A macaroni pie? Elephants blowing ballons? No, it’s Verlinde’s entangled universe. |

It’s taken me some while to get through the paper. Vaguely titled “Emergent Gravity and the Dark Universe,” it’s a 51-pages catalog of ideas patched together from general relativity, quantum information, quantum gravity, condensed matter physics, and astrophysics. It is clearly still research in progress and not anywhere close to completion.

The new paper substantially expands on Verlinde’s earlier idea that the gravitational force is some type of entropic force. If that was so, it would mean gravity is not due to the curvature of space-time – as Einstein taught us – but instead caused by the interaction of the fundamental elements which make up space-time. Gravity, hence, would be emergent.

I find it an appealing idea because it allows one to derive consequences without having to specify exactly what the fundamental constituents of space-time are. Like you can work out the behavior of gases under pressure without having a model for atoms, you can work out the emergence of gravity without having a model for whatever builds up space-time. The details would become relevant only at very high energies.

As I noted in a comment on the first paper, Verlinde’s original idea was merely a reinterpretation of gravity in thermodynamic quantities. What one really wants from emergent gravity, however, is not merely to get back general relativity. One wants to know which deviations from general relativity come with it, deviations that are specific predictions of the model and which can be tested.

Importantly, in emergent gravity such deviations from general relativity could make themselves noticeable at long distances. The reason is that the criterion for what it means for two points to be close by each other emerges with space-time itself. Hence, in emergent gravity there isn’t a priori any reason why new physics must be at very short distances.

In the new paper, Verlinde argues that his variant of emergent gravity gives rise to deviations from general relativity on long distances, and these deviations correspond to dark energy and dark matter. He doesn’t explain dark energy itself. Instead, he starts with a universe that by assumption contains dark energy like we observe, ie one that has a positive cosmological constant. Such a universe is described approximately by what theoretical physicists call a de-Sitter space.

Verlinde then argues that when one interprets this cosmological constant as the effect of long-distance entanglement between the conjectured fundamental elements, then one gets a modification of the gravitational law which mimics dark matter.

The reason is works is that to get normal gravity one assigns an entropy to a volume of space which scales with the surface of the area that encloses the volume. This is known as the “holographic scaling” of entropy, and is at the core of Verlinde’s first paper (and earlier work by Jacobson and Padmanabhan and others). To get deviations from normal gravity, one has to do something else. For this, Verlinde argues that de Sitter space is permeated by long-distance entanglement which gives rise to an entropy which scales, not with the surface area of a volume, but with the volume itself. It consequently leads to a different force-law. And this force-law, so he argues, has an effect very similar to dark matter.

Not only does this modified force-law from the volume-scaling of the entropy mimic dark matter, it more specifically reproduces some of the achievements of modified gravity.

In his paper, Verlinde derives the observed relation between the luminosity of spiral galaxies and the angular velocity of their outermost stars, known as the Tully-Fisher relation. The Tully-Fisher relation can also be found in certain modifications of gravity, such as Moffat Gravity (MOG), but more generally every modification that approximates Milgrom’s modified Newtonian Dynamics (MOND). Verlinde, however, does more than that. He also derives the parameter which quantifies the acceleration at which the modification of general relativity becomes important, and gets a value that fits well with observations.

It was known before that this parameter is related to the cosmological constant. There have been various attempts to exploit this relation, most recently by Lee Smolin. In Verlinde’s approach the relation between the acceleration scale and the cosmological constant comes out naturally, because dark matter has the same origin of dark energy. Verlinde further offers expressions for the apparent density of dark matter in galaxies and clusters, something that, with some more work, can probably be checked observationally.

I find this is an intriguing link which suggests that Verlinde is onto something. However, I also find the model sketchy and unsatisfactory in many regards. General Relativity is a rigorously tested theory with many achievements. To do any better than general relativity is hard, and thus for any new theory of gravity the most important thing is to have a controlled limit in which General Relativity is reproduced to good precision. How this might work in Verlinde’s approach isn’t clear to me because he doesn’t even attempt to deal with the general case. He starts right away with cosmology.

Now in cosmology we have a preferred frame which is given by the distribution of matter (or by the restframe of the CMB if you wish). In general relativity this preferred frame does not originate in the structure of space-time itself but is generated by the stuff in it. In emergent gravity models, in contrast, the fundamental structure of space-time tends to have an imprint of the preferred frame. This fundamental frame can lead to violations of the symmetries of general relativity and the effects aren’t necessarily small. Indeed, there are many experiments that have looked for such effects and haven’t found anything. It is hence a challenge for any emergent gravity approach to demonstrate just how to avoid such violations of symmetries.

Another potential problem with the idea is the long-distance entanglement which is sprinkled over the universe. The physics which we know so far works “locally,” meaning stuff can’t interact over long distances without a messenger that travels through space and time from one to the other point. It’s the reason my brain can’t make spontaneous visits to the Andromeda nebula, and most days I think that benefits both of us. But like that or not, the laws of nature we presently have are local, and any theory of emergent gravity has to reproduce that.

I have worked for some years on non-local space-time defects, and based on what I learned from that I don’t think the non-locality of Verlinde’s model is going to be a problem. My non-local defects aren’t the same as Verlinde’s entanglement, but guessing that the observational consequences scale similarly, the amount of entanglement that you need to get something like a cosmological constant is too small to leave any other noticeable effects on particle physics. I am therefore more worried about the recovery of local Lorentz-invariance. I went to great pain in my models to make sure I wouldn’t get these, and I can’t see how Verlinde addresses the issue.

The more general problem I have with Verlinde’s paper is the same I had with his 2010 paper, which is that it’s fuzzy. It remained unclear to me exactly what are the necessary assumptions. I hence don’t know whether it’s really necessary to have this interpretation with the entanglement and the volume-scaling of the entropy and with assigning elasticity to the dark energy component that pushes in on galaxies. Maybe it would be sufficient already to add a non-local modification to the sources of general relativity. Having toyed with that idea for a while, I doubt it. But I think Verlinde’s approach would benefit from a more axiomatic treatment.

In summary, Verlinde’s recent paper offers the most convincing argument I have seen so far that dark matter and dark energy are related. However, it is presently unclear if not this approach would also have unwanted side-effects that are in conflict with observation already.

## 55 comments:

Thank you Dr. H. I encountered the original paper but was not equipped to really understand it. I even asked him a question but did not receive a reply.. in essence it was "would two equal masses of different densities, hence different surface areas, warp space differently"? Thank you for the review of the latest here. Always remain interested!

Dr B. Thanks for the explanation. I have a question after reading the original paper. I believe it also came up earlier in a different comment.

Erik Verlinde makes it obviously clear that his approach tries to translate models from Anti-de Sitter space to de Sitter space. And he also explains that this is an important source of difficulties, but also of Dark Energy&Matter. As will be clear from this formulation, I really do not understand what he means by this. I vaguely remember having read somewhere that it might have to do with the fact that dS space has a horizon and AdS not (IIRC).

If you plan to go into this question in a later post, I can wait.

Rob,

I'd say he takes inspiration from models that are best understood in AdS. Well, as I explained in my post, he starts with de-Sitter space which means he assumes dark energy. It doesn't make sense to say that this is a source of dark energy, it's the same thing, period. The interesting point is that he shows dark energy gives rise to dark matter. Not sure that helps but "I do not understand" is not a question. Best,

B.

Matthew,

I don't understand what your question has to do with the paper.

Dr B

"Not sure that helps but "I do not understand" is not a question. "

I really forgot the question, I see.

As I understand it, our space is more like dS and not at all like AdS. I would like to know what the difference is between AdS and dS that makes it so difficult to translate the ideas developed on AdS space to dS space?

Rob,

Anti de-Sitter space has a boundary. De Sitter space hasn't. The difference is that in the former case the cosmological constant is negative, in the latter it's negative. We live in a space with positive cosmological constant, but the boundary of anti-de Sitter is what makes the AdS/CFT duality work. Hence the difficulty of translating any insight from AdS to dS. Going from a negative to a positive cosmological constant is not a smooth change to the space-time. It removes the boundary. There's thus a priori no reason to believe that any insights carry over from AdS to dS. Best,

B.

Thanks.

@ Matthew Rapaport "

would two equal masses of different densities, hence different surface areas, warp space differently?" 1.74 solar-mass 465.1 Hz PSR J1903+0327 and a 1.05 solar-mass star form a 95.17-day binary system. –15.3% vs. -0.000369% gravitational binding energy; 1.8×10^11 vs. 30 surface gees; 2×10^8 gauss vs. 5 gauss magnetic fields; compressed superconductive protons and superfluid neutrons vs. 11.8:1 atom-abundance hydrogen:helium plasma; extreme isospin and lepton number divergences; and pulsar 11% of lightspeed equatorial spin velocity are EP violation-inert for orbit, periastron precession, and gravitational radiation orbital decay.By observation, no classical, quantum mechanical, relativistic, and/or gravitational (strong EP) divergence or combination violates the Equivalence Principle to observed 15 decimal places."

51-pages" How is baryonic matter created in excess of baryonic antimatter, 6.1×10^(-10) [hadrons - antihadrons]/[photons]? Trace Einstein-Cartan chiral anisotropic space-time torsion plus achiral isotropic space-time curvature...1) sources Tully-Fisher as 1.2×10^(-10) m/s² Milgrom acceleration from Noetherian leakage of angular momentum conservation given trace imperfect spatial isotropy; and

2) sources matter excess as Sakharov conditions given trace imperfect space-time mirror symmetry.

"

To do any better than general relativity is hard" Observe external to GR in existing apparatus wherein Einstein-Cartan spacetime torsion is measurably active. It is easyl.http://thewinnower.s3.amazonaws.com/papers/95/v1/sources/image004.png

Test space-time geometry with geometry, Look

Dear Sabine,

I think you will enjoy this paper:

https://arxiv.org/abs/1612.00266

Echoes from the Abyss: Evidence for Planck-scale structure at black hole horizons

Jahed Abedi, Hannah Dykaar, Niayesh Afshordi

(Submitted on 1 Dec 2016)

In classical General Relativity (GR), an observer falling into an astrophysical black hole is not expected to experience anything dramatic as she crosses the event horizon. However, tentative resolutions to problems in quantum gravity, such as the cosmological constant problem, or the black hole information paradox, invoke significant departures from classicality in the vicinity of the horizon. It was recently pointed out that such near-horizon structures can lead to late-time echoes in the black hole merger gravitational wave signals that are otherwise indistinguishable from GR. We search for observational signatures of these echoes in the gravitational wave data released by advanced Laser Interferometer Gravitational-Wave Observatory (LIGO), following the three black hole merger events GW150914, GW151226, and LVT151012. In particular, we look for repeating damped echoes with time-delays of 8MlogM (+spin corrections, in Planck units), corresponding to Planck-scale departures from GR near their respective horizons. Accounting for the "look elsewhere" effect due to uncertainty in the echo template, we find tentative evidence for Planck-scale structure near black hole horizons at 2.9σ significance level (corresponding to false detection probability of 1 in 270). Future data releases from LIGO collaboration, along with more physical echo templates, will definitively confirm (or rule out) this finding, providing possible empirical evidence for alternatives to classical black holes, such as in firewall or fuzzball paradigms.

Daniel,

I did enjoy it. It seems to have escaped your attention I'm in the acknowledgements. I also shared a link to the paper already this morning myself.

Please excuse me for using your comment in particular as occasion to tell all commenters here to:

please stop posting links in my comment section unless they are directly related to the topic of the postYou're just adding to the noise in my inbox. Before you think it's necessary to inform me of something you've found widely shard on social media, at least you could check if I've shared it myself before, which is the case for almost every link that someone posts here. I don't live under a rock. If you want to know what links I share and discuss, please follow me twitter or on facebook. Thanks,

B.

Thank you Sabine,

Your detailed professional comments point to a solution to the deeply flawed, anonymous, refereeing process.

This might be more important than the specific case at hand. Louis Clavelli

Lou,

I'm not sure what you mean. For all I know the paper hasn't been peer reviewed yet, so what flaw do you refer to?

I thought the big deal about GR was that you couldn't tinker with it - much. Bob Dicke tried; ruled out. Cosmological constant, bingo. But, no more! Am I wrong? I usually am.

I think there is something very important left out of this paper that relates to an axiomatic idea for black holes. This axiom (unproven so far but a pretty good guess) is that the entropy of the surface boundary at the event horizon equals the entropy of the bulk composing the interior volume. This axiom does NOT apply to all surface entropies equaling all volumes enclosed by those surfaces. It only applies to surfaces enclosing matter that is significant enough that at a certain radius around that matter light does not escape. Anything less or more than that radius and the axiom does not apply.

This paper not only seems to be throwing that axiom out but also seems to be inserting an entropy of volume of space always scaling with the actual volume. I'm sorry, but that just does not seem right on a basic conceptual basis.

I'm sorry Sabine. I didn't know this paper was widely shared. And I didn't know you lived outside a rock!

Hello, Professor Hossenfelder,

My, off the wall question, was inspired by an article you authored a year ago, in Aeon magazine, concerning the idea that a Black Hole could condense itself by natural pressure and spin, to for a naturally, occurring, quantum computer. It was your stirring, words, at the beginning of the article, you said that in theory:

"After you die, your body’s atoms will disperse and find new venues, making their way into oceans, trees and other bodies. But according to the laws of quantum mechanics, all of the information about your body’s build and function will prevail. The relations between the atoms, the uncountable particulars that made you you, will remain forever preserved, albeit in unrecognisably scrambled form – lost in practice, but immortal in principle."

Were you working up a bit of beautiful, prose for a non-professional, physics article, or do you feel that this is more or less, true physics. The beauty of it, nevertheless, for me, is this sort of makes me think of the universe as, like a computer, having a read-write property to it, somehow? Maybe, as the Japanese expression goes,"to a hammer, everything looks like a nail."

Much Thanks,

Mitch

Eric,

The holographic scaling of entropy is assumed to apply everywhere, the volume scaling is a new addition. It doesn't matter whether you think that's "right on a basic conceptional basis", what matters is whether it's right in terms of observational consequences.

Unknown,

That's right. It's hard to modify general relativity without screwing it up altogether, or be left with so tiny modifications you can as well assume they're not there at all. That's why I wrote the first thing you'd want is to demonstrate that you get back general relativity in a well-controlled limit. But that doesn't mean it's not possible. Best,

B.

Mitch,

Ah, I wrote this article after I just finished reading a book titled "Writing well" and I got a little carried away there. I guess it's not my usual style. But, yes, it was indeed me who wrote that (and not the editor).

It's factually mostly correct and essentially a colorful way of saying that the fundamental laws of nature are (to our best current knowledge) one-to-one maps from the past to the future (or vice-versa). That means if you were omniscient, then all the information contained in the universe remains the same for all times (including you and I and every word we say). It just changes shape. In practice, of course, information often becomes scrambled and irretrievable. It's only mostly correct because it disregards wave-function collapse which I don't believe to be fundamental. (And which doesn't happen in the many worlds interpretation.) Best,

B.

I enjoyed your blog on Eric Verlinde's latest paper. The element of his paper that I find most ad hoc, given his explanation, is his introduction of spacetime 'elasticity' to characterize Dark Matter by strain - with the additional assumption of a linear stress-strain relationship (actually, it was only for space, since he notes he's dealing with the static case). However, I know that others have noted that 'spacetime' can be viewed as analogous to a solid (e.g. Christoph Schiller) in some regards - and that the Maximum Force (c^4/4G) in General Relativity can be related to spacetime 'stiffness'. Moreover, I am also aware that Padmanabhan has actually derived the GR field equations by assuming that spacetime is a solid (just as Christoph Schiller has derived the field equations using Maximim Force!). Do you have any additional comments or insights on this specific aspect of Verlinde's analysis?

Thanks, much, Professor!

Mitch

"After you die, your body’s atoms will disperse and find new venues, making their way into oceans, trees and other bodies. But according to the laws of quantum mechanics, all of the information about your body’s build and function will prevail. The relations between the atoms, the uncountable particulars that made you you, will remain forever preserved, albeit in unrecognisably scrambled form – lost in practice, but immortal in principle."

And as a corollary, all the information comprising "you" was there since the beginning...

Excellent Sr. Rossenfelder, como sempre

You mention earlier work by Padmanabhan on a similar topic. Are you aware of his recent work on a thermodynamic origin of gravity?

Phillip,

Depends on what you mean by 'being aware of'. I've seen the papers, I didn't read them. (Too long, too off-topic from my research.)

I took particular note of this in the next to last paragraph: "and with assigning elasticity to the dark energy component that pushes in on galaxies." This made me wonder if Verlinde uses this 'pushing in' mechanism to help explain the enhanced gravitational lensing seen around foreground galaxy clusters, normally attributed to the sum of normal matter and particulate dark matter in the foreground cluster. I'm hoping that Bee can clarify if this is part of the overall framework of Verlinde's theory, for those of us not versed in the intricacies and complexities of General Relativity and Quantum Mechanics, to whom Verlinde's paper is like reading a foreign language.

"Depends on what you mean by 'being aware of'. I've seen the papers, I didn't read them. (Too long, too off-topic from my research.)"Same here. :-( (Well, I'm about 1/3 of the way through one of them.)

My concern (which might be unfounded) is that someone with more hype (by himself or others, intentional or not) gets too much credit and someone else, who might have been there first, too little.

Wikipedia

home page

My guess is that if enough string theorists attempt to model Milgrom's MOND then eventually some of them will arrive at the empirically valid theory of quantum gravity.

Eric and Bee,

With regards to the surface entropy being spread out over the enclosed volume, what does the volume in equation 2.13 represent in Verlinde's latest work: "Emergent Gravity

and the Dark Universe". Which 3d hypersurface is this volume taken on?

Using the coordinatization in the metric in equation (2.10), the volume of a sphere on the constant t hypersurfaces would be infinite between r = 0 and r = L. The volume element is dr* d\theta*d\phi*r^2*sin(\theta)*1/(sqrt(1-r^2/L^2)). Is he just naively assuming a flat spacetime background that "underlies" deSitter space?

Alex,

Don't have time to look it up now, but did you actually check that the integral is infinite? The volume inside the horizon should go with L^3.

Bee,

Indeed I was wrong. It does actually converge.

@Phillip Helbig

Padmanabhan did indeed do his homework profoundly : In his 2010 paper 'On the origin of gravity and the laws on Newton', Verlinde referred to his 2009 paper 'Thermodynamic aspects of Gravity - new insights' where Padmanabhan based his work on no less than 148 references.

But Verlinde has since then been a.o. concentrating more on causal principles of gravity, judging by his latest paper.

From several interviews I read, where they have an occasional remark about each other, it is clear to me that they are in competition with each other, be it with their own nuanced angle of approach.

One says e.g. 'I found this and that before him'. The other says e.g. 'this and that is a circular line of reasoning in my oppinion' etc.

But also in his latest paper, Verlinde references several papers by T.Padmanabhan, so you can't accuse him of 'hiding his sources'.

All in all, such competition is actually healthy for progress I think.

Beqt, Koenraad

Dear Sabine,

I am a condmat postdoc but with a soft spot for QG. Just wanted to thank you for your insighful and extremely useful comments. All the best, Marco Tavora.

@Koenraad Van Spaendonck

"One says e.g. 'I found this and that before him'. The other says e.g. 'this and that is a circular line of reasoning in my oppinion' etc."

This goes back to an unfortunate incident in early 2010. At the end of 2009, Verlinde gave an interview for a national newspaper in the Netherlands where he talked about his new theory. As he had not published anything yet, he was rather secretive. However, alongside the interview a picture was printed with a blackboard in the background. On this blackboard some formulas were visible that gave away his ideas. Within a week, people around the internet were fleshing out his theory. When Padmanabhan published a paper in early 2010 that looked a lot like what Verlinde had written on his blackboard, there were accusations flying around. I understand that they since then have buried the hatched.

Btw, here is a link of a contemporary blog post about the story of Verlinde's interview:

http://www.science20.com/hammock_physicist/holographic_hot_horizons

When I saw how Eric Verlinde was able to extract Newton's empirically derived constant "G" from other unrelated fundamental quantities, in the link provided by Rob above, all I could think of was, wow! Then a cautionary thought flickered through my mind - could this be a circular argument, in the sense of what you put in to an equation will ultimately come out? But that concern quickly evaporated as a quick check showed that none of the variables, or constants, in the equations contained Newton's gravitational constant as a factor. Now I see why this program of research has elicited such tremendous interest, as it ties disparate areas of physics together that is not obvious at first glance.

David,

You misunderstand this. Verlinde doesn't derive G.

Noether's theorems: Symmetries and conserved currents are coupled. Baryogenesis: Matter exists in excess of antimatter. Tully-Fisher: Spiral galaxies' rotations versus radius are anomalous versus visible matter distribution. LIGO GW150914: GR predicts binary black hole mergers, prompt (milliseconds to equilibrium), with incremental small binding energy [(-3 sols)/(30 sols + 36 sols) = -4.5% arXiv:1611.00541 or (-3 sols)/(28.2 sols + 38.3 sols) = -4.5% arxiv:1611.07531].

Einstein-Cartan gravitation is testably supportive of the first three. Test spacetime geometry with geometry. Black holes are soap bubbles, (2 + epsilon) dimension surfaces with no internal singularities to mutually orbit or merge. What proposed gravitation theory tolerates observation?

Bee, I see that I goofed. When I looked up Planck's Length earlier, which is involved in the formula provided at the aforementioned link, it gave the numerical value in meters. But I neglected to look up the origin of this fundamental physical quantity. Checking on that I see that Newton's Constant is integral to the derivation of the Planck Length. So I guess the appearance of Newton's Constant in the outcome of the calculation shown in that link, isn't so startling after all.

Hi Bee,

Reference, "The new paper substantially expands on Verlinde’s earlier idea that the gravitational force is some type of entropic force. If that was so, it would mean gravity is not due to the curvature of space-time – as Einstein taught us – but instead caused by the interaction of the fundamental elements which make up space-time. Gravity, hence, would be emergent."

This paragraph implies that Einstein's curvature of spacetime is not compatible with emergent gravity resulting from the interactions of the fundamental elements which make up spacetime. Is it not possible that the two are equivalent? Consider a scenario in which the interactions of fundamental spacetime elements produce spacetime gradients that are essentially the same as the warped space of Einstein?

Frank Burdge

Frank,

No, the paragraph does not imply that. It implies that space-time is emergent, and so is curvature. Best,

B.

Dear Sabine,

would emergent space-time mean that time is a fake?

Thanks,

J.

akidbelle,

I have no clue what you mean by time being fake. You might find this helpful.

Hello Sabine,

Can you detect from Verlinde's work what his take on the Big Bang is ?

I understand he finds it an illogical hypothesis, but does he also have an alternative ?

How does his universe behave in therms of accelerated expansion e.g. ?

Do you have info on this perhaps ?

Best, Koenraad

Sabine,

Would Verlinde's Theory ultimately be considered an extension to General Relativity (GR), in analogous fashion to how GR is an extension of Newtonian theory?

My reason for asking is that Relativity seems to provide a nice explanation for the appearance of absolute spacetime in (spatial and temporal) local environs under Newtonian physics. (We now know that's all absolute spacetime ever was - an appearance. It might be an excellent approximation to reality in certain domains, but absolute spacetime doesn't exist in reality any more than a perfect circle does) And, the ever popular heuristic analogy of the Earth appearing flat locally, but otherwise curved globally. Stated more technically, the general metric of GR, being a real symmetric tensor, can always be diagonalized to reproduce the metric of Special Relativity, which can be easily replaced with the Euclidean Metric when v << c.

In analogous fashion, does Verlinde's theory offer any explanation as to why reality seems to take on an appearance of spacetime curvature under GR? It just seems like every new, successful theory always explains the "naiveté" of the physical interpretation of reality under the previous theory it extends upon. Do we have something like that here too?

Spacetime curvature is quite the odd appearance for reality to take, but it is also rather rigorously defined (under GR) and experimentally verified. So, seems like maybe this viewpoint should be extended, rather than replaced as something wholly incorrect.

I did download his papers, so maybe some of my questions will also be answered there later.

Thanks Sabine,

I meant something like option 2 of the post you reference. Though option 1 is philosophically appealing.

Best,

J.

Koenraad,

No, I can't.

akidbelle,

In the present formulation the answer to that question is clearly "no". In a more complete variant, maybe yes. But it's really hard to get time to be emergent because the emergence itself needs to happen. Basically the only way I can think of doing this is with some phase-transition from a Euclidean space (that serves as a boundary condition). But I don't presently see a relation of this to Verlinde's approach. Best,

B.

Evan,

Verlinde's model isn't presently an extension of GR because it doesn't reproduce GR. It's a modification that works only in a certain limit.

Verlinde doesn't discuss an explanation for why curved space-time, but the emergent space-time approach (or even AdS/CFT) that he builds on does that already. I don't know why you pick on curvature in particular. It's much stranger to have a space-time and insist it isn't curved. That's a very special case. The space-time is basically a good way to organize stuff and the metric of space-time is the way you quantify the relations of stuff. Most metrics have curvature. Best,

B.

Hi Sabine,

my question was more general than Verlinde's approach. Sorry if that was out of scope.

I like the idea of a phase but not the "hard" transition (like the past being frozen water). I think it needs much better symmetry between past and future, and at the same time this symmetry needs to exhibit an orientation.

Best,

J.

Hi Bee,

Thanks for the review. Do you think there's too much emphasis placed on trying to match new gravity models with astrophysical data alone? The data from observatories don't have enough accuracy to the nth decimal place to show deviations predicated from General Relativity hence the lack of progress in this area. If they want to verify their models, they need to come up with experiments that can be conducted in the lab where the paramaters of the experiment can be changed, with astrophysical data, we can only observe but can't touch.

Cheers, Paul.

Dear Dr.B.

After reading the paper and your review, I also read your essays 'The superfluid Universe' on aeon.co. The explanation of Bose-Einstein condensates seems to fit Verlinde's starting point of universe full of dark energy medium with very low temperature; that suits the long-range quantum effects component of it.

Did Khoury just models dark matter as a superfluid, and not include dark energy? If so, Verlinde's point of view can lead to another model where instead dark energy is a superfluid and dark matter is the consequence of interactions with normal matter? This inspired by Verlinde's argument that matter removes entropy from the dark energy medium.

Your sharp notices are more than welcome!

HansT.

Hi Sabine,

Thanks for the response! I didn't mean to pick on spacetime curvature. I agree with what you say and I guess that's why I personally feel the next theory should probably extend GR. Still though, I do find Verlinde's ideas intriguing, so far.

Has Verlinde's theory been

ruled out observationally?Phillip,

I've seen this (and the other) papers. I'll have a post about this in the coming weeks. The brief answer to the question is "I don't think so."

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