Lots of people have asked me for my views on Erik Verlinde’s latest paper “Emergent Gravity and the Dark Universe“. This fifty-one pages long preprint has attracted a fair bit of media attention. Particularly in the Netherlands, Verlinde’s name being attached to the draft paper has caused a true hype. Un-Dutch roaring headlines in the Dutch national newspapers include: “Breakthrough Theory: Dark Matter Is Utter Illusion – Dutch Professor Rivals Einstein“, “We Are at the Brink of a Revolution that could be larger than Quantum Physics and Relativity Combined“, and “Breakthrough Article on Gravity Renders Verlinde the Most Celebrated Scientist of 2016“.

Last week I found myself standing in the back of a room somewhere in the south of the Netherlands. Erik Verlinde kicking off the session on dark matter at physics@veldhoven was the probable cause for the room being packed.

Just like other physicists, I am eagerly awaiting results from the various dark matter detection experiments. I certainly do not consider myself to belong to the group described by one of the subsequent speakers as ‘dark matter deniers’. At the same time, I do feel the standard model of cosmology contains too many coincidences to convince me dark matter is real. On balance, I remain sympathetic towards papers that provide an alternative to the somewhat baroque ‘gravity + dark matter + dark energy’ description of our universe. Verlinde’s paper states that this trinity can be reduced to the duo ‘gravity + dark energy’. In other words, Verlinde claims that in a universe with dark energy, the long-range effects of gravity get modified such that dark matter*appears*to be present

With a lot of hand waving I can dumb-down Verlinde’s position as follows:

1) Spacetime (and gravity, its curvature) is emergent from the information captured in quantum correlations. This in itself represents by no means a new concept. Emergent spacetime is best understood for a model universe containing nothing else than ‘dark anti-energy’ (so-called AntiDeSitter space) and goes under the cryptic label ‘ER=EPR’.

2) In a more realistic spacetime solely containing dark energy (so-called DeSitter space), the ER=EPR correspondence still applies, albeit with a significant complication: non-local quantum correlations play up. This claim is new. If correct, this implies the breakdown of the much celebrated holographic principle first proposed by Erik’s MSc thesis adviser Nobel laureate Gerard ‘t Hooft.

3) Due to competition between local and non-local quantum correlations, emergent DeSitter spacetime does not thermalize over large length scales, thereby causing a ‘glassy behavior’ and ‘elastic dynamics’ which lead to long-range deviations in the gravitational behavior commonly attributed to dark matter.

So, to eliminate dark matter, Verlinde requires fundamental degrees of freedom that are non-holographic in nature and that also feature non-equilibrium behavior. Particularly at point 3) the paper is rather impenetrable (at least for me) and it is unclear to me how exactly the ‘glassy dynamics’ emerges. In his talk Verlinde didn’t address this point.

For the time being, we may step over any issues in the derivation, as in the end what matters is how successful Verlinde is in quantifying the apparent dark matter. The formula he proposes (equation 7.40 on page 38 in Verlinde’s preprint) adds to the gravitational acceleration a ‘dark acceleration’. The equation he provides applies to static mass distributions with spherical symmetry only, and can be condensed into:

<*a*^{2}> = *c**H _{o}*

**/2**

*g*Here, ** g** denotes the (constant) gravitational acceleration over a spherical surface centered around a spherically symmetric mass distribution, the angular brackets denote averaging over the whole sphere,

**represents the apparent ‘dark acceleration’,**

*a***is the speed of light and**

*c***the current value for the Hubble constant. This represents a MOND-type modified gravity. Just like the phenomenological MOND description, Verlinde’s equation can be expected to struggle in describing dark-matter phenomena such as the acoustic oscillations in the cosmic microwave background (CMB).**

*H*_{o}My final ordeal? I had hoped Verlinde’s lengthy paper to culminate in an equation with wider applicability. Cosmology has evolved into a high-precision scientific discipline thanks to a wealth of quantitative information on the CMB. Verlinde’s paper doesn’t address dark matter effects in the CMB. It is unlikely that Verlinde’s approach will attract a professional following anywhere near to what the Dutch newspaper headlines suggest, unless Verlinde manages to apply his approach successfully to the acoustic oscillations in the CMB or any other area where MOND fails.

Until that happens I am most happy with my tax money going to dark matter detection experiments.

Glad you are back with a great post Johannes. Thank you for helping understand Verlinde’s paper overall idea. I had skimmed through it before, hoping to find in the end some suggestions of possible tests. He argues that CMB results would be the same as with dark matter being particles, as long as these effects he claims can be modeled like a pressureless fluid, although he admits he is unsure about that. But assuming that is correct, would then be possible to check these ideas modeling large structure formation in the Universe?

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You are welcome, Luis.

In his paper, Verlinde makes the remark: “the arguments and calculations that we presented in this paper are not yet sufficient to answer the questions regarding the cosmological evolution of our equations”. The problem is that he presents an idea, not a unifying theoretical framework. Several ad hoc assumptions made in the paper don’t extend to cosmological scales.

If it were easy, Verlinde would have done included it in his paper. That does not mean it is impossible. If Verlinde (or anyone else for that matter) can expand these ideas to cosmological scales and turn it into a viable alternative to lambdaCDM, the physics community will start paying serious attention.

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Thanks again for the clarifications!

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Hello, i found your post surprising, as i considered you one of the main supporters of Verlinde’s entropic gravity theory from 2010 (and i used your posts to get some insights on the theory at the time, thanks!). May i ask you why you have now changed your mind (or maybe it’s just my impression)? I understand that it’s not even a full theory yet and it can’t explain cosmological evolution in the present form, but that was the case in 2010 too. Now it can at least explain (away) dark matter and can be used in a model more similar to our universe (dS space). I remember at the time you were glad he won the Spinoza price and that he received a large amount of money as a consequence, while now you seem to have taken a more conservative approach.

Regarding the acoustic oscillations issue, are you referring to this paper?

https://arxiv.org/pdf/1701.00690.pdf

the paper highlights the problem but at the same time can be seen as a first step to address the problem.

I have the impression you expected more from the theory after so many years and resources spent, but don’t you think Verlinde proposal is still interesting and promising enough to spend significant resources to find out if the gaps (BAO not matching, constant H(z), etc.) can be filled?

I know how media can hype things out of proportion, but i also guess the physics community is prone to be dismissive of new proposals that could mean years of works wasted for all the people that worked on mainstream (but flawed) research (as dark matter would turn out to be if Emergent gravity turned out to be more accurate).

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The quick answer: I didn’t change my mind, Erik Verlinde did. He abandoned his entropic gravity approach. And yes, I had expected more given that six years with ample funding have passed.

However, I don’t want to come accross as ‘clinging to standard (lambdaCDM) cosmology’. if I had to make a bet today, my bet would be that in the near future emergent gravity will overthrow the standard model of cosmology. In any case, dark matter direct detection experiments will soon shed light on the situation.

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Thanks for replying.

Maybe he had to change his approach about entropic gravity because entropy is irreversible and gravity is not, as someone else pointed out, do you think this objection makes sense? I understand my question may not be very interesting for you at this time, so feel free to disregard this comment after the first line.

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I suspect he abandoned the entropic gravity idea as a route from this idea towards a consistent model remained unclear.

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