WHAT IS THE FUTURE OF COSMOLOGY? - cont.
This conclusion has arisen from several points of view. First of all, it seems to be required by the thermodynamics of black holes, as Jacob Bekenstein has been pointing out for years. It also seems to be implied by string theory, as Lenny Susskind and Gerard ’tHooft, among others, have been arguing. In the last few years we have also understood that the ultimate discreteness of space is loosely a consequence of combining the basic principles of quantum mechanics and general relativity. Thus, a few years ago, Carlo Rovelli and I were able to show that, rather generally, quantum gravity predicts that the volumes of regions in space and the areas of surfaces must come in discrete units, like the energy levels of atoms. We are even able to make precise predictions about the discrete units of area and volume.
This discovery was a great pleasure for us because we rediscovered a beautiful set of structures, called spin networks, that our theory tells us are descriptions of the discrete forms of space. These structures were originally invented by Roger Penrose more than thirty years ago, as a first guess of what a discrete geometry of space would look like. It has been very gratifying to be able to confirm that Penrose's intuition was essentially correct.
Once this is understood, we are faced with a new question: How do these discrete bits of space assemble themselves into a smooth structure that looks like the space we see around us? This turns out to be very much like asking why atoms often assemble themselves into solids, like plastics or metals, that look smooth when examined at scales larger than the atoms. It seems to be the case that without some special organization, the discrete bits of space—the networks—do not assemble themselves into big smooth structures that could describe the featureless space we observe. Instead, they typically form chaotic structures that do not resemble any previous notion of space.
Thus, we are faced with the very real possibility that the fact that the world has any spatial extension at all is a contingent historical fact, that also requires explanation by some principle of self-organization. We are working on this now, and there seems to be good progress. I also expect that the outcome of this work will be a unification of the different approaches that have led to an expectation that space is discrete, including string theory and black hole thermodynamics. What for me is most provocative is the possibility that, for this to work, we will have to extend the Darwinian idea that the structure of a system must be formed from within by natural processes of self-organization—to the properties of space and time themselves.