Is Gravity an entropic force after all?

Question

Recently, there was a rapid communication published in Phys.Rev.D (PRD 83, 021502), titled "Gravity is not an entropic force", that claimed that an experiment performed in 2002 with ultra cold neutrons in a gravitational field, disprove Verlinde's entropic approach to Gravity.

The neutrons experiment gave results consistent with the predictions of Newtonian gravity for the lowest energy state.

As I understand it, the author claims that the fact that Verlinde's entropic force comes from a thermodynamic process that is irreversible (or approximately reversible), leads to non-unitarity in the evolution of quantum systems. The non-unitarity then exponentially suppresses the eigenfunctions, predicting results very much different than the Newtonian. Thus, that experiment is in contradictions to what is expected if Verlinde's approach is correct.

My questions are,

1. First of all, is there anything else essential that I am missing?
2. Is there any response to that argument?
3. Is that a fatal problem with Verlinde's entropic approach?
4. Is that a fatal problem for any entropic approach?

updates on the discussion:

1. There is also this recent comment arxiv.org/abs/1104.4650
2. Once more: gravity is not an entropic force arxiv.org/abs/1108.4161

Answer 1

This question has introduced me to the whole "entropic force" area which has several papers during 2010. I see that there are references to "entropic force" explanations for Coulomb's law and other areas too. Here is a link to a simple introduction to these ideas.

The Verlinde paper and others however are deriving Newtons Law, Einstein's GR etc as classical theories. The underlying formulation of course being a stochastic behaviour of unknown microstates. Despite the presence of $\hbar$ and the motivation from the Black Hole area formulae the Verlinde paper does not introduce an explicit link with quantum mechanics. Thus there is no derivation of Schrodinger's equation and no introduction of $\Psi$.

The Kobakhidze paper says "One starts with a "holographic screen” S which contains macroscopically large number of microscopic states which we denote as $\left|i(z)\right\rangle$, $i(z) = 1, 2, ...,N(E(z), z).$ The screen is then described by the mixed state

$$\rho(z)=\Sigma p_{i(z)}\left|i(z)\rangle \langle i(z)\right|$$

However Verlinde does not explicitly introduce microstates as quantum states, with density matrices etc, although this is a tempting extension.

Now it might be that this is the only sensible quantum development of the stochastic basis of the "entropic idea", but Verlinde has not taken it. So what is disproved is a theory that Verlinde has not written down.

Having said this, there is a resemblance between "entropy" and the idea of introducing "stochastics" into quantum theory. One such attempt is known as "Stochastic Quantum Electrodynamics" described in this Wikipedia overview. As you will see from the summary this has had successes with e.g. the Unruh effect, but problems modelling genuine quantum phenomena.

I dont know whether anyone has considered combining the two areas directly.

Answer 2

Dear Vagelford, you're totally right. Gravity cannot be an entropic force because

1. its phenomena would be irreversible
2. the degeneracy of the states coming from the entropy would destroy the interference patterns that have been measured e.g. by neutron interferometry.

More than a year ago, this was also explained on my weblog

http://motls.blogspot.com/2010/01/erik-verlinde-comments-about-entropic.html

and Erik Verlinde much like some of his junior Dutch colleagues tried to react but as far as I can say, none of their reactions has ever made any sense.

The neutron interferometry experiments are pretty impressive. They not only show that the interference pattern survives the action by the force of gravity. But it is exactly as shifted as the equivalence principle implies.

And in fact, the changes of the phases have been measured so accurately that the experimenters may deduce not only the zeroth order gravitational acceleration but also the higher-order corrections to it such as the tidal forces. All of these effects preserve the interference pattern - which wouldn't be possible if there were many states representing a macroscopic configuration - and this pattern exactly moves and behaves according to general relativity.

For these two and other reasons, gravity cannot be entropic. We also know it from the explicit models in the AdS/CFT correspondence and elsewhere: only event horizons may produce a large entropy of this order. A cold binary star doesn't carry any entropy associated with the gravitational attraction, certainly not an entropy comparable to the black hole entropy which is what Erik Verlinde claims.

But a multi-million euro grant has already paid by some European politicians to endorse this "research" so it may be unreasonable to expect that too many people aside from the two of us will say these obvious things too comprehensibly and loudly. After all, many people can be bought very easily and inexpensively.

One additional disclaimer: If you originally encountered the proofs that gravity can't be entropic on my blog, you shouldn't treat this answer as an independent confirmation of my previous claims. ;-)

All the best, LM

Answer 3

I think there has been some confusion over this matter. Of course if makes little sense to think a trajectory around a black hole will exhibit an entropy increase. Verlinde proposed an entropy force of gravity from which Newton's law of gravity may be derived. This is a thermodynamic principle for the entropy variation of a holographic screen $$ \Delta S~=~2\pi k_B(mc/\hbar)\Delta x $$ where $\Delta x$ is the distance between the holographic screen and a test particle of mass $m$. The entropy is then in increments of $2\pi k_B$ according to displacements of the screen equal to the Compton wavelength $\lambda~=~\hbar/mc$. The standard entropy formula $S~=~k_BA/4L_p^2$ indicates a proportionality with respect to area. For the radius of the screen adjusted $S_0~\rightarrow~S~=$ $S_0~+~\Delta S$ by the radial change in the screen $r~=~r_0~+~\Delta r$ then $$ ΔS~=~k_B/4L_p^2(A~–~A_0)~=~(2\pi k_B/L_p^2)r\Delta r~=~(2\pi k_Bc^3/G\hbar)r\Delta r, $$ which is linear in the radial displacement. By equating $\hbar/mc~=~G\hbar/rc^3$ gives a radius $r~=~Gm/c^2$, which is appropriate for the Newtonian result, but is half the Schwarzschild result.

The entropy for an orbit of a test mass is constant, and this entropy is a measure of the holographic screen. So if you place a Gaussian surface around a gravitating radially symmetric body that cloaks the configuration of the body, the entropy of the screen is the maximum entropy of the system. For a particle orbiting the body the entropy is constant, or $\Delta S~=~0$, for the screen remains constant.

Answer 4

The entropy of a gravitating particle in Verlinde's theory CANNOT be constant. Consider a screen placed at a distance $r$ from a mass $M$. It has an entropy $S_{screen}(r)$, and this is the maximal entropy the given region surrounded by the screen can have. Now, if you place a particle of mass m at distance $r+\delta r$, the entropy of the screen becomes $S_{screen}(r+\delta r)$. This later entropy is the entropy of the screen placed at $r+\delta r$, where the particle represented by certain microstates. Integrating out this microstates (coarse graining the screen) gives back $S_{sreen}(r)$. Since, the entropy is an additive quantity, the entropy on the screen with a test particle is $S_{screen- without-neutron}(r+\delta r)+S_{neutron}(r+\delta r) = S_{screen}(r)+S_{neutron}(r+\delta r)$. Thus, $S_{neutron}(r+\delta r)=\delta S_{screen}$, that is, entropy of a test particle $m$ depends on the distance from $M$. Is not that trivial?

Second point -- Time evolution of the system seems to be unitary, since the energy eigenvalues obtained are real. There are systems in QM which have such properties, see e.g. enter link description here

Answer 5

Gravity as the Pressure of ether

Pressure gravitation theory is more than 3 hundreds year old and is discarded mainly on the basis of Le Sage theory where gas filled ether. But today we know that space is filled with electromagnetic waves (let’s call it ether), so the first condition for pressure gravity the totally filled space is given. If we presume that there are ether segments we cannot measure and they interact mass, the only way we can detect their effect is through gravity-like forces. So gravity and ether proves each other.

In the next I’d like to present my interpretation of pressure gravity force through the Pioneer and Fly-by anomalies. In pressure gravity theory gravitation is the difference between the ‘attacking force’ of ether ‘AF’ and the weakened ether leaving the mass ‘LF’. So $g=AF-LF=Gm/r^2$.

I stemmed pressure gravity force equations between masses from the $g/AF = y/(g/r^2) = q$ ratios, where AF=pressure of ether; g= surface gravity of parent mass; r= distance from parent mass; y=gravity deviation in other mass (extra acceleration toward parent mass caused by ether weakening in other mass) and q = gravity coefficient. From this: $$AF= ((g/r)^2)/y$$ Calculating the pressure of ether from Pioneer anomaly where $y= 8,7*10^{-10}$ (extra acceleration force in Pioneer toward Sun at 70AU) I got ~ $380 000 m/s^2$ for the pressure of ether (at 20AU it would be ~ $4,646 million m/s^2$).

Solving fly-by anomaly $$y=q*g/r^2$$ Inserting AF to this equation for Earth I found that $q=2,5087*10^{-5}$ and $y=~ 0,21mm/s^2$ at ~600 km distance from Earth, which means that Galileo needed some 20sec and NEAR some 60 sec to reach their acceleration anomaly not counting with other factors. So the solution of pressure gravity theory is acceptable, and can be managed to these anomalies.

Modified Newtonian acceleration forces according to Pressure gravity: $$F1=((Gm2/r^2)+y2)*m1 = ((Gm1 /r^2)+y1)*m2=F2; m1/m2=y1/y2 $$ Where G is the gravity constant and m1, m2 are different masses.

The spacecraft anomalies show not only that pressure gravity theory works, but that these anomalies may be the consequences of pressure gravitation. While to prove attractive force gravity is highly difficult (particles cannot call each other), to deny pressure force gravity is impossible, as there is no bottom limit for ‘y’. Smaller ‘y’ means only higher pressure of ether.