Entropic gravity is back in the news. Various science blogs again carry headlines dealing with entropic gravity. This time round, the reports are less favorable towards the idea of gravity being entropic, with headlines like Experiments Show Gravity Is Not an Emergent Phenomenon screaming for attention.

Sounds like a death stab to Erik Verlinde's brainchild, right?

What we see happening here is the good old well-established way in which science progresses. A scientist publishes a wild idea. Some other scientists become enthusiastic, others less so. The result is that a group of researchers with varying degrees of skepticism towards the new idea start evaluating it, and chances are soon someone will claim to have disproven the new idea. The whole process repeats again: others start evaluating this criticism, and soon someone will claim... etc.

This process can have only one of two outcomes. One possible outcome is that evidence against the original wild idea starts piling up, and soon the vast majority of the scientific community will consider the whole idea disproven, and will stop exploring what is from that moment on considered a dead alley in research. The other possibility is that the criticism to the new idea will be proven to be incorrect, and that evidence in favor of the new theory starts building.

Often the bright new idea is not yet well defined, and the discussions can get messy. In these circumstances it can take years before one of the two outcomes clearly emerges. Verlinde's entropic gravity idea is an example of such a less well-defined concept, and we should not be surprised if we witness a number of swings of the pendulum in favor and against the concept of entropic gravity before a consensus emerges. In fact, in the twenty months that have passed since Verlinde presented his entropic gravity idea, many papers in favor as well as against the idea have already appeared.

Some papers appeared supportive in the sense that they extend the entropic gravity concept to describe phenomena like  the accelerated expansion of the universe. Other papers dismissed entropic gravity as a flawed theory. Most arguments against entropic gravity could easily be refuted. An example is the claim that entropic forces are necessarily irreversible and therefore can not describe gravity that manifests itself as a reversible phenomenon. This claim can be shown to be based on a wrong intuition about the entropic force concept itself. Also the arguments that closed gravitational orbits would be incompatible with an entropic force concept fall in the same category.

It should come as no surprise therefore, that none of the claims against entropic gravity have received much media attention. But it seems that now has changed. A recent paper by Archil Kobakhidze has  attracted a lot of internet attention. Has entropic gravity entered the realm of disproven ideas?

Time to contact Erik.

Verlinde is quick in his reaction:

"Kobakhidze puts things too simple."

He continues:

"I admit that I have not been very precise in my article. The whole argument presented was heuristic after all."

What follows is a technical explanation focusing on the timescales of the underlying microscopic dynamics. Rather than reproducing here Verlinde's verbatim arguments, let me try to make  both Kobakhidze's and Verlinde's lines of reasoning clear by revisiting the 'Mikado Universe'.

You might recall the basic concept that I introduced more than a year ago with the objective to explain the mechanism behind entropic forces.

The Mikado Universe

Imagine a two-dimensional space spanned by a large number of ray paths. Think of each ray path as extending indefinitely, and the whole network of ray paths forming a discrete Planck-scale configuration from which planar space emerges. Each ray path represents an elementary degree of freedom of the system: it can be occupied or empty.

To introduce particles in our model, we restrict the allowable mikado universe configurations to those containing enough empty ray paths such that we have available two 'holes'. In this model holes are defined as regions not crossed by any occupied ray paths, and large enough to contain a circle of given radius. Below figure clarifies the concept.

The mikado universe. Straight lines represent the ray paths. The ray paths shown in gray are 'empty' and do not contribute to the entropy. As a result two 'holes' exist: regions void of occupied rays, and large enough to contain circles of specified radius (indicated in red).

We label the ray paths '1', '2' ... 'N', and construct a starting configuration with two holes. Now grab an N-sided die. Throw the die, note down the number of spots, and check the corresponding ray path in your mikado universe:

A) If the ray path is occupied, make it empty.

B) If the ray path is empty, occupy it, unless this would cause the combined hole area no longer capable of fitting two circles.

Again throw the die and repeat ad infinitum.

What will you see happening would you be patient enough to go through many of these steps? With time you might expect the holes to move. However, as there is no force acting between the two holes, you might expect a random diffusion of both holes.

Reasonable as this expectation might be, it is wrong. You will not observe a random diffusion, but rather both holes moving towards each other.

Why is that?

The easy answer is "that's because entropic forces are at work". A more insightful answer is that there is a much higher likelihood for the particles to be close together as there are many more micro-configurations corresponding with configurations in which both holes are close together. To see why this is the case, we investigate the number of micro configurations. It should be clear that this number equals 2S, with S the number of ray paths for which there is a choice to be occupied. Note that S is smaller than N, the total number of ray paths as the holes eliminate the occupation choice from a number of ray paths.

How much will S drop below N?

If the two holes are far apart each hole requires a certain number of ray paths to be empty, and thereby each hole reduces S by a corresponding number.

Now place the holes close together. Again, each hole rules out a certain number of ray paths from becoming occupied. However, as both holes are in each other's vicinity, the set of ray paths prevented by one hole from becoming occupied will have an overlap with the set prevented by the other hole from getting occupied. Hence, the two holes being closer together creates a smaller reduction in S compared to the case of the two holes being far apart.

The result is that the likelihood of the configuration, 2S,  is much larger when the two holes are close together than when they are far apart.

That's all there is to entropic forces: counting micro states associated with distinct large-scale configurations.

Now I should stress here that this mikado model is not in any way a model that Verlinde had in mind when he introduced the concept of entropic gravity. Moreover, this toy model does not include any form of entropic inertia that plays an important role in Verlinde's concepts. There is much more wrong with it in case you are after a realistic model that describes our universe. However, despite its numerous shortcomings, this toy model does come in handy when explaining  Kobakhidze's criticism of entropic gravity, and Verlinde's answer to this criticism.

Quantum Coherent Entropic Gravity?

In essence, Kobakhidze argues that Verlinde's entropic gravity description doesn't allow a correct quantum description of gravitating particles. When I translate his criticism to the Mikado model, Kobakhidze's argument boils down to the remark that the movement of the holes is nothing else than the net effect of the occupation dynamics of large numbers of ray paths. Kobakhidze argues that a quantum mechanical descriptions of the ray occupancies can be created, and coherent ('spooky action at a distance') ray states can be constructed. However, in order to arrive at a quantum description in terms of the holes themselves, one would need to 'average out' all coherence in the quantum description of the ray paths, and  inevitably will end up with holes that follow a classical dynamics. These holes would represent non-quantum particles void of any 'spooky action at a distance'. Yet we know that is not what happens in experiments with gravitating neutrons. These neutrons exhibit a 'spooky action at a distance' while gravitating under the influence of the earth.

The end of entropic gravity?

Not quite. Verlinde's rebuttal is that Kobakhidze does not take into account that the separation of time scales between the fast dynamics of the ray paths and the slow  dynamics of the holes. (Again, I am transcribing the arguments put forward in terms of the Mikado model.)

Verlinde: "An important ingredient is that the timescale of the microscopic dynamics needs to be much faster than the macroscopic movements. That is to say, the macroscopic movements should not induce any quantum traditions between the microscopic states."

Kobakhidze vs Verlinde. One of them must be wrong, yet both are contributing to the progress in science.

Verlinde makes a reference to the Born-Oppenheimer approximation, a well-established method to calculate molecular quantum states based on an 'averaging-out' of the fast quantum motion of the electrons. Verlinde argues that just because the electron-averaged motion of the molecule is so much slower than that of the electrons, the molecule itself will stay in a coherent quantum state.  The same, he claims, is the case with entropic gravity.

In 'mikado speak', this translates into the conclusion that a quantum description of the holes is possible simply because the ray path dynamics is much faster that the dynamics of the holes. It takes many ray path updates before the holes will have moved by distances comparable to their diameters.Attentive readers will now ask the question: "what if the timescales of the microdynamics slows down, is that not what happens close to black hole horizons?" Indeed, a stationary distant observer will observe objects moving towards a black hole horizon as beings slowed down or redshifted, with the horizon itself defining the points of infinite redshift.

On this point, Verlinde makes the remark:

"It appears that when one applies this reasoning to gravitation, the result is that the timescale of the fast dynamics is determined by the red shift. At gravitational horizons the separation of time scales will break down, and the system will become truly thermodynamic."

Verlinde seems to be hinting at an entropic description of decoherence at black hole horizons. A sneak preview of things to come?

Verlinde's next article is one to look out for, as he ends the interview with the remark:

"An interesting point is that in the Born-Oppenheimer approximation the next order correction to the adiabatic ['slow macro-dynamics'] approximation is given by a magnetic force resulting from the Berry Phase. This causes vector potentials to appear. I believe this to be at the basis of further emergent phenomena. I can't tell you more at this stage. You have to wait till my next article is out."

OK, we will be watching the ArXiv. In the meantime: be prepared for a few more swings of the pendulum between favorable and less favorable points of view on entropic gravity. Your chance to witness science in action!