In my last report from Physics@FOM, I will talk about something I am truly not competent to discuss: "Holography, ADS/CFT and the emergence of gravity." I realize that I am not always the sharpest knife in the drawer, but I have never found myself so lost so quickly in a presentation. I think this comes from the difficulties in conveying some very new concepts by Erik Verlinde, who is still in the process of grappling with them himself. Nevertheless, let me try.

Holography, and anti de Sitter space/conformal field theory are two ways of describing the bending of space and the entropy associated with it. The two models are very closely related to each other. So close that, according to Wikipedia—the fount of all reliable knowledge—theorists can't agree if they are the same or not. But the point about both is that they resolve the problem of unifying gravity with quantum mechanics by getting rid of gravity.

OK, that's not entirely accurate. Gravity is still a force, but it is generated by something more fundamental: entropy. Entropy can be described in the language of quantum mechanics and conformal field theory is one model for this sort of description. In these models, gravity kind of falls out of the equations for free—where "free" is an enormous amount of work done by someone else.

Verlinde's made several analogies in his talk, but the best is probably that of a polymer in a liquid. A polymer is a long chain of similar units, and it has considerable freedom in how it arranges itself in space. But, given time and the influence of Brownian motion, a polymer will rearrange itself so that it minimizes its volume. Essentially, the act of random collision events results in a macroscopic behavior that is not random at all. How does this relate to gravity?

Space is the set of dimensions that allows motion to take place, but it also stores information via its configuration—no, I don't know how that happens—but the maximum amount of information per unit space is finite. Essentially, there are only so many configurations available to space and, once you have used them all, no more information can be stored. So, we have space, even empty space, that has information sitting in it.

Entropy just involves counting states—that is, space that has information stored in it has some entropy. Since there is more information stored in some parts of space—for instance, in highly curved parts of space—then the entropy is not uniform. And nonuniform entropy drives forces and macroscopic activity, such as the polymer that minimizes its entropy by minimizing its volume.

To get gravity, one takes standard thermodynamics, but replaces temperature with non-local degrees of freedom—and, no, I don't know what that means either. In this system, we find a macroscopic force that attracts mass to mass. Or more precisely, highly curved regions of space tend to have forces acting on them that increase their curvature.

Looking specifically at a black hole, space is curved sharply around it—so sharply that, from the inside, it is closed off from the rest of the universe. As objects fall into the black hole, the event horizon expands (this is the spherical surface that, from the inside, is perceived as a closed surface). That sphere now has more surface area, and so can accommodate more information, all of which remains on the surface of the object. This additional information increases the entropy of the black hole, and, as a result, its gravitational attraction increases.

This seems to be general property. Any massive object can be thought of as a closed surface with a certain amount of entropy. If this sounds a bit like charged spheres and electromagnetism, you are on the home straight, because the mathematics is exactly the same. As a result, you end up with things like a Gauss' Law for gravity, and you can calculate some pretty cool things.

Historically, macroscopic thermodynamics, which describes observable macroscopic forces in terms of macroscopic quantities, was worked out first. However, the foundation of thermodyamics is a microscopic theory that relates the macroscopic features to the detailed behavior of individual units, such as atoms or molecules in an ideal gas. We now await the 21st century equivalents of Boltzmann and Maxwell to provide the microscopic theory of space-time thermodynamics so that there is a nice solid foundation for this very fascinating idea.

For those of who think "Hooray, no more string theory," I have bad news for you. First of all, all of these ideas are born out of string theory, and second, where do you think the microscopic theory is going to come from?

Listing image by Lawrence Berkeley National Labs