Gravity as entropy? Sounds cool but....

A cool paper appeared on ArXiV by Erik Verlinde, arguing that gravity should be thought of not as a fundamental force but rather as arising from the second law of thermodynamics (an "entropic" force) (Link:http://arxiv.org/abs/1001.0785).

The neat thing about the paper is that it ties together many different general principles which have emerged from string and gravity theories. I'll just sketch the ideas involved. It is a long sketch, which I hope will intrigue readers to read more elsewhere - although Verlinde's idea itself seems untenable.

Verlinde first assumes "holography", which is the notion that the physics in a volume of space actually comes from objects that live on the surface enclosing that volume. In other words, the universe really has one less dimension than it appears; the position variable "x" for one whole dimension is really not a fundamental variable, but is an "emergent" property, or grouping of objects in the surface theory.

The first hints of holography came from the fascinating subject of "black hole thermodynamics". It is fairly well established now that black holes have a temperature and an entropy, and that the size of their entropy is given by their surface area, suggesting that the physics of their volume is really all captured at their surface.

Further support for holography has arisen within string theory, where the much-heralded "Ads/CFT" correspondence appears to provide an explicit example. Here, string theories inside certain volumes of space are believed to be fully equivalent to other theories residing on the surfaces of these volumes (theories which are not string theories and do not even have gravity). Ads/CFT was discovered by Juan Maldacena, and his Scientific American article is worth reading.

The second thread which Verlinde's paper picks up is the unexpected appearance of temperature in gravitational and relativistic physics. The most famous of these phenomena is the black hole temperature, discovered by Hawking in 1974. The horizon of a black hole has a temperature and the hole radiates like a light bulb, eventually dissipating to nothing.

Less well known is the "Unruh effect", named after its discoverer, Bill Unruh. Unruh calculated that an accelerating observer should perceive himself to be immersed in a heat bath, with higher temperature the higher the acceleration. The calculation is quite simple and results from the fact that the quantum-mechanical vacuum contains virtual particles which can hit the accelerating observer and then change to real particles.

The Unruh effect then combines with another classic idea, the "equivalence principle" of Einstein. This principle states that the physics in a gravitational field is the same as that seen by an observer experiencing the corresponding acceleration. Applied to Unruh's effect, this means that a stationary observer in a gravitational field (who "feels" the gravity as weight), sees himself immersed in a heat bath, while a freely-falling observer in the same location (who "feels" weightless) sees nothing but empty vacuum. Both of these Unruh effects are generally accepted as true, although they are too small to measure.

These are the ideas Verlinde is playing with. I'm sure this preamble was long enough to tax my readers' patience, yet still not long enough to make any sense; for those who wish to learn more, I highly recommend Susskind's book "The Black Hole Wars".

Verlinde takes holography as his starting point. He assumes that the physics of a region is actually derived from physics on a surface, or "screen", bordering that region. He assumes that the screens have a temperature which is given by the Unruh effect, i.e., the temperature a stationary observer would see if sitting at the screen location - which seems eminently reasonable.

Then the question he is trying to answer is, where does gravity come from in this picture? It has to "emerge" from the screen physics, just as the extra dimension of space emerges. In the Ads/CFT correspondence mentioned above, this happens through string-like groupings of particles in the screen.

Verlinde suggests a quite different possibility: that gravity is an "entropic" force. This means that two masses attract each other gravitationally because, as represented in the "screen" theory, the configurations which are interpreted as "closer together" have greater entropy than those where the masses are "farther apart". The second law of thermodynamics ensures that entropy increases, and therefore the masses will draw together.

To better understand what an entropic force is, Verlinde provides a nice example, which I here modify slightly. Consider a jumprope in a room filled with rapidly bouncing basketballs. The basketballs are bouncing back and forth off the walls, and they hit the jumprope. If you want to hold the jumprope straight it takes force, because the balls keep bouncing off of it, which tends to bend it. If you pull the rope straight and attach two masses to its ends, then when you let go the jumprope will start to fold up and pull the masses together: they will "attract" each other.

From this "microscopic" perspective, it is obvious where the force comes from. Bouncing basketballs provide the force, through innumerable separate impacts. But we can also take a "macroscopic" perspective, where we ignore all the details and focus on the big picture. In this picture, the straight configuration of the rope requires force to maintain because it is extremely unlikely to arise at random. There are countless folded configurations but only one straight configuration, so a straight rope is going to become folded quite easily, while a folded rope is very unlikely to ever straighten out again. Amazingly enough, one can make this mathematically precise, leading to the subject of thermodynamics.

Verlinde argues that gravity not only can, but must, be of the same nature as the jump-rope force described above (given the hypothesis of holography to screens which have a temperature). His reasoning is simply that he can derive the entire force from these assumptions, so there isn't any residual effect left to explain. He produces a really rather elegant "dictionary" which maps the usual quantities of gravity and acceleration onto the temperature and entropy of the screens.

It is beautiful, and nice to read because it draws together so many ideas and the formulas are simple, and it has already generated numerous followup papers.
However, I don't believe anymore that it can be right, after reading devastating commentary on Lubos Motl's blog "The Reference Frame" (which included direct responses from Verlinde).

Motl's criticisms were directed not at holography - which clearly seems possible - but at the attempt to derive zero-temperature physics from an underlying theory which does not have zero temperature. In the case at hand, Verlinde is trying to derive gravity in empty space - zero temperature - from a theory on a screen about which we know nothing except that its temperature is non-zero.

There are two major problems here. One is that the underlying theory will always have some analog of the "bouncing basketballs" which actually cause the forces, and these interactions will have measurable quantum mechanical effects. In quantum mechanics we can take two particles and match their wave functions, and then check them again later to see if they still match - which they will not do if each has been subject to a bunch of random particle interactions. Such experiments have been done with neutrons to high precision.

The second problem is that an entropic force should be irreversible. If a falling ball is really caused by increasing entropy, then it should not be easy at all to make a ball rise - just as it isn't easy to put a broken glass back together. But in fact we can raise a ball just by throwing it. This argument to me is powerful but not as decisive as the first one.

There I will leave it. The paper is relatively accessible and worth reading.