Saturday, March 11, 2017

Is Verlinde’s Emergent Gravity compatible with General Relativity?

Dark matter filaments, Millenium Simulation
Image: Volker Springel
A few months ago, Erik Verlinde published an update of his 2010 idea that gravity might originate in the entropy of so-far undetected microscopic constituents of space-time. Gravity, then, would not be fundamental but emergent.

With the new formalism, he derived an equation for a modified gravitational law that, on galactic scales, results in an effect similar to dark matter.

Verlinde’s emergent gravity builds on the idea that gravity can be reformulated as a thermodynamic theory, that is as if it was caused by the dynamics of a large number of small entities whose exact identity is unknown and also unnecessary to describe their bulk behavior.

If one wants to get back usual general relativity from the thermodynamic approach, one uses an entropy that scales with the surface area of a volume. Verlinde postulates there is another contribution to the entropy which scales with the volume itself. It’s this additional entropy that causes the deviations from general relativity.

However, in the vicinity of matter the volume-scaling entropy decreases until it’s entirely gone. Then, one is left with only the area-scaling part and gets normal general relativity. That’s why on scales where the average density is high – high compared to galaxies or galaxy clusters – the equation which Verlinde derives doesn’t apply. This would be the case, for example, near stars.

The idea quickly attracted attention in the astrophysics community, where a number of papers have since appeared which confront said equation with data. Not all of these papers are correct. Two of them seemed to have missed entirely that the equation which they are using doesn’t apply on solar-system scales. Of the remaining papers, three are fairly neutral in the conclusions, while one – by Lelli et al – is critical. The authors find that Verlinde’s equation – which assumes spherical symmetry – is a worse fit to the data than particle dark matter.

There has not, however, so far been much response from theoretical physicists. I’m not sure why that is. I spoke with science writer Anil Ananthaswamy some weeks ago and he told me he didn’t have an easy time finding a theorist willing to do as much as comment on Verlinde’s paper. In a recent Nautilus article, Anil speculates on why that might be:
“A handful of theorists that I contacted declined to comment, saying they hadn’t read the paper; in physics, this silent treatment can sometimes be a polite way to reject an idea, although, in fairness, Verlinde’s paper is not an easy read even for physicists.”
Verlinde’s paper is indeed not an easy read. I spent some time trying to make sense of it and originally didn’t get very far. The whole framework that he uses – dealing with an elastic medium and a strain-tensor and all that – isn’t only unfamiliar but also doesn’t fit together with general relativity.

The basic tenet of general relativity is coordinate invariance, and it’s absolutely not clear how it’s respected in Verlinde’s framework. So, I tried to see whether there is a way to make Verlinde’s approach generally covariant. The answer is yes, it’s possible. And it actually works better than I expected. I’ve written up my findings in a paper which just appeared on the arxiv:

It took some trying around, but I finally managed to guess a covariant Lagrangian that would produce the equations in Verlinde’s paper when one makes the same approximations. Without these approximations, the equations are fully compatible with general relativity. They are however – as so often in general relativity – hideously difficult to solve.

Making some simplifying assumptions allows one to at least find an approximate solution. It turns out however, that even if one makes the same approximations as in Verlinde’s paper, the equation one obtains is not exactly the same that he has – it has an additional integration constant.

My first impulse was to set that constant to zero, but upon closer inspection that didn’t make sense: The constant has to be determined by a boundary condition that ensures the gravitational field of a galaxy (or galaxy cluster) asymptotes to Friedmann-Robertson-Walker space filled with normal matter and a cosmological constant. Unfortunately, I haven’t been able to find the solution that one should get in the asymptotic limit, hence wasn’t able to fix the integration constant.

This means, importantly, that the data fits which assume the additional constant is zero do not actually constrain Verlinde’s model.

With the Lagrangian approach that I have tried, the interpretation of Verlinde’s model is very different – I dare to say far less outlandish. There’s an additional vector-field which permeates space-time and which interacts with normal matter. It’s a strange vector field both because it’s not – as the other vector-fields we know of – a gauge-boson, and has a different kinetic energy term. In addition, the kinetic term also appears in a way one doesn’t commonly have in particle physics but instead in condensed matter physics.

Interestingly, if you look at what this field would do if there was no other matter, it would behave exactly like a cosmological constant.

This, however, isn’t to say I’m sold on the idea. What I am missing is, most importantly, some clue that would tell me the additional field actually behaves like matter on cosmological scales, or at least sufficiently similar to reproduce other observables, like eg baryon acoustic oscillation. This should be possible to find out with the equations in my paper – if one manages to actually solve them.

Finding solutions to Einstein’s field equations is a specialized discipline and I’m not familiar with all the relevant techniques. I will admit that my primary method of solving the equations – to the big frustration of my reviewers – is to guess solutions. It works until it doesn’t. In the case of Friedmann-Robertson-Walker with two coupled fluids, one of which is the new vector field, it hasn’t worked. At least not so far. But the equations are in the paper and maybe someone else will be able to find a solution.

In summary, Verlinde’s emergent gravity has withstood the first-line bullshit test. Yes, it’s compatible with general relativity.


  1. Nice work. Do you have any idea who were the physicists Anil contacted?

  2. Would this change from volume to surface in the proximity of a large body help understanting something about this effect here?

  3. Shantanu,

    I'll not name names, sorry.

  4. Wow. impressive work. But I would have thought the onus is on the original author to show their new theory of gravitation is covariant, if he/she wants the community to pay attention - have I misunderstood?

  5. Do you have negative kinetic energy in (4)?

  6. Based on Verlinde's theory, can I say that dark energy is conserved, because total matter/energy is conserved? Does it mean that the inflation will gradually weaken as space increases, because it spreads a constant dark energy over an ever increasing space?

  7. "a vector-field that couples to baryonic matter "
    " the kinetic term also appears in a way one doesn’t commonly have in particle physics but instead in condensed matter physics"[1]

    Vector field Milgrom acceleration[2,3,4] ends dark matter. Mirror asymmetry (curl, Beltrami vector field, etc.) selective to hadrons sources baryogenesis[5]. Measure it in one day it as

    a) non-identical and/or non-coincident rotational spectra of
    b) intensely geometrically chiral divergent[6]
    c) C_3 prolate top (simple rotational spectra)
    d) enantiomeric molecular rotors not in 1:1 ratio (self-calibrating[7]) as a
    e) vacuum supersonic expanded molecular beam[8] (vibrations frozen out) in a
    f) chirped-pulse Fourier transform microwave spectrometer[9]

    D_3-trishomocuban-2-nitrile, 2-cyano-D_3-trishomocubane,
    2-cyano-pentacyclo[^(2,6).0^(3,10).0^(5,9)]undecane (stereogram and converged HyperChem .hin file on request).


    1) arXiv:1703.01415
    2) DOI: 10.1088/0264-9381/22/3/007, arXiv:1703.01415
    3) arXiv:gr-qc/0406086
    4) DOI: 10.1088/0264-9381/23/24/013, arXiv:gr-qc/0603128
    5) DOI: 10.1103/RevModPhys.88.015004, arXiv:1505.01076
    6) DOI: DOI: 10.1063/1.1484559
    7) DOI: 10.1016/S0040-4020(98)00211-7
    9) DOI: 10.1002/anie.201300653, Dr. Melanie Schnell,

  8. "I will admit that my primary method of solving the equations – to the big frustration of my reviewers – is to guess solutions."

    I thought that was the basic approach to seeking closed-form solutions of nonlinear PDE. Of course after guessing a few one then tries to notice patterns in what tends to work and exploit this. Then you get an "ansatz" (for some reason saying it in German makes it sound more dignified).

  9. The vector condensate that you say comes about as a consequence of the theory might be a sure sign that Verlinde's theory violates Lorentz invariance which implies that the answer to your blog post title is a "No".

  10. Great piece, Sabine, and nice work on your paper. But why would the "first line bullshit test" be compatibility with GR? As we all know, DM and DE and inflation are all very ugly patches to GR to make it fit empirical data. We should it seems be quite open to alternative approaches that better match the data in a far less ad hoc way.

  11. " ... Verlinde postulates there is another contribution to the entropy which scales with the volume itself. It’s this additional entropy that causes the deviations from general relativity. ... However, in the vicinity of matter the volume-scaling entropy decreases until it’s entirely gone. ..."

    Doesn't a black hole's entropy supposedly scale with its horizon's surface area?
    Does Verlinde's hypothesis have any effect on BH physics?
    Or would the BH be considered "vicinity of matter" and therefore have no volume-scaling entropy?

    -- TomH

  12. Professor R,

    I don't know what you mean. It is quite common that people propose models of which they haven't fully worked out all details and publish them so that other people can work on it too, if they are interested.

  13. Mars,

    No, because total matter/energy is not conserved in GR. It just isn't. It's not a conserved quantity. It's not. It is not conserved. What you have instead is a local conservation law for energy densities and pressure. You can't do GR without this conservation law - it's an assumption to derive the equations and always fulfilled.

  14. John,

    Well, yes, that's what I mean. Essentially it comes down to parameterizing the metric and source fields in a smart way so that you end up with equations that have known solutions. I've tried all the obvious parametrizations and ended up with intractable differential equations, so that's that.

    I haven't quite given up (I think it might be good to take apart the equations into two sets, one relating the stress-energy with the field, and one relating the stress-energy with the curvature, rather than the field directly with the curvature), but I have to wrap up some other projects before I can get back to this (you know how it goes, report deadline and so on). So I thought would put the paper on the arxiv and hope someone else takes an interest in it. Best,


  15. Adam,

    For all I can tell, it reproduces the black hole entropy. It's kind of a matching condition.

  16. Tam,

    GR works extremely well. Every theory that supposedly improves on it must be able to reproduce GR to very high precision. It is very hard to reproduce GR to high precision if you don't have general covariance. When you say "open to alternative approaches" what this really means is "open to approaches that we have good reason to think will not work." You're welcome to try, but I think it's a bad idea.

  17. Stuart,

    As I explain in my post (and in more detail in the paper), in the absence of matter the vector field generates a cosmological constant. That's the one and only form which the stress-energy tensor of the field can have that does *not* create a violation of Lorentz-invariance. In the presence of matter this will no longer be so, but then the matter defines a restframe and what you call "violation of Lorentz-invariance" is exactly what appears like dark matter (stuff dragging, essentially). At least that's how it should work. As I said, I don't actually know the solutions to the equations.

    I had a paragraph about this in the paper, but then thought it's obvious and scraped it. Now I think I should have kept it.



  18. GR by its very nature is background independent.This is because it's axiomatic principles assume spacetime is fundamental and not emergent. The solution you seek should therefore be based on the fundamental elements from which spacetime emerges according to the Emergent Gravity Paradigm which at large scales will reproduce GR.This approach is being pursued by t'Hooft, Liberati and others .In my opinion this approach is a dead end since it will inevitably lead to a case of "its turtles all the way down ".

  19. Stuart,

    What you say doesn't make sense. GR is background independent for what the equations are concerned. The solutions are of course not background independent - they *are* the background. (Which is why this whole issue of background independent is imo somewhat of a red herring.) Besides this, the model that Verlinde has proposed should be thought of as a low-energy effective theory. It is quite common that to obtain such limits one solves parts of the equations already and inserts the solutions into the Lagrangian, ie symmetries or background independence might be entirely non-obvious in such a limit. Best,


  20. Unknown,

    Well, to state the obvious, depends on what \alpha, \beta and \gamma are. More importantly though, note that this is *not* the term that appears in the Lagrangian - it appears in the Lagrangian with a power 3/2. In case that's what you mean, yes, in principle one should do a stability analysis but I'm not sure what one would learn from this without an interaction term. So I don't think it's the most pressing thing to look at. Best,


  21. It seems that 1702.04358 (see e.g. page 5) says alike 1702.04355 that the additional (over MOND) part with derivative in Verlinde gravity goes against observations.

  22. m-artins,

    In my blogpost I have explicitly explained what's wrong with the claims in these papers. Does your comment have any purpose other than demonstrating you didn't even care to read what I wrote before submitting a comment?

  23. Dear Bee,
    I probably missed what you mean; I got to those papers since I've read your post. You wrote about one of these papers (1702.04358, along with another one that I did not mention) that it is wrong since it deals with Solar system, too close to a star. The thing is that 1702.04358 deals with two different situations: i) galaxies, ii) Solar system. The galactic part should be relevant. And it finds discrepancy between Verlinde gravity and the observations. And the source of that discrepancy is the same as found in the 1702.04355 paper.

    If I look at it wrong --it may quite easily happen-- I'll be happy to read what is the right view.
    Thanks both for writing about this stuff and for replying to my comments.

  24. m-artins,

    Yes, one of the papers looks at two cases. The 'big' claim about solar systems is wrong as I said above. The one about galaxies is comparable to the other paper you mention, which is a tension with data. As I explain above, however, the equation in Verlinde's paper is missing an integration constant, so I don't think this means much.

  25. Some other layperson is bound to point this out eventually, so I might as well be the first: Verlinde's hypothesis sounds suspiciously like the "luminiferous aether".

  26. Jeff,

    You could say the same thing about particle dark matter.

  27. "This would be the case, for example, near of stars."

    near of stars ---> near stars

  28. "As we all know, DM and DE and inflation are all very ugly patches to GR to make it fit empirical data."

    Says who?

    GR says nothing about what the sources are; it says nothing about DM but also nothing about baryons. Ditto for DE which, in the form of the cosmological constant (which still fits all the data), has been around in GR for 100 years. As Weinberg says, Einstein's biggest blunder was really thinking that this was a blunder. GR says nothing about the curvature of space on cosmological scales. That the universe is very close to flat is an observational fact. To what extent this is "natural" is a different question. It follows naturally from inflation, though, and inflation explains things such as the isotropy problem for which there is no other credible explanation. It makes falsifiable predictions (e.g. the spectral index) which have been verified, long after they were made.

  29. Very interesting paper and blogpost!
    I stumbled upon this paper, that also dvelves into some of the theoretical aspects of Verlinde's theory, trying to account for the perceived discrepancies in the observations in the papers also cited in this post. From what i can tell (i'm not an expert) it still works inside Verlinde's framework and doesn't try to relate it to GR, but i found it interesting anyway. Being the methodology used in the two papers different i can't say if the two proposals (integration constant on one side and not universal entanglement entropy density on the other) could be related in some way. They doesn't seem to be at first look even if they try to solve similar issues, but, being the tools used in the two papers so different, i can't say for sure.

    There's also this paper that sits at the middle between astrophysical observations and theoretical physics and tries to make a first little step in making Verlinde's theory able to account for BAO (or at least, it highlights the problems with it). Again i can't say if the proposal made in the paper to find a mechanism to suppress the strenght of BAO signals in EG can be in some way related to the Covariant version of EG proposed here.
    Well, in this regard, it seems nowadays one can't even be sure about acquired and tested knowledge regarding some aspects of our universe
    i find all of this very exciting and i'm very grateful to the people spending their time trying to produce something new!

  30. Ch4rli,

    I had seen the first paper (but haven't had time to read it), but not the one from January - Thanks for pointing out!

  31. Nice summary of Verlinde's paper and your paper!But there could be a problem.I understand every field has a particle associated with it and your paper requires a new vector field. Then are you not back to the old problem that dark matter experimentalists cannot find a new particle? Is it possible that it is in condensed matter and HEP people will not find it? I do not quite understand but perhaps Verlinde's modification of GR does not require a new particle.

  32. Congratulations, to my limited understanding this seems like an important result!

  33. kashyap,

    Yes, this can generally be said about modified gravity approaches with additional fields, (and indeed I have said this myself several times elsewhere if only to point out the two ideas - modified gravity and particle dark matter - aren't as different as they are often portraied). In principle one should quantize the field and then it'd have particles associated with them. These particles would however look very different from the type of particles that are currently being looked for which are commonly assumed to couple with a strength comparable to the weak scale. Compared to gravity (at low energies) even the weak interaction is extremely strong.

    That is to say, I haven't really looked at the details and of course this should be done but I don't expect difficulties in this scenario to explain the non-detection of dark matter particles. Best,


  34. Hi Bee,

    What keeps φ (equation 2 in your paper) from becoming imaginary?


  35. Hi Sabine, we went back and forth on this issue (does GR actually work empirically?) a few months ago and you ended up in part agreeing with me, that it has serious issues. You stated: "GR is on all accounts a dramatically successful theory. The issues that I mention above are anomalies. All theories constantly have to struggle with anomalies. The big question is how seriously do you think they are? What I have, maybe not very successfully, tried to convey is that the current consensus is that they're not very serious. They're some puzzles. Most in the field think that we'll figure these out sooner or later. The cusp-core problem might be an issue of misunderstood energy flows. The dwarf galaxy issue really might not be one. The alignment of the satellites might merely be coincidence. The regularities in the galaxy rotation curves which I wrote about here are imo the toughest issue. I don't know any good explanation in terms of the concordance model."

    When we have galaxies showing up in our telescopes that require literally 99% DM to explain their rotations with GR I would suggest that we are far beyond " anomaly" range and well into "this theory has very serious issues" range. No?

  36. Jeff, see this. Einstein thought of space as a something rather than a nothing. See his 1920 Leyden Address: "Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether".

  37. Tam,

    Lots of physicists are looking for an answer to these puzzles. Isn't that sufficient evidence that they take it seriously?

  38. Arun,

    Excellent question. I don't know. Actually I treated 'u' as a complex vector field in my calculations, but (at least for the purposes of the present paper) it turned out to be unnecessary because the solutions were real valued, so I removed this added complication when I wrote the paper up.

    The phi itself, I think, should be real by definiton (easy enough to define it as the absolute value), but I see no reason why it shouldn't appear in 'u' together with a phase factor. You don't want a complex number to appear in the metric of course, so the coupling should go with uu^*/|u| in this case. Anyway my guess is that this will only matter for propagating modes. Best,


  39. Hello Sabine,

    Concerning the interpretation in your paper :

    "..improved interpretation of the underlying mechanism. It suggests that de-Sitter space is filled with a vector-field that couples to baryonic matter and, by dragging on it, creates an effect similar to dark matter."

    "In the vicinity of matter, the imposter field can condense. This reduces the volume of the
    imposter, causing the surrounding to push in, thereby dragging on the matter and creating an additional force."

    Are we to understand that this additional force upon matter, say a planet, serves as a substitute for the extra gravity caused by dark matter ?

    My remark here is of a conceptual nature.

    More force exerted upon the surface area of say planets is one thing, but how does that link to higher orbit velocities ?
    That would require higher gravitational accelerations also because they are linked. And this pushing force cannot explain you accelerating more when dropped from an aeroplane from higher altitude, it can only explain you having a hard time jumping away from the surface.

    Unless of course we start drifting away to Le Sage types of push gravity where 'stuff' obtains speeds to move you, not an option I believe, and certainly theoretical physicists either.

    The point is that if you want something to mimic dark matter with such extra force, it has to explain how more gravitational acceleration is obtained because without it, you can't have higher orbit velocities.

    So this pushback-force may very well be present but not as the actual dark matter impersonator.

    I think the key here is to interprest the compression (*) of that medium - I believe you called it condensation - consists of local increases of energy density of the field.

    (*) Van Spaendonck, K.M.L.L. (January 2017), Emergent Gravity from Discrete Geometry [ EG from DG ], Mol:
    K.M.L.L. Van Spaendonck, ISBN 9789402158601

    And then there's the question of how such a force would only be at work at cosmological distances and leave everything unchanged at shorter range.
    At the moment the interpretation of the mechanism seems to obtain the opposite effect :

    You speak of condensation close by, leaving GR intact (did i get that right, not sure), ok. But how then would less condensation at cosmological distances mimic dark matter if you need increased force there? This is the opposite effect i am speaking of.

    Best, Koen

  40. Koen,

    As I said it's an interpretation. I don't see the point of discussing it - I like math for a reason and the reason is that it doesn't matter what words you assign to the equations. If you want to use another interpretation, fine by me. Also, note that I explicitly wrote all the stuff about condensation etc isn't yet backed up by the equations.

  41. Hello Sabine,

    Thank you for responding. It was not intended as a criticism, but as a means to further open the discussion on novel approaches to emergent gravity. I believe in an integrated approach, meaning here that neither physical interpretation nor math is the most important component of a research method (along several other criteria). It is respecting both similtaneously which leads to progress because they influence each other as equally valued constraints, leading to more balanced - thus hopefully less and less wrong - hypotheses.

    Best, Koen

  42. Koen,

    I did not understand it as criticism, it's all fine by me really. I just meant to say personally I'm very much a math person - I don't trust words.

  43. Small correction : 'cosmological distances' should be replaced with 'larger distances e.g. galaxy outskirts', in the context of dark matter.

  44. Sabine, are you agreeing now that GR has issues that in fact being examined seriously by many physicists? If so, I would ask again why agreement with GR is your first line test for any alternative approach, as you write in your OP?

  45. Tam,

    I already answered this question above. GR works extremely well. Any theory trying to improve it must first reproduce its achievements. I understand that you don't want to believe this, but that's how it works. You find me any theory as good as GR that isn't GR and we can talk about doing something else.

  46. I'm again confused by your seemingly contradictory statements. How can you seriously say that GR works extremely well when it, for example, requires positing 99% dark matter (which we have never actually detected despite decades of trying) to explain the rotation of certain galaxies? And similar massive anomalies with respect to dark energy and inflation. These are all very ugly patches required to make GR "work extremely well."

    At what point do we all start saying things like "GR has some major anomalies that cast serious doubt on its validity as our best theory of gravity," instead of the trope you and others repeat about GR being an excellent theory despite these massive anomalies?

    Moffatt's modified gravity, as an example, claims to be a far better fit to the empirical facts and without all of the epicycles.

  47. Tam,

    It doesn't make sense to attempt to quantify how 'well' a theory works by the amount of stuff that it describes. I told you that before. It's a meaningless number. Yes, that's what Moffatt claims of his theory, but it's a claim and it's a not an accepted claim. Show me it gets the CMB right and explain how to select the 'right' solution for galaxy clusters or solar systems.

    I don't care what you think is 'ugly' much like I don't care what some scientists think is 'pretty'. It works, and for what I am concerned that's all that matters.

  48. How can you seriously say that GR works extremely well when it, for example, requires positing 99% dark matter (which we have never actually detected despite decades of trying) to explain the rotation of certain galaxies? And similar massive anomalies with respect to dark energy and inflation. These are all very ugly patches required to make GR "work extremely well."

    See my comment above.

    GR says absolutely nothing about sources. What do you expect? That GR says "these baryons exist, and here are their masses and number densities"?

    As to alternative theories, if all they do is explain known facts, then they are not falsifiable.

  49. Hi Sabine,

    I want to react to your response to Phillip Helbig. GR says nothing about the sources, all right. But it states that there is a source. So I agree with Phillip when he states that 99% of the source terms is ugly patch - though I would rather name this oversold fairy tales. When I read "A galaxy (namely Dragonfly 44) is composed of 98% dark matter" (not on this blog but I think in the original paper), I cannot understand that it is not necessarily "dark matter particles".

    Right now what I see is that physicists have a choice between modified gravity and dark matter particles - if memory serves, this is what you wrote - and both are incredibly difficult to prove. I think both are wrong, because a source term can be stress; and if you recall the reference I gave you some time ago, it is fairly obvious to compute the stress given by dark energy - it fits perfectly with the measured DM density.

    As for your last sentence, if there is a way to compute exactly the DM density from the DE density, this is not falsifiable. (In fact in the paper I refer to, both are computed from the universe age).


  50. Hi Sabine, you have with your statement that you "don't care" if patches to GR are ugly entirely eliminated the possibility of falsifying GR. That, of course, is patently unscientific.

    When literally 99.9% of a galaxy must be conjured up as DM in order to explain its dynamics we have gone well into the realm of unfalsifiable epicycles, no? How can you argue with a straight face that GR works "extremely well" in the face of these manifest examples of it NOT working well at all?

    More generally, what are your criteria for a theory to work "extremely well" if it's not about explaining "the amount of stuff that it describes"? Are you suggesting that good theories shouldn't be about explaining or predicting observations? I'm quite sure that's not what you mean but it appears that this is what you wrote above!

    As for getting the CMB right, do you think that GR gets it right? Based on GR and LCDM cosmology the CMB should be entirely homogeneous, but it's not at all homogeneous, as we know now.

  51. Philip, GR is a theory of gravity, of how observable mass behaves. As such, arguing that it is unaffected by problems like the Dragonfly galaxy, and it's supposed 99.9% of DM to explain observations, is more than a little absurd. Oh, it's a theory of gravity that can't explain 99.9% of observations unless we add other massive (in all senses of this term) to our universe, "by hand"? Ah, yes, that makes sense....

    GR is the heart of our cosmology today, but the parade of horribles now required to make GR "work" in this manner are indeed horrible, including inflation, which you cite. Have you seen Steinhardt's critiques of inflation and alleged empirical support for some version of inflation? He argues strongly that we should view Planck data as disconfirming, not supportive.

  52. Tam,

    Uhm, let me see. You comment here on a paper I just wrote that, erm, proposes a modification of general relativity that does away with particle dark matter but you complain that I'm too narrowminded to ever consider maybe general relativity should be modified. Ok, then. It happens all the time that commenters here build a strawman of my alleged opinions which they then attempt to tear down, but you certainly excel at this.

    You also misunderstood the point of my above comment that I don't care if you think something is an 'ugly patch'. I generally don't care about aesthetic considerations and if you think that I am the one being unscientific you should look up scientific method.

  53. Let me return to the more basic questions, since I note that you didn't respond substantively to any of my questions. I do value your responses and your taking the time to respond further here, so let me ask you more specifically: if GR can incorporate major add-ons like DM, DE and inflation in order to "make it work" with observations, how can we falsify GR? Again, the iconic Dragonfly galaxy, with 99.9% DM required to explain its motions, highlights this very real problem. When would GR be considered falsified if the game we continue to play is just to keep adding decorations to the GR Christmas tree in order to make it work empirically?

  54. Tam,

    I'm getting quite tired of this. Both I and Phillip have repeatedly explained that you are *wrong* to claim that dark matter and dark energy are 'add ons' to General Relativity. General Relativity does not tell you anything about the sources (other than that stress-energy is conserved). The types of sources that are necessary to get something that behaves like dark matter and dark energy are the simplest and most straight-forward types of sources one can have. That we do not have a microscopic theory for dark matter and dark energy is a sore point, and it's one that many physicists work on, but it's not a problem for GR. How do you falsify GR? Find deviations in any of the numerous precision tests - but none have been found. I understand you don't like to hear it, but as I said, GR works dramatically well.

    Unless I get the impression you think about what we are trying to tell you I'll not approve further comments on this, it seems a waste of time.

  55. What precision tests of GR are you referring to?

  56. Cliff Will's Was Einstein Right is a good starting point. Will has authored several reviews over the years comparing predictions of GR to observation.

  57. Thanks Philip, but I was asking Bee about the specific precision tests of GR that she thinks would be able to falsify GR if they returned negative results. Again, my point that it seems clear to me that GR has acquired the status of an unfalsifiable theory, in principle, b/c any cosmological or empirical results that seem to cast doubt on GR simply lead to new patches/epicycles, rather than considering that the theory itself may need some serious revisions. Saying that GR doesn't say anything about "sources" is simply a dodge to render the theory unfalsifiable, in my view. Of course, GR was proposed specifically as a theory about the nature of matter, energy, space and time and was meant to be able to explain observables in the universe around us. And yet it hasn't done that in many cases now, hence the patches of DM, DE and inflation. DM is proposed solely b/c GR couldn't explain observed anomalies, and yet now we are at a point where we can't argue (according to you and Bee) that such failures should reflect negatively on GR itself. This is a major problem to those who aren't wedded a priori to GR being the final theory of gravity.

  58. Tam: GR is one of the best-tested theories we've got, and it handles "dark matter" just fine. The problem isn't with GR, it's with other theories about WIMPs and inflation etc that haven't been tested at all.

  59. Tam,

    Sorry for not adding a reference, I just saw that jonduffield (comment above) beat me to it - this was the exact review I had on mind. Even if you don't have the time for such a long review, Googling "precision tests of general relativity" should help.

  60. Hello Sabine,

    I've been looking into the paper above with GR tests. I could not find the Hafele-Keating experiment on Special Relativity.

    Concerning the verification of the existence of a locally preferred frame, this is however a pretty important test, aside from testing the sheer quantitative validity of the gravitational and kinetic time dilatation factors. Nobody could disagree on the latter, but the former - as a preferred frame test - does give surprising results :

    * C = control tower clock at earth surface
    * A = clock A flying east at speed v
    * B = clock B flying west at speed v
    * E = earth centered inertial frame located at the center of the earth

    •Using sheer SR:

    Viewed from C, A and B should indicate the exact same time on the clocks (same relative velocity used), thus differing both with the exact same amount from C.
    The experiment clearly shows this is not the case : 1 clock gained seconds, the other lost seconds compared to C.

    • Using the ECI as a locally preferred frame, you add up the speed of A to C, and you substract the speed of B from C, yielding the differing times on the clocks as experimentally established.

    An undisputable assessment for the preferred frame approach.

    Now, one might argue that SR is not suitable for rotating frame setups, but then of course you disqualify SR as the theory to explain the clock times of events as banal as airplanes taking of and landing 24/7 all over the world.

    One cannot ignore these results.

    Now, one might wonder why particle accelerators do not feature this prob lem, and give correct predictions concerning kinetic time dilatation, or the related relativistic mass increase predictions.

    Consider a particle accelerator on the equator shooting particles east and west, to get a nice parallel to the HK-setup:
    This is of course due to the relativistic speeds in contrast with the every day speeds of the airplane clocks. Meaning that the prediction discrepancy is extremely small because c plus earth orbit speed or c minus earth orbit speed is practically speaking the same value.

    Having said that,
    I would like to reconnect to the subject of your post :

    The fact that HK proves the necessity and existence of a locally preferred frame to get the predictions right, is of course excellent news for emergent gravity scenario's, if we are to hypothesize on microdynamic physical processes at the subemergent basis of the emergent theory of GR.

    None of this will diminish the validity of GR within certain boundaries, just as nobody will be able to dispose of Newton's theory just because GR came along.

    Facing the facts however, of the HK-experiment, is an important step towards a theory which could generalize GR, because it lifts what was assumed to be a strong contradiction or a big problem.

    Note that I am not the only one who concluded the same things on HK.It's not exactly a miraculous finding either, it is clear to anyone who is willing to spend an hour of critical analysis on the matter.

    Note however, that this does not mean we have to conclude that Lorentz's eather theory was right. He was only right on the preferred frame issue and the correctness of the Lorentz factor, but he was dead wrong of course when assuming light could be slowed down by some kind of aether. The correct physical interpretation is as yet unknown.

    Best, Koen

  61. A small correction on the particle accelerator velocities there :
    e.g. earth orbit speed + 0.9c. and earth orbit speed - 0.9c would be the more accurate comparison, yielding practically speaking no significant difference for the relativistic mass increases.

  62. "I could not find the Hafele-Keating experiment on Special Relativity."

    Suffice it to say that if anything were wrong with GR at this level then GPS would not work.

  63. @Tam Hunt: You have a serious misunderstanding about what a scientific theory is. Your history is off as well. GR is probably the best example of a theory which was not constructed to explain observations. Of course, it does explain observations, makes testable predictions which have been confirmed, etc---otherwise it wouldn't be a scientific theory. When a reporter asked Einstein what would have happened had an observation not confirmed his theory, he joked that he would feel sorry for God because the theory is right. :-) That says it all.

    Look at the famous Hulse-Taylor binary pulsar, which was observed decades after GR was formulated. Look at the precision between theory and observation. Had they been different, GR would have been falsified.

    The fact that Einstein didn't know about all of the constituents of the universe says nothing about GR. Claiming that it does is like saying that Linnaeus's binomial nomenclature is flawed because it didn't predict the existence of gorillas.

    Yes, there is give and take between theory and observation. But no observation has led to a change in the structure of GR. Why would "dark matter" be a change to GR since GR doesn't even mention baryons?

  64. @Phillip Helbig

    "Suffice it to say that if anything were wrong with GR at this level then GPS would not work"

    >The gps-sattelite orbitting one way cannot say anything about a locally preferred frame, it only confirms the time dilatation factor quantitatively (*), as i explained above.
    It would take - hypothetically of course.. - a sattelite orbitting the other way, in which case predictions for corrections made from the ground frame, would be wrong, because they would predict no change compared to the former.
    The difference only shows up correctly for the case, if and only if you use the ECI, completely analogical to the HK-experiment setup, where an airplane clock is able able to orbit the other way.

    Best, Koen

    (*) Special and general relativity predict that the clocks on the GPS satellites would be seen by the Earth's observers to run 38 microseconds faster per day than the clocks on the Earth. The GPS calculated positions would quickly drift into error, accumulating to 10 kilometers per day. The relativistic time effect of the GPS clocks running faster than the clocks on earth was corrected for in the design of the GPS (Wikipedia)

  65. Phillip, Tam,

    I think I should add that Tam has now submitted two long comments which I didn't approve because they merely repeat (with many words) the questions that have now been answered by various people.

  66. @KVS: Non-inertiality is commonly called, alike in the twin case. Anyway, see this proposal.

    @Bee: Regarding VG vs. FLRW metric, do you mean something similar to Schwarzschild solution vs. FLRW? A quick search for that gives gr-qc/0307006, 0812.3740, 1503.08803, 1607.08219, etc.

  67. m-artins,

    It's a vector field, not a scalar field, so JNW won't help. Also, it's got a very unusual power of the kinetic term, so I doubt any solution that is in the literature will 'coincidentally' fit.

    There are two solutions that are missing:

    a) Spherically symmetric with the massive vector field (asymptoting to dS), preferably for a density distribution (of baryonic matter) but for starters a point mass would do.

    b) Homegeneous with both the massive vector field and baryonic matter. Problem here: The stress-energy tensors aren't separately conserved (as is often assumed in the cosmological setting).



  68. It's mentioned on page 8 of your paper that the "imposter field" can "condense" in the vicinity of matter, (galaxy scale, I think is implied), with a resultant local decrease in the volume of this field, so that the field outside the galaxy "pushes in" and "drags" on the matter, mimicking dark matter, if I'm interpreting it correctly. When the density of matter is even greater, (solar system scale), the imposter field can enter a "superfluid phase", "and the friction with normal matter is basically zero", recovering the dynamics of general relativity.

    I don't fully understand all the aspects of a Bose-Einstein condensate, beyond the fact that most of its constituents have attained the lowest possible quantum state. But I thought that there was some interactions occuring between the constituents of a BEC in order for it to achieve macroscopic quantum behavior. So, my question is would a condensate 100,000 light years across pose a problem with interactions of its constituents when it takes thousands, and tens of thousands, of years for signals to propagate between them?

  69. David,

    It's a good question, but I don't know the answer. Roughly speaking, the whole ansatz assumes some kind of equilibrium condition already, but clearly that assumption already would require a justification. For this you'd need not only an interaction term but also at least an estimate of the time-dependence and - as the phrase goes - it's beyond the scope of this current work. (The paragraph you refer to has actually very little to do with my paper - it's merely a reinterpretation of what's in Verlinde's paper.) To put it differently: One has to start somewhere. Best,


  70. More news incoming: kinda Aether Redux?

  71. @Koenraad Van Spaendonck

    I don't follow your argument for locally preferred frames. You mention rotating frames then dismiss it's relevance on the grounds that it disqualifies SR. It no more disqualifies SR than GR disqualifies SR. We also know that a rotating frame is an accelerated frame. Which is absolute except in degree. So those effects must be accounted for in order to know whether the SR effects are also properly accounted for. So modeling requires combined SR and GR effects. But you seem to be presuming that that GR effects layered with SR effects must depend only on SR to model, else SR requires a locally preferred frame. Simply not so because the GR effects layered in the outcome, along with SR effects, means that both (not SR alone) must be properly accounted for to model that outcome. It would be like boosting a rocket with two engines pointed in different directions and insisting that the boosting effects must only be modeled by the thrust of one of the engines.

    In particular the westerly traveling plane is going to be accelerated less than the tower clock, while the easterly flying plane will be accelerated more. Just like a person running in the opposite direction of a merry go round, while on that merry go round, will experience less acceleration than the person just riding the merry go round. The person running in the same direction as the merry go round while on it will experience even more acceleration. Acceleration is a GR effect which SR by definition doesn't account for. Yet your description seems to insist that SR and SR alone must account for everything or else SR requires a locally preferred frame. Which simply doesn't follow. To properly model the situation you described requires a proper modeling of both SR and GR, not just SR. The use of the center of the Earth as an approximate inertial frame does not convert either the planes or the clock tower to an inertial frame. They could have just as well used any arbitrary inertial frame and got different predictions and outcomes that agreed just as well with those predictions. The source you provided explains all of this. If it was somehow wrong to claim SR doesn't contain a locally preferred inertial frame then how did they get the prediction right to begin with? Because they weren't dealing with an inertial frame even when they chose an arbitrary approximate inertial frame to base there calculations on.

    Something else to note is that two distinct inertial frames can nonetheless define simultaneity quiet differently. Which one you choose to represent "proper time" is completely arbitrary. Just because they chose one inertial frame to represent "proper time" does not make it a "locally preferred frame." Even when it effects the predicted numbers.

  72. My_wan,

    I certainly appreciate your elaborate explanations.
    But the thing is that to make the correct predictions in the context discussed, you need only the Lorentzfactor and a locally preferred frame, in this case the ECI, and as you called it: the principle of the merry-go-round. No SR is needed and no GR needed, no discussions on inertial or non inertial frames needed etc.

    And these simple assumptions even make more accurate predictions for particle accelerators than SR does, as I indicated by the fact of the neglectibly small orbit velocity of the earth compared to the particle velocities near the speed of light.

    As far as GR is concerned, to say it has to be involved, means in this context talking about spacial curvature , due to the presence of the spherical earth. And that calls for radius r. And that calls for the ECI because without assuming that location, you cannot determine radius, hence not determine spacial curvature.

    So this locally preferred frame, ECI in this case, is structurally embedded in GR from the start.

    Conclusion: still only 3 tools needed in the context of the rotating frame setup, all pre-Einstein (*). And a theory with less assumptions should prevail.

    (*): We also don't need gravitational time dilatation, because that was only needed because of the height difference between the earth control tower and the airplanes, and I don't need the tower clock to determine the difference between the 2 airplane clocks, the ECI does that for me.

    Needless to say that I appreciate the great insights that GR brought us. And it is not a question of wrong here, but of the fewer assumptions the better.

    Given the reality of the locally preferred frame, we should reconsider the mechanisms or principles at hand for energy conservation. The Noether theorem states: IF there is a symmetry THEN there is conservation of energy, nothing wrong with that, except where is the symmetry in the experimental reality here, as opposed to the theoretical formulation? But that discussion would take us to far here I presume.

    Best, Koenraad

  73. Sabine, can you make available the Maple worksheet again in order for me to better understand the equations? I'm mainly interested in the Cosmological solutions. In Eqs. (28)-(29) T stands only for normal matter? You have assumed T=0 before, neglecting baryons.


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