### entropic gravity

Recently, Erik Verlinde proposed that gravity can be described as entropic force. I am not sure yet what to think about this, but Lubos explains why he is certain this can never work.

Meanwhile, Lee Smolin published a preprint using Verlinde's idea to derive Newton's law from loop quantum gravity. I am not convinced by his argument.

Verlinde considers the change in entropy dS for displacements dx assuming a holographic principle and in his calculation he implicitly assumes the geometry of a smooth and indeed flat geometry.

There is of course nothing wrong about that, but if Lee Smolin wants to use this argument, then he has to first show that there is a reasonable limit of loop quantum gravity which reproduces this smooth and (almost) flat spacetime and I don't see that.

added later:

More discussion Lubos vs. Erik (scroll down through the comments).

Lee Smolin responds to my comment here.

Robert Helling comments on entropic everything.

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## 5 comments:

Hi Wolfgang, good that you're interested in these things.

I won't write a special text about Lee's article but it's kind of impressive how many independent faulty assumptions he's ready to build upon.

Erik's picture really can't work for very general reasons. But if it could, it would be a general argument - whose whole virtue is that it is completely general and it therefore doesn't need to assume anything more specific about the theory - i.e. it doesn't constrain the theory.

So it's a complete misconception to use the argument as a support for a particular construction.

However, his particular example is even worse because LQG manifestly doesn't obey the assumptions in Erik's paper - e.g. holography is not satisfied unless it is "artificially" imposed by manually removing the bulks of the volume in some ill-defined way - and it doesn't allow the objects to live separated in the empty space because the empty space probably doesn't follow.

Just imagine how space research would look like if the spaceships and satellites were made of pieces that not only haven't been verified - but that have been verified and failed, even each piece separately, in fact.

And some people will still celebrate this complete crackpottery and junk science as a symbol of rebellion, courage, and independence. Holy cow.

Best wishes

Lubos

Lubos,

thank you for the comment.

>> it would be a general argument

what bothers me is that there seem to be large classes of systems which show an area law for entanglement entropy.

Does it mean that they all contain gravity somehow?

If this would be the case we would never be able to find out what physics really is about (at the Planck scale).

I should add that the obvious thing to do would be to take one of those models and check if/how they actually contain 'entropic gravity'.

Dear Wolfgang, good question but no, the proportionality of entanglement entropy to the area is not a sign of holography (or gravity) by itself.

Holography means that the whole information that can be stored in a volume must only scale with its surface. But that's just not the case of the general systems with the area-dependent entanglement entropy.

The area-dependence of entanglement entropy only says that the information in one system/box that can be effectively correlated with an adjacent system/box is proportional to the surface. That's not surprising because these entangled degrees of freedom are degrees of freedom that sit near the boundary.

But that doesn't mean that there are no other degrees of freedom, which is what holography would require.

One must carefully study the statements and conditions and not to be misled by superficial words or slogans. Holography is not "anything that has the area-dependence" in a sentence. Holography only occurs when no information besides one that is encoded on the surface exists.

More generally, however, people have discussed the question whether holography and AdS/CFT vulgarizes the notion of gravity - so that everything is included. Any field theory can have a gravitational dual, the story says, so any field theory "is" gravity.

I disagree with this interpretation - which really depends on your definition of gravity. I only use the word "gravity" if there is a useful geometry with the Einstein-Hilbert term in the low-energy effective action. That requires some emergence of large enough a bulk space. That doesn't happen for generic field theories (unless they have a large number of colors or something like that).

Of course, one may generalize the notion of "gravitating theories" so that all field theories but that won't change the fact that there exists a sharper definition of gravity that makes it very special at the quantum level. What is rare is a quantum consistent theory with large enough space so that the GR effective action is useful in it. All of the solutions to these conditions fall into string/M-theory, at least according to some definition of string/M-theory, and in fact, even in the string/M backgrounds, only a part of them satisfies the condition (the fully non-geometric ones should probably be eliminated).

If we generalize or weaken the notion of gravity, it's not shocking that we get many more solutions. That much is a tautology.

Best wishes

Lubos

Lubos,

thanks again for your comment.

Obviously I need more time to think about this.

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