## Is gravity an entropic spring?

Two nanoparticles connected by a polymer will tend to be drawn together at finite temperatures (though not at absolute zero) because as the polymer chain explores the states available to it, there are many more tangled and balled up ones than stretched-out straight ones — even though there is no overt force pulling the chain to any particular tangled state. Such a situation is called an entropic spring, and behaviors like this are some of the more interesting aspects of physics at the microscale.

An arXiv paper by physicist Erik P. Verlinde purports to show that gravitational effects have the same mathematical logic behind them (in a very broad analogical sense), arising from the holographic universe description of physics (a far-out variant of string theory). Now I don’t come close to having the physics to evaluate the theory, but Verlinde appears to be a respectable physicist. Czech physicist Luboš Motl blogged about it:

So I remain undecided whether or not there is a sharp insight waiting along the lines of Verlinde’s paper.

and then allowed Verlinde to guest-post a long explanatory comment.

The derivation of the Einstein equations (and of Newton’s law in the earlier sections) follows very similar reasonings that exist in the literature, in particular Jacobson’s. The connection with entropy and thermodynamics is made also there. But in those previous works it is not clear WHY gravity has anything to do with entropy. No explanation for this apparent connection between gravity and entropy has been given anywhere in the literature. I mean not the precise details, even the reason why there should be such a connection in the first place was not understood.

My paper is the first that gives a reason why. Inertia, and hence motion, is due to an entropic force when space is emergent. This is new, and the essential point. This means one HAS TO keep track of the amount of information. Differences in this amount of information is precisely what makes one frame an inertial frame, and another a non-inertial frame. Information causes motion.

This can be derived without assuming Newtonian mechanics.

“Space is emergent”??? Yep, in the holographic theory, 3D space is an emergent phenomenon of a 2D information pattern (see the link above). Weird stuff, but no weirder than other forms of string theory.

As mentioned, I don’t claim to follow this at the technical level, but given how important the math of entropy is at the microscale, it’s fun to speculate about its being important at the most macro of macroscales as well.

January 15th, 2010 at 11:54 AM

Well, I don’t have the physics to really understand this in depth, either. But, I am at least sympathetic to the arguments being made.

The connection between physical entropy and information entropy were noted for years (decades, really) by no less luminary figures than Claude Shannon, and remarked as mere curiosities and quirks of mathematical form. Of course, we now know they’re not, and that the connection is deep, fundamental, and informative: Information

isphysical, and there is no two ways around it.So I force myself to maintain a sympathetic eye to arguments which run, “this math over here corresponds to that math over there,” as long as the reasoning behind the comparison is itself deep and mathematical. That this is one involving entropy (again) is just gravy.

January 15th, 2010 at 6:22 PM

/*…3D space is an emergent phenomenon of a 2D information pattern (see the link above). Weird stuff, but no weirder than OTHER forms of string theory….*/

Such assumption has nothing to do with string theory, so it cannot be another form of it (until we consider, every suffuciently abstract insight is in fact sort of string theory). But every theory is defined by its postulate set and everything else is just grant politics.

January 16th, 2010 at 4:35 PM

In Order Out of Chaos, Ilya Prigogine and Isabelle Stengers wrote about thermodynamics, especially the stuff that won Ilya the Nobel prize in 1977 or so. It involves the Second Law, about closed systems, and how there are no closed systems in nature. Open systems, with a real flow of energy and matter through their boundaries, have the opposite sign to the entropy function — in other words systems which experience a flow of energy and matter through them decrease their interior entropy.

One of the ideas in that book revolved around the linkage between Quantum Mechanics and General Relativity. The authors believed it would have the best odds of being found in Thermodynamics or a related field.

This article is making my hair stand up….

If you can handle stoichiometric algebra and mid level calculus, then you can get full mileage out of OOoC. Don’t be bashful: Just Dig Right In!