or attract space/time. We know that mass/energy distribution is not universally uniform and therefore this accounts for local distortions. The resulting picture is not Escher-like. Something to think about …