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Verlinde's de Sitter MOND is highly incomplete, to say the least

The Dutch media brutally overhype a generic speculative idea

Five independent Dutchmen have contacted me and told me that the Dutch media are obsessed with a new preprint by Erik Verlinde. Verlinde's fame among the inkspillers has already beaten Einstein's by an order of magnitude. (The echoes in the English-speaking media are so far a tiny fraction of the Dutch coverage.) I didn't know what to think about it but now I have spent a significant amount of time with the paper

Emergent Gravity and the Dark Universe
and I have an opinion.

Note that about 7 years ago, Erik Verlinde started the claim that gravity is an entropic force. Well, it can't be an entropic force because whenever entropic forces act, the entropy goes strictly up so the entropic forces are intrinsically irreversible – while a comet may be closer to the Sun, further from the Sun, closer to the Sun, and reverse things just fine. Also, it's not possible that the number of microstates attributed to a pair of objects depends on their distance: such an assumption would destroy interference in the gravitational field which has been experimentally demonstrated to exist using neutrons.




Seven years ago, I didn't immediately know what to think about Verlinde's paper when it was published. He's one of the guys who rediscovered my matrix string theory – or at least translated it from Lumo English to Dutch English – and he has authored dozens of similarly real physics papers so he isn't quite stupid. But within weeks, it became clear that his theory was just a wrong collection of speculations and misunderstandings about the relationships between the fundamental concepts of physics.

I wouldn't okay this wrong piece of work as an undergraduate term paper but he got 6.5 millions of euros for this absolutely worthless pile of feces so many people who are impressed by the money but don't have an idea about science – which includes virtually all journalists – started to think that Verlinde is a top physicist. And he may have decided that he must justify the award by producing even greater piles of bogus hype.




The new paper has an extremely similar style to the "gravity is an entropic force" seven years ago. It's all about problematic claims about forces and entropy and only uses some simple high school equations or inequalities where all terms are just products or ratios of several simple quantities. But my understanding is that Erik Verlinde has abandoned the claims he was spreading 7 years ago. In this new paper, gravity is no longer an entropic force.

But it's a similar collection of heuristic comments that are likely to be shown as "sharply wrong" as the "entropic force" claims once someone studies the claims carefully enough.

OK, what does Verlinde say now?

He positively mentions the recent "spacetime is about entanglement" minirevolution in theoretical physics but he doesn't directly add anything on "top" of these insights – which were made by others, just to be sure. Instead, he says that dark matter doesn't exist. The phenomena attributed to dark matter are actually due to some modified laws of gravity, he says. These general comments don't differ from those of other generic "dark matter skeptics".

And his modifications to the laws of gravity should arise from some terms originally meant to describe the dark energy – which isn't quite the cosmological constant in his picture. So Verlinde's goal is to reduce the number of independent "dark" concepts in physics by one. Once you assume dark energy and you interpret it in some fancy but largely ill-defined "entanglement entropy" fashion, the effects associated with dark matter automatically arise, if you believe his optimism.

What is his modification of gravity?

Sadly, he doesn't have any particular microscopic model – like string theory where you can, at least in some vacua in practice, describe the set of actual microstates. He doesn't have any particular field theory model similar to Einstein's equations or any other effective quantum field theory. To summarize, he doesn't have any model at all.

But he wants to assign some entanglement entropy to things in his non-existent model, anyway, and claim that he can deduce some encouraging consequences even in the absence of the crucial knowledge.

In the "spacetime is entanglement" minirevolution, we often talk about the entanglement entropy between two subsystems of a physical system, e.g. two parts of the spacetime separated by a domain wall (or the event horizon). He talks about the entanglement entropy between the interior of the de Sitter causal patch and its exterior.

So this entanglement entropy has some term similar to \(S=A/4G\) proportional to the area of the horizon. But he argues that the dark energy implies that there must be some term proportional to the volume as well. Is that defensible? Well, the area-extensive entanglement entropy is natural from the viewpoint of locality. In the vacuum, the degrees of freedom are only entangled with the nearby ones, so only those near the boundaries of the entangled regions significantly contribute to the entanglement.

When you assume a volume-extensive entanglement entropy, it automatically means that the "contributors" to the entanglement entropy live everywhere, including the deep bulk of the regions. This assumption clearly implies some degree of non-locality. Locality holds experimentally, with a good accuracy. So any violation of locality should be small. I don't think that Erik Verlinde really proves that it's small. It doesn't seem to me that he cares much.

Instead, he wants to get the "useful" consequences from the new volume-extensive terms in the entanglement entropy. And he says that these terms imply some "failure of thermalization" and "memory effects" whose influence on moving matter is similar to that in MOND (Modified Newtonian Dynamics) theories – he wants to "derive" Milgrom's phenomenological fitting formula from a "microscopic" starting point.

I don't really believe that anything "very important or persuasive" that would go beyond my paragraphs above may be found on those 51 pages. In other words, I believe that if you asked a good enough student to write 51 pages of text with some formulae that would seem like an "elaboration" on my paragraphs above, the result would be almost indistinguishable from Verlinde's paper.

By the way, I think that Verlinde's proposal is fully analogous to my holographic MOND idea – also a way to justify dark-matter-like effects using some cosmological-constant-related corrections of mechanisms in fundamental physics – except that 1) my proposal is arguably cleverer, 2) I exposed it many years before Verlinde, and 3) I haven't sold it as a revolution in physics or demanded millions of euros for it.

So this Verlinde's new paper is some speculative picture making claims about the behavior of the entanglement entropy that could have the potential to "unify" dark energy and dark matter effects – but it doesn't really give us any model (neither string theory nor field theory...) and it doesn't really give us any tangible evidence that such a model could exist and be compatible with everything else we know about particle physics, including general relativity and particle physics. The well-known Einstein's and other field-theoretical equations aren't really derived so Verlinde can't really quantitatively say what his corrections to these equations are, either. A priori, his framework looks very different from local effective field theory or string theory and whenever someone starts to invent physics from scratch in this sense, he should first show that everything that physics has explained so far may also be explained in his completely different picture. No contemporary self-described "physics revolutionaries" seem to appreciate the difficulty of this task and they don't care. Erik Verlinde unfortunately doesn't seem to differ from them too much.

It seems conceivable to me that some form of MOND is right. And assuming MOND is right, it seems rather likely to me that dark energy and dark matter effects must be explained simultaneously. And those explanations are likely to have something to do with the "spacetime is entanglement" ideas because "the spacetime is entanglement" and this fact must be consistent with everything that the science of gravity may study. In this sense, Erik Verlinde's paper could be a sketch of something that is on the right track. However, I would bet that the bulk of those 51 pages are just wrong and will have to be replaced.

Media are untrustworthy, corrupt manipulators of stupid sheep

A lot has been written about the fact that Trump's victory – that took place despite the 99% support of Hillary Clinton by big newspapers – shows that people just don't have much respect towards the media anymore. The (hostile) media were named "The Fifth Power" by Napoleon Bonaparte – and that's why we refer to them as "The Seventh Power" today. But despite the seemingly high circulation and lots of money that flow through the media, people generally see the tricks and distortions once they become obvious enough. And they already have many alternative ways to find the information or make their mind about something. In some cases, these alternative ways are (even) worse than what the confidence in the media can do, in many cases, they are better, however.

Sadly, the science journalism is no better. A vast majority of the "revolutionary" stuff that you may encounter in the popular mainstream science media is bogus. These "journalists" heavily copy from each other – their degree of group think is staggering – and they care about the money that they're paid or someone else is paid. Meritocracy and careful, impartial efforts to find the truth – "investigative journalism" – are basically dead in the science media (and other media).

At any rate, I do believe that if you're thinking about reading Erik Verlinde's paper but you're not certain and you have read my abstract, you may save the time because it's unlikely that you will find something important yet sensible there. I think that he wrote 51 pages primarily to create the illusion that he's doing "lots of work" on his "revolutionary" ideas. But there's really no content that would be proportional to the volume (to 51 pages) here. ;-)

Someone else may find some crisp ideas that make the same or similar picture convincing – e.g. derive the volume-extensive entanglement entropy terms in de Sitter space from string theory etc. But without such an advance, I think that Erik Verlinde's preprint is a mediocre vague paper that everyone may ignore and it's too bad that the science media act differently. By the way, if you care, Frank Wilczek has attended a talk by Erik Verlinde and his words were harsher than mine.

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