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In 2010-2011, Verlinde's theory for explaining gravity as emergent from thermodynamics started to get known in the physics community.

It was (and seemingly still is) lacking evidence, and faced strong opposition.

Recently, a new article appeared, and some experimental results are said promising. I tried reading Verlinde's latest article, but I fear I do not have the necessary background and distance from his arguments.

What significant improvement have been made in the theory since 2011? Are the experimental measurements really significant? Do they really make Verlinde's theory more viable than others'?

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  • $\begingroup$ As far as I can tell, Verlinde simply elaborates on his argument (without significant modification) and outlines how his theory predicts modified gravity at some scales. This can be compared to data, and at least one paper by experimentalists seems to say that it fits quite well. I don't find this very surprising because I note that the collaboration of experimenters includes people working at the same university as Verlinde (and Utrecht, Groningen), so it's rather probable that Verline already consulted with these people before publishing his paper. $\endgroup$ – Danu Dec 17 '16 at 16:17
  • $\begingroup$ Of course, the data is also compatible with dark matter, but that's the whole point of Verlinde's theory: Giving a hopefully experimentally "viable" alternative to the traditional dark matter explanation. $\endgroup$ – Danu Dec 17 '16 at 16:19
  • $\begingroup$ I'm not sure this question is really suitable for our site, since it seems to be esentially asking us to review Verlinde's new paper. $\endgroup$ – ACuriousMind Dec 17 '16 at 22:11
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I am not an expert in Verlinde's theory. But I found this. The recently published paper "First test of Verlinde's theory of Emergent Gravity using Weak Gravitational Lensing measurements" by a group of astronomers with lead author M.M. Brouwer of Leiden University, compares astronomical gravitational lensing observations on 33.613 galaxies explicitly to Verlinde's extended model of Emergent Gravity (2016). It states:

In this paper we test the predictions of a different hypothesis concerning the origin of the excess gravitational force: the Verlinde (2016) model of Emergent Gravity (EG). Generally, EG refers to the idea that spacetime and gravity are macroscopic notions that arise from an underlying microscopic description in which these notions have no meaning. Earlier work on the emergence of gravity has indicated that an area law for gravitational entropy is essential to derive Einstein's laws of gravity (Jacobson 1995; Padmanabhan 2010; Verlinde 2011; Faulkner et al. 2014; Jacobson 2016). But due to the presence of positive dark energy in our universe Verlinde (2016) argues that, in addition to the area law, there exists a volume law contribution to the entropy. This new volume law is thought to lead to modications of the emergent laws of gravity at scales set by the `Hubble acceleration scale' a0 = cH0, where c is the speed of light and H0 the Hubble constant. In particular, Verlinde (2016) claims that the gravitational force emerging in the EG framework exceeds that of GR on galactic and larger scales.

This citation gives a short description of the change of Verlinde's EG theory of 2016 with respect to his 2011 paper. According to this paper, Verlinde's extended theory explains the apparent dark matter effects from its basic principles without the assumption of dark matter or additional free parameters.

Verlinde's 2011 paper has been cited 153 times in peer reviewed papers. For reliable scientific criticism, I would look at the peer reviewed scientific literature, not at the mentioned blog which, unscientifically, is full of animosity and sanguinary language. Erik Verlinde is an internationally renowned and respected Professor of Theoretical Physics at the University of Amsterdam in the Netherlands who has done highly cited (H-index 33) significant contributions to theoretical physics prior to his theory on Emergent Gravity.

The astronomical paper by M.M. Brouwer et al. is a first observational confirmation of the the extended Emergent Gravity model of Verlinde. Many more will probably be necessary. His theory is, of course, not yet widely accepted. It will be interesting to see what the verdict of the serious scientific community will be.

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I recently commented on the more recent paper by Verlinde, so I will reference that. The recent astronomical evidence is tentative at this point. I think the issue is that emergent gravity (EG) has a different quantum vacuum structure than standard classical gravitation. The result is then similar to Schwinger's observation about the production of charged pairs of electrons and positrons. There is then I think an instanton associated with the tunneling of EG to the standard vacuum corresponding to Einstein GR. This I think should produce elementary particles or entangled elementary particles.

In reading Verlinde's paper I do think he is on to something with this. I am just not sure that it means spacetime is modified into some sort of MOND-like gravity. that in some ways we might just be stupid with this whole dichotomy between particles and EG with a different vacuum. If the mass gap between the EG vacuum and the Einstein vacuum plus DM particles is very small or zero, then in effect the two are equivalent. Seeing the world according to this modified gravity, where the EG is due to entanglement entropy physics of cosmology, and DM produced as an tunneling instanton from the EG vacuum to the Einstein spacetime may simply be entirely the same thing.

We start with the energy $$ E~=~\frac{1}{2}NkT, $$ for $N$ units $N~=~A/L_p^2$ of area on the holographic screen. The mass of the holographic screen is $M$ and so $E~=~Mc^2$ The temperature of a mass held above the screen with an acceleration $a$ is $$ T~=~\frac{\hbar a}{2\pi kc}. $$ We now compute the acceleration according to this as $$ a~=~\frac{L_p^2 c^3}{\hbar r^2}~=~\frac{GM}{r^2}, $$ which is the acceleration of gravity.

We recognize from the energy that $E~=~TS$ that $$ \Delta S~=~\frac{1}{T}\Delta E $$ and from $\Delta E~=~F\Delta r$ that we recover the acceleration law. This approach alternative to considering change in entropy of the test mass, $$ \Delta S~=~k\frac{\Delta x}{\lambda_c}, $$ for $\lambda_c~=~\hbar/mc$ the Compton wavelength of a test mass or particle of mass $m$ and $\Delta x$ a small distance between the holographic screen, or event horizon, and the test mass. We also have the Bekenstein entropy of a black hole $$ S~=~k\frac{A}{4L_p}, $$ for $L_p~=~\sqrt{G\hbar/c^3}$. The change in entropy is similarly computed. The results are the same, but this makes more use of the idea of the holographic screen.

The objection that gravitaton does not involve entropy is a confusion with citing the Newtonian potential and force $\vec F~=~-\nabla V$ for $V~=~-GMm/r^2$ as a conservative force with the concept of evolving a holographic screen. This objection has largely been muted, and those who think clearly know this distinction.

The entropy force is in line with the idea that spacetime is built up from entanglements. Entropy $S~=~-k\sum_np_n~log~p_n$ with $p_n~=~\rho_{nn}$ and the use of relative entropy and changes of entropy is commensurate with the concept of spacetime built from entanglements.

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    $\begingroup$ What is the "quantum vacuum structure" in "standard classical gravitation" (classical and "quantum vacuum" are kind of exclusionary)? What observation of Schwinger are you referencing? What is that expression for energy "on a holographic screen"? The answer uses a lot of jargon but I don't see that it's actually connecting the jargon in meaningful ways. Most importantly, how is this an answer to "What significant improvement have been made in the theory since 2011? Are the experimental measurements really significant? Do they really make Verlinde's theory more viable than others'?"? $\endgroup$ – ACuriousMind Dec 17 '16 at 22:16
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    $\begingroup$ I am not making a big pitch for Verlinde, but I am open minded about this. The vacuum is a CFT corresponding to AdS, or a similar theory with dS. I had limited time to write this. Schwinger's observation I am referring to is pair creation of e e^+ in a large E field. The energy of the holographic screen is the mass of a black hole. $\endgroup$ – Lawrence B. Crowell Dec 18 '16 at 0:24
  • $\begingroup$ Thank you for this effort. However, the question was not about explaining the theory, but about explaining the changes from 2011 and the impact of experimental results. $\endgroup$ – fffred Dec 18 '16 at 10:44
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    $\begingroup$ I have not read the paper arxiv.org/abs/1612.03034 as yet. In fact I am still nibbling at Verlinde's paper. Astronomical papers are to me rather difficult to read because I am not as familiar with these techniques. My honest advise is to keep one's eyes and mind open and see how this develops. Maybe there is something here. The thing to watch is follow up stats on weak lensing that gives added support. $\endgroup$ – Lawrence B. Crowell Dec 18 '16 at 23:31

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