Dark Matter: Just Fine, Thanks

By Sean Carroll | February 26, 2011 2:07 pm

Astrophysical ambulance-chasers everywhere got a bit excited this week, and why wouldn’t they? Here are some of the headlines we read:

Wow. More evidence against dark matter? I didn’t know about the original evidence.

Sadly (and I mean that — see below) there is no evidence against dark matter here. These items were sparked by a paper and a press release from Maryland astronomer Stacy McGaugh, with the rather more modest titles “A Novel Test of the Modified Newtonian Dynamics with Gas Rich Galaxies” and “Gas rich galaxies confirm prediction of modified gravity theory,” respectively.

I’m the first person to defend journalists against unfair attacks, and we all know that headlines are usually not written by the people who write the actual articles. But we can legitimately point fingers at a flawed system at work here: these articles are a tiny but very clear example of what is wrong wrong wrong about our current model for informing the public about science.

McGaugh’s new paper doesn’t give any evidence at all against dark matter. What it does is to claim that an alternative theory — MOND, which replaces dark matter with a modification of Newtonian dynamics — provides a good fit to a certain class of gas-rich galaxies. That’s an interesting result! Just not the result the headlines would have you believe.

It’s obvious what happens here. Nobody would read an article entitled “Gas rich galaxies confirm prediction of modified gravity theory” — or at least, most editors doubtless feel, fewer people would be interested in that than in evidence that went directly against dark matter. So let’s just spice up the story a bit by highlighting the most dramatic possible conclusion we can imagine drawing, and burying the caveats until the end. Net result: a few more people read the articles than otherwise would have, while many more people just read the headlines and are left with less understanding of modern cosmology than they started with. Scientists and journalists together have a responsibility to do a better job than this at making things clear, not just making things sound exciting.

But let me take this opportunity to lay out the problems with MOND. It’s a very clever idea, to start. In galaxies, dark matter seems to become important only when the force of gravity is not very strong. So maybe Newton’s famous inverse-square law, which tells us how the force of gravity falls off as a function of distance, needs to be modified when gravity is very weak. Miraculously, this simple idea does a really good job at accounting for the dynamics of galaxies, including — as this new result confirms — types of galaxies that weren’t yet observed back in 1983 when Mordehai Milgrom proposed the idea. Whether or not MOND is “true” as a replacement for dark matter, its phenomenological success at accounting for features of galaxies needs to be explained by whatever theory is true.

Which is an important point, because MOND is not true. That’s not an absolute statement; among its other shortcomings, MOND is not completely well-defined, so there’s a surprising amount of wriggle room available in fitting a variety of different observations. But to the vast majority of cosmologists, we have long since passed the point where MOND should be given up as a fundamental replacement for dark matter — it was a good idea that didn’t work. It happens sometimes. That’s not to say that gravity isn’t somehow modified in cosmology — you can always have very subtle effects that have yet to be discovered, and that’s a possibility well worth considering. But dark matter is real; any modification is on top of it, not instead of it.

Let’s look at the record:

  • MOND is ugly. Actually, that’s very generous. More accurately, MOND is not a theory; it’s only a phenomenological rule that’s supposed to apply in a limited regime. The question is, what is the more general theory? Jacob Bekenstein, in an heroic bit of theorizing, came up with his Tensor-Vector-Scalar (TeVeS) theory, which hopefully reduces to MOND in the appropriate limits. Here is the action for general relativity:

    And here is the action for TeVeS:

    Don’t worry about what it all means; the point is that the theory underlying MOND isn’t really simple at all, it’s an ungodly concatenation of random fields interacting in highly-specific but seemingly arbitrary ways. That doesn’t mean it’s not true, but the theory certainly doesn’t win any points for elegance.
  • MOND doesn’t fit clusters. Long ago, rotation curves of galaxies were the strongest evidence in favor of dark matter. Very long ago. We know better now, and a mature theory has a lot more hoops it needs to jump through. The nice thing about MOND is that, despite the ugliness above, when you get down to making predictions for large astrophysical objects, there really isn’t any wriggle room: you fit the data or you don’t. It works for galaxies, but when it comes to clusters — you don’t. Not close. Proponents of MOND understand this, of course, and they’ve come up with a clever workaround. It’s called “dark matter.” That’s right — even MOND’s biggest supporters admit that you need dark matter to explain galaxies. Let’s just emphasize that for those who find all this text kind of tedious:

    Even with MOND, you still need dark matter.

    Some people try to claim that the necessary dark matter could be neutrinos rather than some brand-new particle, and that’s supposed to be morally superior somehow. But there’s no two ways around the conclusion that dark matter is real.

  • MOND doesn’t even fit all galaxies. For almost twenty years now we’ve known that MOND fails for a certain type of galaxies known as “dwarf spheroidals.” These are small (thus the name) and hard to observe, so MONDians have come up with various schemes to explain away particular galaxies. That might even be okay — nobody said fitting the data would always be easy, even in the correct theory — except that it’s precisely this kind of extra work that is being scoffed at in the case of dark matter in these recent news items.
  • Gravity doesn’t always point in the direction of where the ordinary matter is. This is the lesson of the famous Bullet Cluster (and related observations). The evidence from gravitational lensing is absolutely unambiguous: to fit the data, you need to do better than just modifying the strength of Newtonian gravity. Once again, people try to wriggle out of this in TeVeS and other MONDian approaches. However, the way they do it is by imagining that other fields have energy, which warps spacetime, and therefore a gravitational field. We have a useful phrase to describe new fields whose energy warps spacetime: “dark matter.” MOND-like theories don’t replace dark matter so much as they make it much more complicated.
  • MOND doesn’t fit the cosmic microwave background. Saving my favorite for last. One of the coolest things about the temperature anisotropies in the cosmic microwave background is that they are sensitive to the existence of dark matter. In the early universe, dark matter just collapses under the pull of gravity, while ordinary matter also feels pressure, and therefore oscillates. As a result, the two components are out of phase in the even-numbered peaks in the CMB spectrum. In English: dark matter pushes up the first and third peak in the graph below, while suppressing the second and fourth peak. That would be extremely hard to mimic in a theory without dark matter; indeed, this was predicted before the third peak was precisely measured. But now it has been. And…

    See that dotted line? That’s the theory with dark matter, fitting all the data. See the solid line? That’s the MOND (really TeVeS) prediction, definitively inconsistent with the data. Can some clever theorist tweak things so that there’s a MOND version that actually fits? Probably. Or we could just accept what the data are telling us.

Having said all that, I’m glad that some people are still thinking about MOND-like approaches. You can still learn interesting things about galaxies, even if you’re not discovering a new law of nature. And dark matter, to be honest, isn’t established with 100% certainty; it’s really more like 99.9% certainty, and you never know.

What’s less admirable is people (mostly outside the professional community, but not all) hanging onto a theory because they want to believe it, no matter what new information comes along. Personally, I think it would be much cooler if gravity were modified, compared to the idea that it’s just some dumb new particle out there. I’ve put some thought into the prospect myself, which helped lead to some productive research ideas. But ultimately the universe doesn’t care what I prefer. Dark matter is real — gravity could also be modified, but there’s no reasonable doubt about the dark matter. So let’s try to figure it out.

  • http://home.uchicago.edu/~sgralla Sam Gralla

    I thought the more interesting thing about that paper was the claim that CDM doesn’t reproduce the data without some extremely weird fine tuning of the mass to light ratio of the galaxies. At least I think that was the claim. I don’t have the paper in front of me.

  • joe

    Is the wriggle room filled with gum?

  • Ben

    Sean, everything that you say here is right, dark matter *DOES* exist, and even most MOND proponents fully agree with this. It might however depend on what dark matter precisely means. But what most MOND proponents try to say is “In spiral galaxies, MOND is right as a scaling relation, whatever dark matter is. And that IS right, and that IS amazing.” … What can be shocking for people working on galaxies is that cosmologists seem to deliberately ignore this fact, because they do not care about the details of messy astronomical systems such as galaxies… And this might be a big mistake. In short, as you say yourself, but as should sometimes be emphasized more, what the success of MOND might tell us about the nature of dark matter might really be fundamental… And how much you think the latter sentence is true depends on how far away from the galactic scale your main research interests lie. What strikes me is that when people say “MOND is wrong” or “MOND is right”, they dont necessarily mean the same thing, because some think it is a synonym for TeVeS (the equations you showed hereabove), and those people are mostly *NOT* working on galaxies (and obviously they are mostly finding problems with the whole modified gravity approach), while some others (mostly working on galaxies) just think it is the most awesome scaling relation to date, summarizing almost all scaling relations of both spiral and elliptical galaxies, let alone dwarf spheroidals, but including tidal dwarf galaxies that are much less well understood in the CDM context. And they simply think: “It works too well to be meaningless”. Again, this absolutely doesnt mean “dark matter doesnt exist”. There is a big difference between believing in dark matter, and believing in the current LambdaCDM model. As a conclusion, as Stacy points out, the success of MOND is just a huge fine-tuning problem that we need to understand, as there are many in physics. The problem right now is the vast majority of astronomers and cosmologists *completely* (and often deliberately) ignoring this fine-tuning problem just because they fear that they could give the wrong impression about what we actually know and what we actually dont. And that is, I think, not right. And that is why, for me, Stacy is right to point out what he does point out.

  • Jake

    To be fair to the reporters the author seems to argue pretty hard for MOND over Dark Matter in the paper. For example claiming that the bullet cluster supports MOND “with equal vigor” as it does Dark matter. It seems to me (in my very non expert opinion) the easy solution would be to assume dark mater distributions are different in galaxies where the mass is dominated by gas instead of stars. I wouldn’t really consider that fine tuning.

  • Shantanu

    do you think both MOND and lambdacdm are right? This is the pov advocated by Luc Blanchet
    starting with this paper.
    Somehow I don’t think these series of papers have been on the radar of cosmologists

  • Sili

    I saw the BBC piece and swore at it when I got to the end without seeing any mention of the Bullet Cluster. Bloody waste of time.

  • http://www.theeternaluniverse.com Joseph Smidt


    What a great write up! This is hands down the best written critique of MOND I have ever seen. I’ve known MOND has issues but I’ve never seen them written up so well. Thanks.

  • Cosmonut

    This is off-topic, but:
    Which is an important point, because MOND is not true. That’s not an absolute statement; among its other shortcomings, MOND is not completely well-defined, so there’s a surprising amount of wriggle room available in fitting a variety of different observations.

    Does that (especially the second sentence), also describe the state of String Theory today ?
    Not trying to ask rhetorical questions, just genuinely curious.

    Great write-up on MOND. I knew the theory was ugly, but actually seeing the action was a revelation.

  • Valatan

    Bekenstein claims that the coupling of the vector particle is chosen specifically to make the galactic cluster observations work out. Otherwise, according to him, you just need the scalar particle.

  • dg

    Thanks Sean. I often come back to your explanations when I need a refresher on the full case for dark matter. Actually, for the benefit of everyone else, here’s a very nice talk where you explain the same thing:


  • http://bearspace.baylor.edu/VH_Satheeshkumar/www/ V H Satheeshkumar

    Great contribution to the public understanding of science. I also recall a similar article you wrote in Nature many years ago. I wonder if you too received similar headlines (Sean Carroll Kills Dark Energy) when you wrote that paper on modified gravity accounting for the cosmic acceleration?

    On a lighter note, I am sure Fritz Zwicky would have called those journalists ‘spherical bastards’!

  • Shantanu

    Sili, The buller cluster also presents problems for Lambda -CDM.
    See this

  • aa

    the action for GR is very nice, but we also know GR is wrong/incomplete.

  • publius

    Great post, thank you for making the issue crystal clear.
    just a detail: it seems that the tilde over g in the Einstein-Hilbert action should not be there

  • Capt. Galectro

    Dark matter does not exist people. It’s most matter, but gee we can’t detect it . Common sense people, common logic tells you something else is in play. What is in play is that all light from all galaxies is bent by the space-time warp of gravity. What we see, what we detect is all an illusion. http://bigbangabust.thecomicseries.com

  • David George

    In your graph of the angular power spectrum of the CMB anisotropy, the left side of the graph is missing(90 degree anisotropy). In other reproductions of this graph, that “low l” is usually there, but it shows a data point that is not even within the range of “cosmic variance” (according to NASA, “cosmic variance” is “a measure of how likely random chance of our position relative to other matter in the universe is affecting the results”). It is too low even for random chance! But it is not on your graph. I can only assume you intentionally took it out. I seem to recall some years ago when the WMAP results came out, you said the task is to find the missing — (electrons?). Since the “low l” deficit is not shown, I imagine the “anomaly” remains unexplained. (I am not a physicist.)

    Is suppression of unwanted data on a public website such a great contribution to public understanding of science? It seems to me you are promoting some agenda – for example, “Big Bang cosmology is on the right track!”.

    As for “dark matter”, that label gives the impression that there is some matter that moves only according to gravitational influence, and so does not radiate light. Even though you would prefer some modification of theory, you say, “dark matter is real”. But it seems to me (I am not a physicist) that what is real is anomalous motion. So a more accurate phrase than “dark matter” would be “anomalous motion for which we have no explanation”. And what is alive and well is the lack of an explanation for the anomalous motion. But maybe public understanding of the progress of Big Bang cosmology would be harder to come by with such a longwinded phrase, so “Dark Matter” — that’s the ticket!

  • http://www.astro.umd.edu/~ssm/mond/ Stacy McGaugh

    Hi Sean,
    Thanks for noticing.

    I agree with much of what you have to say, but certainly not all.

    For example, I agree about the third peak of the CMB power spectrum. But you neglect to mention that I was the only person to correctly predict the amplitude of the second peak. That the third peak is high simply means ΛCDM survives this test, not that MOND fails it. For as you say, we need a proper covariant theory to do that, and it is not yet clear what that is, or indeed, if it is even possible to construct.

    The success of ΛCDM for the CMB hardly guarantees its success in galaxies. It too has its problems in dwarf spheroidals. The data in the particular paper you cite were really rather ambiguous. MOND does poorly in two cases (Draco and Ursa Minor) but does pretty well in the other five cases. So which is the forest, and which are the trees?

    More recently, I’ve looked into this very subject with Joe Wolf. The new “ultrafaint” dwarfs are much worse for MOND than Draco and Ursa Minor. I was ready to declare MOND dead myself because of this. Then I thought I should check the literature one last time, and discovered that Brada & Milgrom had in fact discussed how tidal effects (which are stronger in MOND) could plausibly cause the failing Joe and I were seeing. Indeed, they quantified the point at which the apparent failure should set in, and we found that is exactly where it does set in. So what I initially thought was a clear falsification is not.

    As for the press, it is a curious spin. In my initial submission to PRL all I said was “here is a specific prediction of a hypothesis, MOND, and geez, it works surprisingly well.” It wasn’t just the reporters who asked about the implications for dark matter, it was also (quite reasonably) the referees. As Ben notes above, that MOND works even to the extent it does poses a fine-tuning problem for dark matter models.

    Much of the evidence that we often point to for dark matter is ambiguous. More properly, we should say there is clear evidence for mass discrepancies. What you see plus Newton does not explain the data. So either there is dark matter, or we need to modify Newton. Like yourself and many other scientists, I am more comfortable with the former approach. I have noticed, however, that the universe does not seem too concerned about my personal comfort zone. If it were, it would stop handing me results that have MOND written all over them just as clearly as you say the CMB has dark matter written all over it.

    If we’re right about dark matter, why does MOND get any prediction right at all?
    I’m open to an explanation for this in the conventional context. Indeed, I have spent an enormous amount of my research time trying to come up with one myself. So far I have failed. That doesn’t mean it is impossible, but I can say it is a lot harder than most scientists seem to realize. Usually people invoke “feedback,” but this has become a code word for excusing anything we don’t understand. (Remember step 2 of that old cartoon “then a miracle occurs”?) Maybe it will. But please forgive me if I require a somewhat higher standard of proof than faith that what works at cosmological scales must inevitably work for galaxies.

    Indeed, you mention that it is not admirable to “hang onto a theory because [you] want to believe it.” I could not agree more! We must hold ourselves to very high standards of intellectual honesty. That’s how I got involved in this issue in the first place. I believed in cold dark matter as much as you obviously do. But MOND cropped up in my data. Should I deny that? Should I not report it?

    What I should do is consider the other evidence. I was already familiar with dark matter, but I had to learn a lot about MOND. I have. I’ve written lengthy reviews about it, long ago addressing many of the points above – though not always favorably to either theory. I can tell the story from either side, both positive and negative, warts and all. Indeed, I decided that to be fair, I had to work as hard on behalf of MOND as I work on behalf of ΛCDM.

    Have you tried that?

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Hi Stacy–

    Thanks for responding. I’m not sure what it means to “work on behalf” of a theory. I’ve certainly tried to be as fair as I can be in evaluating the theories. But I haven’t spent as much time thinking about MOND as I have thinking about dark matter, since one theory is ruled out by the data and the other is not.

    I’m very happy to point to the circumstances in which the MOND phenomenology is successful, and argue that we should try to understand it. People are working on that. But the time is long past when we should take seriously the idea that MOND replaces dark matter. It’s the implication otherwise in the news stories that I was objecting to.

    Nobody says you shouldn’t report on what you find; that’s just a straw man.

    It would have been great if, in your press release, there had been something along the lines of “of course we have more than sufficient evidence to conclude that dark matter exists, we’re just trying to understand how it works and what else might be going on.”

  • onymous

    Is there any nice place for a particle physicist without a lot of astrophysics background to read a little about the “fine-tuning problem” that some in this thread claim that MOND phenomenology poses for dark matter models? This has something to do with the physics of galaxy formation, right? Naively I would think that different kinds of plausible dark matter (WIMPs, axions, gravitinos, etc) could have different effects on galaxy formation, and that surely people would have tried to study this and see if consistency with “MOND phenomenology” (meaning, what, things like the Tully-Fisher relation?) prefers some models over others. But if such things exist, it at least doesn’t seem to be part of the folklore among particle physicists. Can it really be the case that any realistic dark matter candidate (regardless of mass, interactions, etc) is equally tuned with respect to the phenomenological facts that fit MOND?

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    onymous — Roughly speaking, most viable DM models are astrophysically equivalent. They’re cold, they’re non-interacting, and their perturbations are adiabatic. As far as galaxy formation and dynamics are concerned, they’re indistinguishable.

    The “fine-tuning problems” are (perfectly reasonable) questions about the relationship between the dark matter distribution and the baryon distribution. They have nothing to do with particle properties.

    Of course you can consider interacting dark matter models as well, but they’re less minimal, and the evidence in favor of them is sketchy. (It’s very likely that DM has some non-gravitational interactions, but they may or may not be relevant for astrophysics.)

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  • Shantanu

    onymous, see this paper. esp figure 4 (and also fig2)
    Also the only papers which discuss about differences in effects of WIMP vs axion dark matter is
    http://arxiv.org/abs/astro-ph/0211325 (and you can references to it)

  • Bud

    Until they can fit dark matter into Einstein’s relativity it will remain an unproven speculation, not even a scientific theory.
    All matter must be convertible to energy, else it is not matter.
    Let’s all play by the rules
    James E Gambrell

  • TimG

    Bud (post #23), you have no idea what you’re talking about. Dark matter is in no way in conflict with the theory of relativity. Moreover, what Einstein said was that the mass of a body is equal to its energy content, not that matter is “convertible into energy” as if energy is some sort of special substance. Energy is a property of matter and radiation, and no one doubts that whatever interactions dark matter experiences, these will produce matter and radiation with an equivalent energy content to the dark matter you started with — this is just conservation of energy.

    The fact that Sean can list multiple empirical observations in support of dark matter and you respond by calling it “unproven speculation” suggests you haven’t even been paying attention.

  • Bud

    TimG, I respect your right to have an opinion and to express it but until you understand that energy is the first cause of all that is you will be one of the blind that is being led by the blind.

  • onymous

    Shantanu, your first link is broken.

  • Eric


    Dark matter is no different than ordinary matter, except that it is non-baryonic and doesn’t interact with light. There is absolutely nothing about it which is in conflict with GR or even basic physics. A dark matter particle can annihilate with it’s anti-particle to produce radiation as ordinary matter does.

  • Low Math, Meekly Interacting

    Quick question: I think I recall seeing somewhere that TeVeS amounts to another dark matter theory, and a poor one at that. I.e., these fields have quanta, and they must behave somewhat like DM (little or no interaction with normal matter except pertaining to gravitation) or be in even worse trouble than they are. I.e. all you get is extra Dark Stuff that makes some curves fit better while failing to fit even more. Is this correct? If so, TeVeS seems rather too costly to justify, i.e., it violates Occam’s Razor rather blatantly even before failing certain observational tests (which it does), and so is highly unlikely to prove to be a fruitful area of research.

  • David George

    Wikipedia: “As important as dark matter is believed to be in the cosmos, direct evidence of its existence and a concrete understanding of its nature have remained elusive.”

    Eric #27: “Dark matter is no different than ordinary matter, except that it is non-baryonic and doesn’t interact with light. There is absolutely nothing about it which is in conflict with GR or even basic physics. A dark matter particle can annihilate with it’s anti-particle to produce radiation as ordinary matter does.”

    Eric, you seem to know quite a lot about a phenomenon whose nature eludes concrete understanding. This appears to be a common tendency in public discussion. Why do people continually speak as if their hypotheses are known fact? Even the author of the Wikipedia article cannot bring himself (or herself) to state clearly that there is no understanding of the “dark matter” phenomenon.

    Reading Wikipedia, it appears that modern cosmology now accepts cosmic inflation as a fact. The measurement uncertainty principle provides theory with room to hide natural events. Talk about a shell game! Meanwhile ignoring topological defects.

  • Eric


    Well, we do know that neutrinos make up some fraction of the dark matter, and I believe that these particles are non-baryonic and do not interact with light. We know that dark matter doesn’t interact with light because otherwise it would be possible to see it. We know that it is non-baryonic from Big Bang Nucleosynthesis and from WMAP. Thus, any non-baryonic matter that doesn’t interact with light is by definition dark matter. The real question is, what type of particle makes up the bulk of the dark matter? Of course, it is not impossible that topological defects such as cosmic strings could make up a portion of the dark matter, however I believe this is possibility has been strongly constrained.

  • Shantanu

    I meant figures 2 & 4 of

  • David George

    #30 Eric — We don’t know that the observed phenomenon is due to matter particles at all. All that is “known” is what is observed, and what is observed seems to be anomalous motion of what is observed! Big Bang nucleosynthesis is not “known” — it is postulated to explain observations. The Big Bang is not “known” — it is postulated to explain observations, and “constrained” so that it agrees with the observations. What is “known” is what is observed. There does not appear to be any model that explains all that is observed. So there is no theory here, only a number of hypotheses, which as far as I can figure out are used to “justify” each other. These stem from Friedmann; the basic assumption is that all the energy we now observe was at one time in a point of infinite density and virtually infinitely hot. In order to let the universe out of that GR straitjacket, the measurement uncertainty principle is invoked. Quantum mechanics transfers measurement uncertainty onto nature itself. I believe that is a fundamental mistake.

    I know zero about string theory, the topological defects I referred to are those which ought to occur after inflation, when the forces “freeze out” during symmetry breaking. There is no reason why the electromagnetic interaction for example should have the same strength throughout the universe when various regions are not in causal contact. This is not me, this is Penrose (as far as I understand what he says). But it makes sense. But it appears to be ignored.

    So I do not believe you can state as a species of fact that there are particles of matter which you describe as “dark matter”. Promoting the assumption of “fact” or “known entity” is not right.

  • Eric


    It was never stated that dark matter is a fact, only that it is a theory which is accepted by most cosmologist as the most likely explanation for the anomalous motion of galaxies. I should also state that there is other evidence for the existence of dark matter apart from the motion of galaxies. Some of this evidence comes from microlensing and some of it comes from the acoustic oscillations in the cosmic microwave background. It is true that the precise properties of the dark matter are not presently know, however there are many good candidates.

    As for your statement about the “GR straightjacket”, I simply do not understand what you are talking about. Also, the cosmic strings I referred to have nothing to do with string theory. They are in fact examples of the topological defects that you mentioned and have been extensively studied.

  • David George

    #33 Eric — The “GR straitjacket” is described this way by Wikipedia: “According to general relativity, the initial state of the universe, at the beginning of the Big Bang, was a singularity.” How did the universe escape from its infinitely curved spacetime? The modern assumption is that the first moments of the universe are smeared out by the measurement uncertainty principle. Given a head start, Friedmann takes over. He gave a solution to the Einstein field equations (I only read this; I don’t know how) in the form of “metric expansion”: the universal “space” expands. Can you explain how “space” expands? The whole of modern physics seems to assume that the space-time continuum and the energy in the space-time continuum are two separate entities. But according to Einstein, spacetime is merely a structural quality of the gravitational field. So there is an ambiguity: spacetime and energy are somehow integrally connected in the “spacetime-energy complex”, which can be expressed as “space tells matter how to move, and matter tells space how to curve”. And yet, according to Friedmann, space has this independent ability to expand. It doesn’t make any sense. A more likely (and simpler) initial condition would be expanding space. But that would require rewriting the past hundred years of “theory”. Not much profit for institutionalized Science there. But I have sneaking suspicion it will have to be done eventually.

    If you can explain away the ambiguity, please do. I have not come across any sensible explanation for this yet.

  • http://www.astro.umd.edu/~ssm/mond/ Stacy McGaugh

    What we got here is a failure to communicate. Have we detected non-baryonic dark matter particles in the lab? No. Until that happens, we can’t be sure that the stuff exists.
    The rest all boils down to what Landau said: “Cosmologists are often wrong, but never in doubt.”

  • Joseph J Veverka

    Did it ever occur to anyone that we have space gravity and the big bang all wrong! If the universe is 93 billion lights years in diameter we are going to need a lot of dark matter. This obsession is preventing science from moving forward and making the kinds of advances needed to survive in a tiny corner of the cosmos. With everyone looking for dark matter I sure we will miss the real story of how we got here.

  • Greg

    thank you Sean!

  • Ben

    @Low Math, Meekly Interacting: your message is a clear example of the total misunderstanding I was talking about hereabove. You think that MOND is a synonym of TeVeS. Because TeVeS has problems, your throw away what the *DATA* are telling us about the successes of MOND, calling it “highly unlikely to prove to be a fruitful area of research”. Yes, TeVeS has problems, especially if you want to quantize it, as its Hamiltonian is generally not bounded from below (no, the fact that the fields can behave as dark matter is not the problem), but the whole point is that there are many other theories of MOND than TeVeS. To name a few, generalized Einstein-Aether (http://arxiv.org/abs/astro-ph/0607411), bimetric MOND (http://arxiv.org/abs/0912.0790), non-minimally coupled scalar field (http://arxiv.org/abs/0811.3143), dipolar dark matter (http://arxiv.org/abs/0804.3518), and others. Many of them have their own problems too, but that does not make them “highly unlikely to be fruitful”. And as I was stating above, most of them do recognize the existence of some form of dark matter (some form being important here, it all depends on what one means exactly by “dark matter”). LambdaCDM has problems too, mostly fine-tuning problems linked to the success of MOND itself: that doesnt make LambdaCDM “highly unlikely to be fruitful”! Someone was asking about what these fine-tuning problems were. Well, Stacy wrote an excellent paper about that back in 2005: http://arxiv.org/abs/astro-ph/0509305. So, let’s remain honest and admit what the galactic-scale data are telling us, and let’s admit that direct detection experiments haven’t proven yet the existence of non-baryonic cold dark matter particles, as Stacy righteously points out. In that respect, I can’t wait for the next results of XENON100: exciting times ahead.

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  • http://www.astro.multivax.de:8000/helbig/helbig.html Phillip Helbig

    Off-topic, but: is anyone else having problems with the RSS feed?

  • http://cosmicdarkmatter.com Tissa Perera

    Mass and curvature of space are complementary. That is, mass creates curvature and if space can have an intrinsic curvature of its own it will mimic matter i.e. dark matter. This is the crux of my argument for the existence of the so called dark matter. The emperical MOND formula is a direct consequence of the intrinsic curvature due to the existence of a cosmic size bounded 4th space dimension and I derive a modified MOND formula out of that concept. We could call that as the Dark Space, because it is as hard to detect as Dark Matter. But this at least legitmizes MOND as a viable alternative and get some respect. The modified mond formula might rectify some of the current shortfalls in MOND. I do not have the resources to further study the concept. Thank you.

  • Valatan

    David, you are taking an interpretation of a calculation as more fundamental than the calculation. This is completely backward. Also, theorists don’t extrapolate from the big bang, they extrapolate from today, and conclude ‘hot dense phase’. The evidence is overwhelmingly consistent with a hot dense phase. And yes, at a certain point, our knowledge of the universe breaks down, and we need new physics. No one claims to know this, and there are several people actively working on it.

    What’s your issue?

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Phillip, in what way is the RSS feed acting up?

  • chris

    “Have we detected non-baryonic dark matter particles in the lab?”

    well, yes. neutrinos for example.

  • Ben

    @chris: don’t fuss so, what was meant was “non-baryonic COLD dark matter particles”, and everyone understood it. Anything more interesting and/or constructive to say? For instance, any idea how to explain the successful MOND phenomenology on galactic scales within the LambdaCDM framework?

  • Joerg

    The RSS does not validate and is thus unreadable for a variety of aggregators:


  • David George

    Valatan #42 wrote,

    “David, you are taking an interpretation of a calculation as more fundamental than the calculation. This is completely backward.”

    I would appreciate it if you point me to my error. I’m not sure what you are referring to.

    “Also, theorists don’t extrapolate from the big bang, they extrapolate from today, and conclude ‘hot dense phase’. The evidence is overwhelmingly consistent with a hot dense phase.”

    I understand ‘running the film backward’. That includes the assumption that all the ‘mass-energy’ we now see was at some past time ‘compressed’ into a gravitational singularity. I think I understand the assumption: energy can neither be created nor destroyed. Right? Except it isn’t ‘right’, and all that mass-energy hasn’t necessarily always existed. And what is evident, i.e. observed, is light emitted from a hydrogen plasma at approx. 3000 degrees K. Right? The hot dense phase is an assumption based on the previous assumption. And the model is built to satisfy the requirements of the assumptions in the context of the evidence. So of course it is ‘consistent’. That doesn’t make it right.

    “And yes, at a certain point, our knowledge of the universe breaks down, and we need new physics. No one claims to know this, and there are several people actively working on it.”

    Certainly if some layperson, unconvinced by Creation According to Tribal Myth, were to spend a few years studying the detail of the various models, he or she would come across the caveat in the fine print: “this model is speculative and should not be taken for literal truth”. Meanwhile the unsuspecting masses are enthralled by how the universe arose out of a Big Bang, elegantly promoted as well understood truth, with just a few loose ends to clear up, requiring a few billion-dollars’ worth of high energy collisions whose debris can be sorted for clues. I would suggest rather than seeking “new physics” (does that mean new superparticles, new dimensions, or what?) you take a look at the existing physics. The point at which our ‘knowledge’ of the universe breaks down is the foundational point of the universe as we ‘know’ it.

    “What’s your issue?”

    Apart from the ‘issues’ above, that issue of “space” remains unexplained.

  • Truly Anomalous

    I think at this point it might be useful to recall Sagan’s Baloney Detection Kit, (especially the fifth point below):

    # Wherever possible there must be independent confirmation of the facts
    # Encourage substantive debate on the evidence by knowledgeable proponents of all points of view.
    # Arguments from authority carry little weight (in science there are no “authorities”).
    # Spin more than one hypothesis – don’t simply run with the first idea that caught your fancy.
    # Try not to get overly attached to a hypothesis just because it’s yours.
    # Quantify, wherever possible.
    # If there is a chain of argument every link in the chain must work.
    # “Occam’s razor” – if there are two hypothesis that explain the data equally well choose the simpler.
    # Ask whether the hypothesis can, at least in principle, be falsified (shown to be false by some unambiguous test). In other words, it is testable? Can others duplicate the experiment and get the same result?

  • http://washparkprophet.blogspot.com ohwilleke

    There is, of course, not one dark matter model out there. There are several competing versions. Many of the earlier models were not too specific on the question of why dark matter is distributed in the manner observed and had many “moving parts” that could be adjusted to fit the data.

    What would be very helpful to see, but I haven’t seen, is an analysis that shows how lamba CDM produces results that are very precisely approximated by the MOND formula that has far fewer moving parts at the galactic scale, and what about lamba CDM causes that relationship to break down at the galactic cluster level. MOND’s phenomenological success means that this must necessarily be possible in any accurate dark matter theory.

    MOND’s accuracy in approximating results like rotation curves and galaxy color for a very broad range of galaxies (it fails at the galactic cluster level, not as mentioned in the original post, the galaxy level), are certainly right up there with the approximations of classical physics like Newtonian gravity, Maxwell’s equations, classical optics and classical thermodynamics. Why?

    Also, does it matter that dark matter cosmologies were constructed with the assumption that there is far less ordinary matter than there actually is (as a December 2010 study published in Nature discovered that we had underestimated the amount of ordinary matter by a factor of three by assuming that elliptical galaxies have similar amounts of hard to observe stars to spiral galaxies)?

    So, the dark matter model used to make some of these predictions may have made accurate predictions for the wrong reason (a surprisingly common problem in all sciences since theories are crafted to match data), even though a dark matter model of some kind is probably correct.

  • http://washparkprophet.blogspot.com ohwilleke

    “Some people try to claim that the necessary dark matter could be neutrinos rather than some brand-new particle, and that’s supposed to be morally superior somehow.”

    Describing cosmology without having to invent a particle which has never been observed clearly is superior to describing cosmology in a manner that requires one to invest a particle which has never been observed, all other things being equal. When both dark matter and MOND require new physics, neither is strongly favored by Occam’s Razor. So the distinction between neutrinos and other kinds of dark matter, if it could be established, would be very pertinent.

    Occam’s Razor proponents often go on to argue that SUSY and String Theory make undiscovered particles well motivated even if not actually found, but the parallel argument would be that there isn’t a good quantum gravity theory out there and that we know that general relativity needs to be tweaked to accomodate quantum gravity, so MOND like phenomea are also well motivated by the proposition that quantum gravity would be expected to modify GR at some scale with some phenomenological results. See e.g. M. Reuter, H. Weyer, “Do we Observe Quantum Gravity Effects at Galactic Scales?”

    The argument from beauty likewise has little to recommend it (Newton’s theory of gravity is an absolute ten on the beauty scale as was the proton-neutron-electron model of the atom that saw each of those as fundamental), particularly when one compares the quite ugly equations that tell you how dark matter halos are distributed that are required to do what MOND and TeVeS do. The fact that a TeVeS is even possible mathematically is pretty remarkable.

    McGaugh’s observation on tidal effects in dwarf galaxies is likewise on point, as is the point that the cosmic microwave background issue could simply be the result of receiving somewhat less theoretical attention, since it has flowed from phenomenology to a greater extent.

    The Bullet Cluster is the one piece of evidence that does seem to clearly favor dark matter over MOND. Fair enough. There is a good piece of evidence favoring one theory over another, although to play the devil’s advocate — if clusters don’t work MOND because of massive ordinary neutrinos providing dark matter, it is harder to be sure that those massive neutrinos aren’t making the Bullet Cluter act as it does.

  • Eric Habegger

    Ohwilleke, what you are presuming in your previous statement about avoiding new particles is suspect. Science is never about perfection. One takes all the observational facts together and uses the preponderance of the evidence to come to conclusions. For example, you imply neutrinos as dark matter is good because no new particle. However, three facts go against it:

    1. There are not enough of them in the universe to account for DM.
    2. They aren’t really dark, just dim.
    3. Why are they so heavily distributed at the periphery of of galaxies.

    What you are saying goes against the preponderance of the evidence. It also ignores that all the facts above taken together, but using neutrinos as the DM, might imply a new kind of force. Do you even want to consider that if you hold occam’s razor dear? I wouldn’t. I would much rather except that there just might be new particles we are seeing bound together by one of the four forces we know. Scientists have tried to use the weak force and used it to speculate on the idea of wimps. But so far no luck detecting them and there sure isn’t any good reason why most all the wimps would be distributed near the perimeter of galaxies. That contradicts all known physics and also would imply a new force.

    What about the strong force? The strong force really is a fairly good fit for how galaxies behave at the perimeter where they are tightly confined. Perhaps the new particle IS the galaxy, but instead of gluons confining quarks one has the cold expanded version of it, i.e. Cosmic strings confining baryonic matter. So far they haven’t eliminated this possibility. One just needs to scale the temperature and the corresponding cross-sectional distance of space together. This would involve a varying Newtonian constant G that scales with the temperature and volume of the universe.

  • Low Math, Meekly Interacting

    Hrm. Well, I certainly didn’t mean to equate TeVeS with MOND, but my understanding was that it was a much-improved theory that reduced to old-school MOND, and so was more worthy of attention. I don’t know enough about the other MOND-derived or inspired variants to comment much, but it seems like the field is plagued with models that fit certain galactic rotation curves nicely, yet inevitably wind up in contradiction with some other fact about the universe on a different scale. Meanwhile, the worst we can say about lambda-CDM is that, as of yet, it cannot explain everything, and we have not observed DM particles directly. That said, is LDM in actual contradiction with much of anything? Wanting for help, maybe, but is there robust data that threatens it in any way?

    Sincere question: Could some of these galactic rotation observations go the way of the Pioneer anomaly? Is there a general consensus that they do in fact constitute a real problem, or is there legitimate reason to harbor some doubt that a problem exists, despite what we think we see?

  • Brian137

    Good article, Sean. Thanx.

  • Ben

    To the question “Could some of these galactic rotation observations go the way of the Pioneer anomaly?”, I would personnally say that there is a huge difference between one single controversial observation (the Pioneer anomaly), and more than a hundred rotation curves of galaxies (nearby-enough to measure their rotation curve accurately) agreeing with the mond scaling relation (that is, pretty much all of them). In the same vein, some people would like to compare the mond phenomenology with a sort of galactic Titius-Bode law, except that again, the latter was applicable only to some inner planets of the lonely Solar System. That is, in my opinion, not exactly comparable with dozens of *independent* galaxy rotation curves. Indeed, wherever possible there must be independent confirmation of the facts, and that’s precisely what we have here. To make the fine-tuning problem clear, in LambdaCDM, the respective distribution of baryons and CDM should depend on the individual history of each galaxy (number of mergers, interactions with the environment, gas accretion, etc.), and yet all of them seem to harbor the same scaling relation (the mond scaling relation) at redshift zero. I am surely ready to admit that this does *not* imply that the only solution is an extreme one such as modified gravity, and that something we dont fully understand yet could be happening in the process of galaxy formation in the context of LambdaCDM. But what I find damaging is to ignore such observational evidence because we dont fully understand it yet. And until an explanation has been found (and/or until CDM has been detected directly), I think it is also dangerous to call for not exploring alternative explanations (and yes we agree, these should involve the existence of dark matter of some kind, be it HDM in the form of sterile neutrinos + modified gravity, or mass-varying axions inducing modified gravity effects, or dipolar dark matter, or the “twin matter” of Milgrom’s bimetric theory, or whatever…), even though I also agree that these often end up having usually their own theoretical or phenomenological problems. But we know that they have such problems because people are working on them!

  • http://www.astro.multivax.de:8000/helbig/helbig.html Phillip Helbig

    “Phillip, in what way is the RSS feed acting up?”

    I have a handful of RSS feeds, mostly for blogs. Occasionally, Firefox says “Live bookmark failed to load” instead of displaying the most recent topics. Usually, it’s just a short-lived problem and usually occurs when there are problems with the site itself. However, in the last few days (much longer than the typical outage), the problem at Cosmic Variance has remained, while the blog itself is directly accessible.

    Since my other RSS feeds work, including the one for Bad Astronomy (also a Discover blog), I’m assuming that the problem is not at my end and is probably a problem with the Cosmic Variance RSS feed itself.

    On a related topic, I miss an extra RSS feed for comments (both here and at Bad Astronomy); since there are relatively many comments, an extra feed would be nice, otherwise one tends to miss new comments, especially on other topics. Many blogs, such as those of Telescoper and Ted Bunn, have extra RSS feeds for comments (as well as for new blog posts, of course—two separate feeds).

  • http://www.astro.multivax.de:8000/helbig/helbig.html Phillip Helbig

    “The RSS does not validate and is thus unreadable for a variety of aggregators”.

    Right. And replacing “cosmicvariance” with “badastronomy” in the URL above indicates that the latter is a valid feed, so it seems to be a problem with the Cosmic Variance feed itself. I started having problems a few days ago.

  • http://www.astro.multivax.de:8000/helbig/helbig.html Phillip Helbig

    “Even with MOND, you still need dark matter.”

    Some people see this as an argument against MOND: it was invented to solve a specific problem, it failed when the bigger picture was taken into account, so it must be wrong. This is how Einstein viewed the Cosmological Constant. However, the Cosmological Constant very probably exists and is probably the most interesting scientific issue of the 20th century (or 21st, depending on when one was convinced, but of course we don’t know what is yet to come in this century). Hubble’s discovery of the expansion of the universe was a great observational discovery, but, at least in retrospect, it is theoretically trivial (i.e. one would expect the universe to either be expanding or contracting, and missing this obvious point is what led Einstein to his “biggest blunder” statement (though as far as I know the only source for this is an anecdote in a book by Gamow)).

    Thus, merely the fact that MOND cannot explain all observations which otherwise require dark matter does not, per se, disqualify it as a theory. Maybe the universe is more complicated.

    Not that long ago, there were people who weren’t as unprejudiced as those who said “we measure the cosmological parameters, whatever they turn out to be” but a bit more open than the “the Einstein-de Sitter model is correct, let’s move on” school. A common argument was: lambda is non-zero and the universe is flat OR lambda is zero and Omega (Omega_matter of course) is not 1—but not both. The universe could of course be so simple, but a) it might not be and b) there is no a priori reason why we cannot have a universe with a cosmological constant which is not spatially flat.

    I think one of the most interesting things in the next, say, 10 years will be whether a significant deviation from spatial flatness is observed or, if not, what constraints are placed on any deviation.

    One needs to keep an open mind. Someone once said to me, well, we have this data, and constrain the cosmological constant to a value less than x. With this new, better data set we will have in the future, how tight will the constraints be? My reply was that it depends on what the value of the cosmological constant actually is, whereas my partner in conversation was assuming it was zero. What actually happened, of course, is that we now have both a lower limit to the cosmological constant and an upper limit and it is non-zero.

  • Low Math, Meekly Interacting

    Sean, Ben, etc.

    I very much appreciate your responses and the overall discussion. I do find some of the arguments for MOND and MONDian ideas at least partially persuasive, and I’ve actually learned a couple new things in this discussion.

  • CL Kuo

    “For example, I agree about the third peak of the CMB power spectrum. …. That the third peak is high simply means ΛCDM survives this test, not that MOND fails it. ”

    I can’t make sense of this statement at all. What does it take for a theory to fail, if a poor fit to data couldn’t do it ?!

    Also I want to point out that the third, fourth, fifth peaks are now measured and they look nothing like the solid curve (ACBAR, QUAD, ACT, and soon SPT).

  • TRM

    Are you guys familiar with Dr. John W. Moffat’s work on Gravity Theory?

    It’s been around since 2008, and as far as I have heard it has yet to be shown in error.

  • Ben

    @Low Math, Meekly interacting: you’re very welcome; @TRM: if you mean this paper: http://arxiv.org/abs/gr-qc/0506021 , yes I know it, and it is just plain wrong. It all relies on the arbitrary choice of one constant of integration (see eq. 53). This constant is arbitrarily chosen to reproduce the MOND phenomenology, but that has nothing to do with that so-called “MOG theory” itself. This integration constant K depends explicitely on the mass M, so each object has a different constant of integration depending on its mass, but the theory does not tell why, yet that constant is the most important ingredient of the “theory”. Well, in my opinion, that’s called cheating, and makes a big difference between the serious MONDian approaches I was mentioning hereabove, and this “theory”, much closer to “crackpotry”

  • Ben

    Note finally that it is this same pseudo-theory (sometimes called MOG, sometimes STVG) that has subsequently been applied by Moffat to the bullet cluster in http://arxiv.org/abs/astro-ph/0702146. So there: nothing to worry about for dark matter, definitely.

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Problems with the feed should now be fixed. It was just a cut-and-paste issue from the LIGO post.

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  • melior

    To stoke the apoplexy of some of the more amusingly fist-shaking dark matter haterz, here’s another example of an inspiring true-life timeline similar to the Neptune/Vulcan example Sean linked above:

    In 1934 Walter Baade and Fritz Zwicky proposed the existence of the [invisible!] neutron star, only a year after the discovery of the neutron by Sir James Chadwick… [Thirty-one years later,] in 1965, Antony Hewish and Samuel Okoye discovered “an unusual source of high radio brightness temperature in the Crab Nebula”. This source turned out to be the Crab Nebula neutron star that resulted from the great supernova of 1054… In 1974, Antony Hewish was awarded the Nobel Prize in Physics “for his decisive role in the discovery of pulsars” without Jocelyn Bell who shared in the discovery.

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  • AThinkingScientist

    Interesting and partially sad discussion here. Once upon a time not too long ago everyone knew for a fact that there was phlogiston and an aether . . .

    Peeles & Nusser quite nicely show that LCDM doesn’t really work to make the Local Volume (they find one needs to introduce extra forces or some modified gravity): “Nearby galaxies as pointers to a better theory of cosmic evolution” (2010, Nature):

    Independently, Kroupa et al. quite nicely show that LCDM doesn’t really work to make the Local Group (they find one needs to introduce extra forces or some modified gravity): “Local-Group tests of dark-matter concordance cosmology. Towards a new paradigm for structure formation” (2010, A&A): http://adsabs.harvard.edu/abs/2010A%26A…523A..32K

    And finally, there is a science blog with some interesting contents as to overall issues with the current cosmological scenario: The Dark Matter Crisis:

    So in view of this, Prof. Stacy McGaugh’s work is quite brilliantly pointing into a very specific direction we should be taking very seriously indeed.

    Dark-Matter advocates are likely to ridicule all of this, of course.

  • http://linasc.net/ Leif

    @Sean: Thanks for a clear comparison.

    @67. AThinkingScientist
    No need to ridicule. Of course dark matter is not the whole thruth(tm), but the evidence seems to me to support dark matter over mond at this time.

  • David George

    #67 AThinkingScientist —

    Hallelujah! Cheers, Applause, Hugs & Kisses, you made my day, week, month….

  • http://www.astro.multivax.de:8000/helbig/helbig.html Phillip Helbig

    Yes, the RSS feed is working again now, thanks!

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  • Gary Godfrey

    Approximately 90% of the baryonic mass in galactic clusters is gas. Based on dispersion velocity, MOND predicts an additional ~1 gas mass of “unseen matter” in clusters of galaxies. If the phase space of the cluster is filled (up to the measured radius and max velocity seen in the cluster) with a Fermi-Dirac distribution of neutrinos (times 12=3 gen x part/antipart x 2 spin states) with masses of ~1 eV each, the total mass these neutrinos is coincidentally ~ 1 gas mass. KATRIN claims it will measure the electron neutrino mass down to .2 eV. By 2013 KATRIN (big tritium beta decay end point experiment) may have its first results.

    Case 1: KATRIN says neutrino mass <.2 eV. Then the MOND relation does not extend up to clusters of galaxies. Exotic dark matter is needed. LambaCDM is looking good.

    Case 2: KATRIN measures a neutrino mass of 1 eV (last beta decay experiment said <2.2 eV 90%CL). The MOND relation now extends up to clusters of galaxies (including explaining the non-interacting yet lensing mass in the Bullet Cluster). More over, neutrinos would now account for Omega~.18 in the matter+dark energy sum to 1, now leaving no room exotic dark matter in the sum. This massive neutrino would slow down structure formation (the present increased cooling argument against a massive neutrino)….which fortunately the increased attraction of the MOND relation at large distances would speed up.

    Exciting! Experiment will decide…even if the direct dark matter detection measurements continue to see nothing, the KATRIN result could strengthen the need for exotic DM in galactic clusters by ruling out MOND there, or a massive neutrino could rule out exotic DM in the Omega sum ! …waiting

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  • Brian137

    I am excited about KATRIN also. I was not aware of the impact of the results from Katrin on the credibility of MOND; I am more interested in the neutrinos themselves. Hopefully, projects such as CNGS, Daya Bay, KATRIN, T2K, NOvA, and several others can tell us more about them.

  • http://tispaquin.blogspot.com Douglas Watts

    Have we detected non-baryonic dark matter particles in the lab? No. Until that happens, we can’t be sure that the stuff exists.

    True. This was also argued for the non-existence of anti-particles and the entire neutrino family. See this humorous anecdote by David Griffiths (1987):

    “By 1950, there was compelling theoretical evidence for the existence of neutrinos, but there was still no experimental verification. A skeptic might have argued that the neutrino was nothing but a bookkeeping exercise — a purely hypothetical particle whose only function was to rescue the conservation laws. It left no tracks, it didn’t decay; in fact, no one had ever see a neutrino do anything.”

    Perhaps it’s a similar deal with whatever dark matter is. All’s it seems to want to do is interact with gravity. Neutrinos were first theorized because beta decay appeared to completely violate conservation of energy laws. Only then was it looked for. DM is probly going to be a hell of a lot harder to find in a lab, though. At least with neutrinos, we have a giant source of them 93 million miles away shooting them at us constantly, plus beta decay in nuclear reactors, where they were first discovered empirically. With DM there are no “intense” sources nearby to give us a nice thick flux to see if they’ll maybe bounce of something even once in a quadrillion times. So it is a problem.

    At least with neutrinos, they’re tangible. If you have a piece of uraninite, you can hold a neutrino source right in your hand. DM, on the other hand, whew …

  • AThinkingScientist

    #72. Gary Godfrey:

    To case 1: In this eventuality (neutrino mass < 0.2eV) LCDM will, unfortunately, not look good, because its failure on Local volume and Local Group scales will persist without any physically viable solution at hand.

    Instead, this result would mean that either MOND breaks down such that some other alternative would be needed which contains MOND on galaxy scales (e.g. Moffat’s MOG needs no dark matter in clusters according to its arranged scaling) or MOND is fine but the dark matter is in baryons, as suggested by Milgrom himself.

    This latter possibility is not unreasonable because about 60% of all baryons (i.e. 60% of all normal matter) has gone missing since the Big Bang and astronomers do not know where they are. Part of it could be hiding in galaxy clusters in an undetectable form.

  • Emanuela Pompei

    I agree with the statement by Ben: if we see something in the data that doesn’t fit with what we know from theory, we should be open-minded and look for all possibilities, in a scientific way. Just saying this theory works in a lot of cases, it doesn’t matter that it doesn’t work here is not satisfying for me. And we do not have any direct observational evidence for dark matter. What we know is that there is something we do not understand, call it dark matter, dark energy or something else. So the question is: what is it? Can we explain it?

  • Brian137

    @ Stacy McGaugh, in re post #17,
    Great post. Thank you.

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  • David

    The difference here between critical and uncritical thinking hinges on the recognition of the importance of the scaling relation emerging from spiral galaxies and the emphasis on understanding it in a DM framework. For those of you who ignore the above and insist on addressing the ubiquitous problem of flat velocity curves via a global face-to-face confrontation between LCDM and MOND, you are missing the boat and draining my scientific soul. Please make the effort to read the comments by Stacy and Ben with the idea of understanding them.

  • AThinkingScientist

    @Ben# 81:
    We are not discussing scientific souls. We are discussing scientific progress and testing of theories/models/hypothesis to achieve this progress,

    LCDM (Einstein’s GR + cold dark matter and inflation and dark energy with unsolved issues concerning energy conservation) is being tested on real data, e.g.via rotation curves of galaxies (McGaugh’s paper under discussion here) or the distribution of matter in the Local Volume of galaxies (Peebels& Nusser’s 2010 paper) or the distribution of matter in the Local Group of galaxies (Kroupa et al. 2010 paper). And LCDM unfortunately fails to account for the data, however hard many excellently funded research groups have been trying over more than a decade now to solve the problems.

    MOND is also being tested, just as rigorously. It seems to be doing much much better, but it also has fundamental issues (e.g.what does the parameter a_0 mean)?

    What is a problem, not of a scientific soul but of scientific careers especially in the USA(!) is that there are too many who continue claiming that dark matter is a fact and that the standard cosmological picture is correct and excellently accounting for data. These are untruths, usually told to undergraduates, and they propagate through to how tax-payers’ money is distributed to research grants.

    Thus, in the USA MOND research is essentially not possible, at least not via the funding agencies (compare with Lee Smolin’s book on “The trouble with physics”). I admire Prof. Stacy McGaugh for nevertheless having the guts to write such papers – I happen to know how difficult it actually is to get such science published nowadays. Prof. McGaugh stands out as one of the truly leading astronomers of the USA, and will be remembered for it.

    In my classes, when I explain to students the problems with LCDM (showing the facts and the literature) and that there are alternatives like MOND, they get totally thrilled. You can see the spark of true scientific interest in their eyes – the students of physics, who study physics because they want to learn where the current physics fronteer is ,who try to recapture those times of Einstein and Bohr, of Planck and Heisenberg.

    Suddenly they discover that today is like being back in the early 1900’s when quantum mechanics was being discovered, bit by bit, progress by progress, research paper after research paper, over many decades, to what we have today. Back then classical mechanics was the cry (as was the aether), but spectra had lines and this did not fit. Also, the measured black body spectrum just didn’t make sense. Planck started it all by introducing a trick – his h is a fitting parameter (“hilfsgroesse” in German) which made the spectrum fit. Nobody understood what it was, that it was related to energy quantisation came out much later.

    So, after mentioning MOND in class, discussions arise. Can one improve on MOND? What’s the underlying physics? What does a_o mean? Is it again a “hilfsgroesse” hinting at some deeper meaning? How does structure formation work in this alternative gravitational approach, or perhaps even in other alternatives?

    But then I also have to explain to the students that in order to have a scientific career, i.e. to get support through funding agencies and universities, the students have basically no option but to do LCDM. And once on that train, jumping off becomes nearly impossble, unless you live in France or Italy, perhaps in the UK, definitely _not_ in present-day Germany (which just copies the USA but in a strongly archaic-hierarchical system).

    This is draining scientific progress, or, if you like, the scientific soul of today.

  • Evan Keane

    Wow, lots of comments for this one! I thought I should mention that any alternative theory of gravity really needs to explain the solar system tests, not just rotation curves of galaxies etc. (which are much less stringent). These are the really tricky ones to explain! :)

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  • AThinkingScientist

    #83 and 84:

    MOND is perfect for the solar system (this is trivial).

    Quantum mechanics: try computing the dynamics of a simple molecule from Schroedinger’s equation …
    The field equation of MOND is quite simple, in fact a small generalisation of the Newtonian case as shown by Milgrom and Bekenstein in 1984: its field equations can be derived from a simple Lagrangian such that the conservation laws hold.

    I am impressed how much misconception exists concerning MOND (it has even been called evil by a blogger elsewhere who obviously knows little about science). This does not mean to say I am MOND fan.


    I’m not as well versed in this field as most of you so maybe someone can assist me in understanding something first so I can follow the discussion better. You all are talking about large scale mass movements with extremely weak accelerations derived from gravity. The universe is such that space is expanding (growing). This is not evident within gravitationally bound objects as they do not grow in size with time. But to what extent is this true, what constitutes the boundary in these extremely weak gravitational systems at which the expansion of space takes hold? And further, shouldn’t the expansion of space modify the gravitationally derived force at this boundary? Of course I’m wondering if this effect could somehow be related to MOND.

  • AThinkingScientist


    This is an excellent and highly relevant question! This is the type of question we need to be asking, rather than blogging about MOND as being bad astronomy. This sort of question is at the very heart of modern theoretical physics research which needs the most brilliant minds to work on.

    First of all we need to note from observations that _in_all_stellar_systems_ (!!) whenever the force from gravity becomes extremely small we “suddenly” see that the stars or gas move differently than they should. This is the centerpiece content of Stacy McGaugh’s research paper under discussion here, as well as many other research papers already published.

    It is as if a resistance disappears, and this is perfectly calculated by the MOND formula which Milgrom discovered in about 1983. This change in motion happens at such a weak gravity that we cannot reach it in our solar system,not even in the vicinity of the Sun, where our Galaxy is exerting too strong a pull.

    Dark-matter enthusiasts interpret this deviation from Newtonian motions to come about because of the “sudden” appearance of cold dark matter.

    Now, what does this critical very weak force (or technically critical acceleration, a_0) mean? For those of us who have tested the cold-dark matter model to its demise it is quite clear that this new constant a_0 (call it Milgrom’s constant) is truly new physics at a fundamental level which is not understood yeat but which is at the very heart of the issue of the origin of mass (Higgs boson), space and time. Theoretical physicists have, so far, not arrived at a good description or theory of these problems.

    Here is a citation from http://en.wikipedia.org/wiki/Modified_Newtonian_dynamics where we read:
    “To explain the meaning of this constant, Milgrom said : “… It is roughly the acceleration that will take an object from rest to the speed of light in the lifetime of the universe. It is also of the order of the recently discovered acceleration of the universe.” ”

    Another way of looking at a possible deeper phyiscal meaning of MOND is at the very centre of modern physics:
    What is inertial mass? What is gravitational mass? And, why should they be equal?

    Inertial mass: take a perfect ball in free space, push it and you feel resistance. This resistance is governed by “inertial mass”. The larger the inertial mass, the more difficult it is to push the object. This is why an astronaut would be squashed by a space shuttle but not by a ping-pong ball even if both travel at the same speed.

    This ball also curves space time about it (according to Einstein’s ideas) which we interpret as the force of gravitation. This force depends on the mass of the ball, its “gravitating mass”.

    One way of looking at MOND is as follows:
    When the gravitational field becomes extremely weak, inertial mass and gravitational mass are not equal any longer. If this were the case, then this would revolutionise physics at a most fundamental level.

    How can this come about? Again, Milgrom has a suggestion which is summarized in the appendix of this paper by Kroupa et al.: http://adsabs.harvard.edu/abs/2010A%26A…523A..32K

    Take the ball in completely empty flat space and push it. As it gets faster, as it accelerates, it begins to “see” the vacuum in front of it getting hotter (the energy fluctuations in front of it get blue shifted). This exerts a force against the ball (Unruh radiation) and may be related to what we feel as the inertial mass.

    The same ball, if it is pushed extremely weakly but now in curved space will additionally “see” a radiation field which comes from the cosmological horizon (the Gibbons & Hawking radiation). This radiation is basically the same radiation you would observe coming from a black hole as the energy vacuum fluctuations at its event horizon get split to a part that ends up in the hole and a part that is left in our universe. That is, we can think of our universe as being the inside of a black hole.

    When the push on the ball is extremely weak, the Unruh and the Gibbons & Hawking radiation cancel, such that pushing the ball gets easier.

    The ball can then move faster more rapidly, and this is exactly what we see in those regions of all stellar systems where the gravitational pull is very weak.

    That is, MOND emerges from the quantum mechanics of the vacuum plus the whole universe.

    This is why MOND is so amasingly exciting.

    And it is so painful to see the constant misunderstanding, misinterpretations, misrepresentations and barking and biting at what is probably one of the most significant physics discoveries (by Milgrom) of the second half of the 20th century!


    For our sun MOND like effects should appear at ~0.1 light year, or ~10^15 m, if the sun’s gravitational field dominates. It is interesting that the acceleration to the sun from the Milky Way is about 10^-10 m/s^2 or about a_0. I think any stars in the vicinity of our solar system will have much weaker accelerations than a_0 at 0.1 light years so only the sun and the galaxy dominate acceleration (about equally but not necessarily in the same direction) at 0.1 light year. But we also need to keep in mind that 3.3 lbs held at 1 meter has the same acceleration!

  • http://mingus.as.arizona.edu/~bjw Ben (different from above)


    The conventional answer to your question is basic to the theory of structure formation in cosmology. If you consider an overdensity in an expanding universe, a spherical shell of matter at some radius sees both the expansion and the gravitational attraction of the overdensity. There is a turnaround radius which depends on the mass of the overdensity, redshift and so on. A shell of matter at the turnaround radius will begin to fall back onto the overdensity, so it transitions from expansion to belonging to a gravitationally bound object. As this continues, the overdense mass grows with time. The growth rate depends on the cosmology, including the values of Omega_matter (mass density) and Lambda (cosmological constant).

    Note that I didn’t mention dark matter. This structure formation theory is based on matter and standard GR gravity (Friedmann cosmology) but it doesn’t depend specifically on the matter being dark. Dark matter is something incorporated into it from observational motivations. This part of structure formation has been worked out for a long time (Press and Schechter 1974; White and Rees 1978; etc).

    In my opinion, MOND gets about the correct amount of attention. It is not suppressed – people can publish papers on it in mainstream journals. MOND is sort of a pain to work with on large scales because it violates the strong equivalence principle, and since it’s not 1/r^2, far-field effects are not zero. That means, in Newtonian gravity if you sit inside a spherical shell of matter, you feel no force, but in MOND this is technically no longer true.

    One needs to remember that the vast majority of astronomers are not working on dark matter cosmology. For someone working on, say, star formation or quasars or dust in galaxies, as long as MOND reproduces Newtonian gravity on small scales and TeVeS can be tweaked up to produce the right rate of structure formation, it doesn’t make a difference to their research. It’s the places where it doesn’t reproduce the current standard model that are going to matter, so making testable predictions (for say the mass spectrum of bound structures in the universe) is important.

  • Eric Habegger


    “The same ball, if it is pushed extremely weakly but now in curved space will additionally “see” a radiation field which comes from the cosmological horizon (the Gibbons & Hawking radiation). This radiation is basically the same radiation you would observe coming from a black hole as the energy vacuum fluctuations at its event horizon get split to a part that ends up in the hole and a part that is left in our universe. That is, we can think of our universe as being the inside of a black hole.
    When the push on the ball is extremely weak, the Unruh and the Gibbons & Hawking radiation cancel, such that pushing the ball gets easier.”

    Unruh radiation during acceleration is on firm theoretical ground. However, one can’t just say a body far removed from any gravitational attraction is receiving the same effect as Gibbon & Hawking radiation. Just because someone noticed and published somewhere that this “might” be able to counteract and neutralize hawking radiation induced inertia does not make it true. To me it is just wild speculation that an object far on the perimeter of a galaxy would see the same effects as one near a black hole. Why would that have any credibility beyond pure speculation?


    Thanks Ben and ATSS for the replies. ATSS your response has much to consider as you are contemplating the origin of inertia itself. Ben, I think I follow what you say and it makes sense as there are models of the structure of the universe in terms of mass distributions that fit observations into deep space. These models must incorporate expanding space and clumping matter. I would like to understand that boundary better especially when considering the acceleration of the expansion, does the boundary of expansion to clumping move deeper into the clumping matter to pull more matter away? If so, how does that appear in terms of dynamics from the reference frame of the earth?

    At any rate, if I’m thinking about this right, if MOND is at all related to the expansion of space then it does so within the local overdense portion (as opposed to the overdense boundary because that is too far away) and appears to enhance the local gravity slightly.

  • Shantanu

    Hi all,
    Just wanted to pointed out , since Sean also had a recent post on LIGO, coincident gravity
    wave observations(and photons) from a GRB or supernova, once they are observed should be able to settle the dark matter vs MOND debate definitively with a much more stronger case
    than the bullet cluster. See arxiv.org/abs/0804.3804

  • AThinkingScientist

    @Eric Habegger(#90):

    Sure, it is speculation to a certain degree. Better refer to it as a theoretical proposition.

    But it is noteworthy that Milgrom was able to derive the MOND transition function, which defines how the dynamics changes from the Newtonian regime to the MONDian regime, from this proposition. The coincidences between this critical acceleration a_0, below which either cold dark matter appears or effective gravity becomes MONDian, and the cosmological parameters is also tantalizing.

    So MOND might be giving us astronomical hints on the connection between inertial mass and gravitational mass and the vacuum. It might also just mean that Einstein’s field equation is not complete.

    Note that we might also think of Planck’s introduction of the new constant h as pure speculation (which it was at that time). It’s relation to energy quantisation was realised much later.

  • Eric Habegger

    I don’t think there is any difference between inertial mass and gravitational mass. Mass responds the same in both circumstances. An everyday example is when people try to bury old tires at garbage dumps. Because tires are voluminous but not dense they are very susceptible to a field density gradient of the dirt, just like helium balloons on the atmosphere. Tires just keep popping to the surface because there is a density gradient in the dirt moving towards the less dense at the earths surface. You must expend a small constant force to keep old tires buried underground.

    Gravity works the same but with the force exerted on it in the opposite direction to the example given. Gravity is a force that is only due to a gradient in the field, not absolute values. That gradient is equivalent in action to a force. At the edge of galaxies the gradient “should” diminish to practically zero. That is, a value low enough for massive objects there to not remain in orbit around the galaxy.

    People assume the gravitational gradient does not diminish like it should to keep massive objects orbiting. One theory for this is modified gravity, Mond, which says the gradient doesn’t diminish below a certain level basically because that is what we observe. But it is a curve fitting formula used to closely match observations and so far, from what I can see, it is curve fitting only with no good physical arguments for it besides speculation. Plus, as Sean said, the math is ugly. If you could think of GOOD reasons for the formula besides curve fitting I’d be more convinced.

    There is also problems with the conventional particle theories, so Mond isn’t alone in being inadequate. Things like reasons for the odd distribution of massive particles near the the perimeter of of galaxies. I think people tend to implicitly assume that gravity is keeping those perimeter objects in line, even if the gravity is coming from new particles. It may not be gravity that is keeping those objects in orbit. People Should start thinking about analogues of confined objects that do not use gravity. There are plenty of examples in the quantum world and in the macroscopic world also. They should also start combining those thoughts with the fact that space itself is a lot bigger and a lot colder than when baryons and later atoms were formed. Atoms are hugely bigger than baryons and they formed when when space was colder. There is no good reason to say this process of particle formation isn’t still occurring and that it scales with the changing volume and temperature of the
    universe. Scientists need to be a LOT more imaginative than they have been up to now.

  • http://tispaquin.blogspot.com Douglas Watts

    “One needs to remember that the vast majority of astronomers are not working on dark matter cosmology. For someone working on, say, star formation or quasars or dust in galaxies, as long as MOND reproduces Newtonian gravity on small scales and TeVeS can be tweaked up to produce the right rate of structure formation, it doesn’t make a difference to their research. It’s the places where it doesn’t reproduce the current standard model that are going to matter, so making testable predictions (for say the mass spectrum of bound structures in the universe) is important.”

    I’ll take epicycles for $500, Alex. I’m intrigued reading the deeply theoretical pugilistics here. It reminds me of some other famous bouts in 20th century physics, much of which involved the alleged existence of elementary particles first required by theory and only confirmed later by experiment. Absent confirming data, it does kind of gravitate toward theoretical aesthetics. Do we patch up the hole in the boat with a new particle or by tweaking a fundamental law? Either way there’s still a hole in the boat. Which is good. It would be terribly boring if we found we had discovered everything.

  • AThinkingScientist

    @Douglas Watts(#95):
    Indeed, holes there are. A historical review:

    There were 2 instances when unknown matter was postulated, on the basis of existing theory, to exist and then discovered: Neptune and the neutrino.

    There are at least 3 cases, when unknown matter was postulated, on the basis of existing theory, to exist and then falsified: Phlogiston (solved by thermodynamics and atomic physics = new physical laws)
    aether (solved by special relativity = new physical laws)
    a planet within Mercury’s orbit (solved by general relativity = new laws of physics)
    There might have been more.

    The case with phlogiston is an interesting parallel, because well before modern concepts were in place discrepancies had arisen within the phlogiston framework such that it became untenable centuries before quantum physics allowed oxidization for example to be understood at a fundamental level.

    Concerning cold dark matter, we already have exactly this same situation at hand: within the LCDM framework insurmountable discrepancies have been arising despite a practically fantastic effort to solve these, only one of them being the Fritz Zwicky Paradox. For me this is the clear signal that LCDM is not viable, and we need to move on, whereby the success of MOND is giving essential clues.

  • Brian137

    For me this is the clear signal that LCDM is not viable, and we need to move on, whereby the success of MOND is giving essential clues.

    Whoever wants to “move on” now should do so. You really don’t have to wait for everyone else.

  • AThinkingScientist

    #97: Good hint. And yes, they are … But, I happen to know that there is unfortunately significant hindrance from the traditionalists… Surely this hindrance is not in the best interests of the taxpayer who are lead to believe, employing scientific tricks, that the traditional picture works perfectly well.

  • Brian137

    Great discussion – lots of information and insight.

  • Brian137

    Here is another pertinent link:

  • http://canonicalscience.org Juan R. González-Álvarez

    Dear colleagues, dark matter has passed away…

    But first some words to defend MOND “against unfair attacks”.

    MOND is ugly. Ugly is a subjective term. We, scientists, do not care about ugliness but about if the model fits to data, the predictions made… and we know that MOND rocks




    whereas the dark matter models cannot fit the fine data (only give us a rough description) and make no predictions (dark matter fits are done a posteriori)



    MOND would not be associated with TeVeS (i.e. with ONE attempt to mix GR with MOND). In any case, neither ugliness or elegance are scientific requirements for evaluating a theory as TeVeS.

    MOND doesn’t fit clusters. A non-relativistic theory having problems to fit some relativistic data does not look as a problem for MOND, which continues explaining the rest of data very well. Moreover, dark matter models have problems to explain the same clusters as well



    Even with MOND, you still need dark matter. Only if you want to apply a non-relativistic theory to relativistic regimes and fill the holes between relativistic data and a nonrelativistic model with unobserved dark matter. A more serious alternative is to apply a relativistic theory to relativistic regimes. Then you do not need dark matter at all!

    MOND doesn’t even fit all galaxies, How many entries you can find in “Galaxies which are NOT fit by MOND”? (I count exactly zero)


    For almost twenty years now we’ve known that MOND fails for a certain type of galaxies known as “dwarf spheroidals”. But your claimed “fails” are associated to taking certain values for high-uncertainty parameters.

    MOND doesn’t fit the cosmic microwave background. As has been said to you above, the first prediction was done using a MOND cosmology. MOND people predicted the correct first and second peaks, whereas dark matter cosmology gave wrong first and second peaks. Only after the final data was known the dark matter community modified parameters in dark matter cosmological models for their posteriori fit to the data. MOND just predicted the correct values before the experiment was run. This part of the history would not be omitted!

    About the third peak, well again this is the regime where relativistic corrections enter. Again nobody serious would wait MOND (a non-relativistic theory) to apply to relativistic regimes.

    Why is dark matter a dead end?

    Because (i) it has never explained the data


    and because (ii) nobody has found dark matter. Sometimes one read in the news that dark matter has been finally ‘found’, but they only mean that some data has been more or less explained assuming the existence of dark matter. The current claims of observation of dark matter have the same validity that the ancient claims of observation of Vulcan planet.

    At the same time as emphasized in Dr. Corda FQXi Essay forum,


    We already developed theoretical alternatives that rule out dark matter (and dark energy). We can already explain observational data that cannot be explained neither by dark matter models, nor by other models as MOND, TeVeS, PCG… Moreover, we can combine both the cosmological and the astrophysical models and then solve some other mysteries, such as why the astrophysical constant a0 used in MOND is numerically close to the Hubble aH. Our new theory predicts a0 = 1/8 aH.

    Our new theory gives a correction to GR that explains all the data including cluster mass limits, cosmological data, etc. We can rewrite this theory in GR form plus a fictitious distribution of matter and show that this fictitious distribution of matter is that you call dark matter. Since the expression for this fictitious distribution of matter follows from first principles, we can derive the properties of that ‘matter’. In this way we can explain its anomalous density, its interactions… in direct correspondence with your empirical data, but this matter is not real, the real picture is an novel gravitational interaction beyond GR.

    The same about dark energy, it is not real, but a fictitious energy that arises from an extension of GR and, I am sorry to remark this, the concordance between our new theory and observation is excellent, specially when compared with other approaches.

  • http://canonicalscience.org Juan R. González-Álvarez

    By reasons of size (and because this is a blog, not a formal paper) I have avoided many important details in my previous post. For instance, consider the point (i). The link given above


    compares the dark matter fit with the MOND fit for the dwarf galaxy NGC 1560.

    However, I did not comment that the dark matter fit is the best fit obtained with a two free parameter model, whereas no such freedom exists for the MOND model. As everyone can see still MOND fits the data better…

  • AThinkingScientist

    101-102: Many thanks for putting up these convincing results.

  • Albert

    There is, of course, a problem with the fit to the “data” of NGC 1560, which is well documented, but nearly always swept under the carpet by our MOND enthousiasts. The situation is nicely illustrated in Figures 9 and 13 of the recent paper by Gentile et al. on this galaxy (see http://arxiv.org/abs/1004.3421). They show that the galaxy is asymmetric, and that the wiggle, so easily fitted with MOND, but not with the smooth curves thought to represent dark matter models, is only seen on ONE side of the galaxy. This was already clear in the original paper by Broeils (1992). Prudent researchers would thus discard such a galaxy from the discussion, since the non-circular motions are localized, and the averaged rotation curve (with half the wiggle amplitude) is probably not representative of the axisymmetric force field.

    On a positive note, Stacy’s paper definitely caught the attention of some pundits, one of them reporting a couple of days ago informally in my institute about an effort to explain the ‘fine-tuning’ of the detected baryon fraction in LCDM models. I think that is the way to go about it: it is no use sweeping problems under the carpet, and selling claims that either dark matter is doing just fine, or that some MOND stuff is convincing, when neither is perfectly the case.

  • http://canonicalscience.org Juan R. González-Álvarez

    I could not find any fig 13 in the pre-print by Gentile et al. (the above link by Albert does not work and I rewrite it here)


    But I can find that they report new data with twice the previous resolution and that the new data continue being better reproduced by MOND than by dark matter models.

    As the authors report, only MOND gives both a good fit and reproduction of the wiggle. The Burkert dark matter model gives a good fit but does not reproduce the wiggle, whereas the Navarro, Frenk, & White dark matter model (based in a cosmological ΛCDM framework) FAILS BOTH.

    Evidently, the problem is not only in the wiggle, as Albert seems to believe, but that ΛCDM based models once again cannot reproduce the data. The article is very clear “ΛCDM simulations result in a bad quality fit“.

    The conclusion for “our MOND enthousiasts” is that MOND continues being this ‘ugly’ model which is able to explain observations which cannot be explained using ‘beatiful’ dark matter models even when using twice (or more) parameters that in MOND models.

    “our MOND enthousiasts” are also rather proud of that all the predictions done by our ‘ugly’ MOND have been confirmed (see links in #101-102), whereas the ‘beatiful’ dark matter models did none of those…

  • Albert

    Juan (#105): thanks for correcting the link. You will find Fig. 13 on page 11 of the preprint. You have not addressed my concern: at the basis of the derived rotation curve is a velocity field, which is asymmetric. Since the wiggle is only at one side of the galaxy, it is doubtful whether the rotation curve has a wiggle. Once that is clearly understood, it does not matter what you fit to it: you fit models to derived ‘data’, which are derived from more basic data using a wrong interpretation. If you are not familiar with how velocity fields and rotation curves are derived, there is nothing I can do for you: you are just out of your depth.

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  • AThinkingScientist

    106: Albert, from looking at the paper http://arxiv.org/abs/1004.3421 by Gentile et al. it is rather clear that NGC1560 is fit on both sides separately by MOND very well, while the LCDM model (i.e.NFW) fails (the Burkert prifile is not LCDM, it has no theoretical dark-matter basis, but it is a good description of the phantom dark matter halo you would derive if you wrongly interpret the rotation curve in Newtonian dynamics – Burkert profiles are essentially a confirmation of MOND, interestingly).

    From Fig.9 it follows that this galaxy is quite symmetric, apart from the one side being more”wiggly” than the other. My interpretation of the data and the MOND calculcations , done without fine tuning!, is that the local velocity field is reproduced by MOND very well, as should be the case if the normal (gas+stars) matter is the sole source of gravitation. NGC1560 does not appear to be highly perturbed at all, that is, the velocity field is not significantly affected by a possible interaction with another galaxy. The galaxy appars to be quite isolated:

    So the point you are trying to make is not clear.

  • Albert

    #108. The basic point is that the rotation curve gives you the circular velocity of a test particle at a given radius, independent of azimuthal angle. In NGC 1560, at one side of the galaxy there is a local perturbation which causes a wiggle in the position-velocity curve at that side. This is mainly due to an uneven distribution of neutral gas. It is not clear to me that that wiggle can be interpreted as accurately reflecting the circular velocity there. Hence the ‘true’ rotation curve of NGC 1560 is not necessarily the average of both sides, at least in my opinion. Whether or not MOND fits both sides separately (not even well) is immaterial : a galaxy in equilibrium has one rotation curve (and not two).

    Gentile et al. don’t give a chi-squared for the fits, but by eye the Burkert model gives a better fit than MOND. Furthermore, they assume a distance of 3.45 Mpc when fitting DM models, and for MOND they adopt a distance of 2.94 Mpc. The 3.45+-0.36 Mpc distance comes from the tip of the red giant branch method. So there is an inconsistency here – the best MOND fit is for a distance different from the best distance estimate -, as is also known for NGC 3198. Note that on Stacy’s page the comments are the other way around : the Begeman et al. fit for D = 3.0 Mpc was not good enough, so they said the galaxy ought to be at 3.4 Mpc for a good fit! So not all is well here (OK, a 13% problem).

    The dip in the wiggle in NGC 1560 coincides with a relative depletion of the HI in the northern part. Interestingly enough, there is an extension in the vertical direction in the HI there, see Figure 3 of the paper of Gentile et al. This is not further discussed in that paper, but it could be related to the uneven gas distribution in the main plane.

    As for the Burkert model fitting better than a model using the NFW profile (Figures 10 and 11), this graphically illustrates the ‘core-cusp’ problem in LCDM. It is indeed true that it took observers a lot of time to convince cosmologists that LCDM had that problem : their general attitude was (and partly is) still very close to the attitude displayed above by Sean (attitude of saying DM doing “just fine”, despite all the glaring problems; declaring MOND is ugly, as if 4% baryons + 23% unknown matter + 73% ‘dark energy’ is not messy). In that sense, LCDM was, and continues to be, oversold. But that does not mean that MOND should be oversold as well: it also has subtle problems, such as the one I am pointing out about NGC 1560.

  • Ben

    Albert, about NGC 1560, it is still intriguing that the wiggles in the rotation curve and in the HI surface density are at exactly the same position and on the same side of the galaxy. As stated in Gentile et al., it is unlikely that this is due to strong non-circular motions as in NGC 3031. It rather seems to be a true wiggle in the gas tangential velocity for orbits that are only slightly perturbed (but it is true that they are of course not circular stricto sensu). To settle this debate, mildly non-axisymmetric models of NGC 1560 reproducing the HI surface density on both sides and a mock “rotation curve” should be produced both in MOND and within a dark matter halo, and why not also by considering molecular gas in an “HI-scaling” fashion, which would probably produce an excellent fit too, apart from the very outer data points (see the impressive “HI scaling” rotation curve fits in http://arxiv.org/abs/astro-ph/0403154)… but I doubt the dark matter models (even the Burkert-based ones) will succeed… Related to HI scaling, an intriguing possibility to explain the baryonic Tully-Fisher relation and the MOND phenomenology in galaxies would be to investigate the consequences of internal physical factors in self-regulated gravitating disks where “dark matter” would mostly be in the form of molecular gas (i.e. multiplying the HI mass by a large factor, that could be of the order of 15 or even more depending on the galaxy), as advocated by, e.g., http://arxiv.org/abs/astro-ph/0409621 … Of course, if this would be the true explanation of the success of the MOND phenomenology, it would be as unlikely as in the modified gravity hypothesis that XENON100 and other similar experiments will ever ever find a CDM particle…

  • Ben

    Just to clarify things, I am (a) not claiming that it is possible to simply replace *cosmological* DM with baryonic DM, we know that this is a priori impossible, (b) not even claiming that it is possible to *fully* replace galactic DM by baryonic DM, which is what I meant with the fact that HI-scaling would have troubles fitting the outermost datapoints of rotation curves (while in addition it also couldnt explain the near-sphericity of the potential obtained from fitting orbits of tidal streams, so you’d still need an additional DM halo or modified gravity in the outermost parts), just that *a lot* of DM in galaxies could actually be in cold gas form, which could (i) help explaining the wiggles a-la-NGC 1560 and (ii) perhaps even ease the understanding of the baryonic Tully-Fisher relation from feedback mechanisms (and incidentally, it would drastically reduce the local non-baryonic DM density at the position of the Sun: no luck for direct detection experiments). I still think this last point about feedback is far from easy, and that “plain MOND” is still by far the easiest way to explain the baryonic TF relation. I am just not closed to the idea of a lot of baryonic DM being present in galaxies in the form of H2… easing the understanding of some observations but somehow also complicating the whole picture, both from the DM and from the modified gravity points of view… Who said it was all gonna be easy?

  • http://canonicalscience.org Juan R. González-Álvarez


    thanks for pointing to the figure in the reference page. In early posts, I did a series of corrections to unfounded attacks on MOND and added information about a hundred of galaxies being perfectly described by MOND as well as about a dozen of predictions done by MOND and that have been verified.

    You have only focused in one wiggle around 300” in one galaxy! Still, I commented about this wiggle and about how this would not hide the subsequent difficulties for the ΛCDM model, which, I repeat, has been experimentally falsified in galaxies (ΛCDM systematically fails to reproduce both the velocities and the shape of the observed rotation curves).

    In fact, you cite now the “core-cusp” problem in ΛCDM and confirm the attitude of cosmologists as Sean Caroll to ignore empirical evidences and to make unfounded comments against MOND.

    You affirm that “by eye” the Burkert model gives a better fit than MOND. I find that you again are missing the whole picture because you are ignoring (i) the fit to the wiggle (curiously the best-fit curve in the Burkert model goes through the region of the wiggle), (ii) the number of FREE parameters used in each fit (TWO in the Burkert model, ZERO in MOND), (iii) that MOND gives better M/L ratio that Burkert, and (iv) that ΛCDM gives a bad fit.

    There is not inconsistency about distances but uncertainty. Adopting the 3.45+-0.36 Mpc in MOND reduces the fit quality (chi-square) about a 0.13 and there is lower distances than 2.94 Mpc reported by other methods. The comments in Stacy McGaugh’s page are about the Broeils 1992 data not about Gentile et al. recent data. McGaugh emphasizes that “The CDM fit is not unique” and that “Its prediction is more vague than that of MOND, and misses the mark by a wider margin.” The same conclusions are found by Gentile et al.: “bad fits using the a Navarro, Frenk & White halo” (CDM), “and good fits using MOND”.

    Now cosmologists as Sean Carroll would explain how is possible than the ‘beautiful’ ΛCDM model once again fails to explain data, whereas ‘ugly’ models as MOND explain the data (without free parameters).

  • Albert

    Ben, as far as I understand it, the bump in the HI causes the wiggle in the expected rotation curve. Unfortunately, the MOND fits never show the contributions of the individual components in MOND (i.e. they show the individual contributions for the Newtonian case).

    Juan, NGC 1560 has ‘iconic status’ for MOND, i.e. the ‘remarkable’ ability to fit the wiggle is widely quoted as a good reason to take MOND seriously. As for the hundred other galaxies ‘perfectly well described’ by MOND, I advise you to read
    http://arxiv.org/abs/1005.5456 where more counterexamples are discussed. Good distances might indeed tighten the constraints on MOND, since now de facto distance is used as a free parameter in MOND fits, in addition to the M/L ratio. Note that the M/L ratio is not predicted by MOND, contrary to your statement that MOND has ZERO free parameters. M/L ratios are rather uncertain, since the IMF is not very well constrained.

  • http://canonicalscience.org Juan R. González-Álvarez


    MOND ability to fit the wiggle in NGC 1560 is not the reason for which MOND advocates consider “to take MOND seriously”. The reasons are (i) a hundred of galaxies explained by MOND as well as (ii) the dozen of predictions done by MOND and verified up to the date.

    Regarding the recent preprint by Gentile et al. they do not claim “to take MOND seriously” because of the wiggle, as you continue to believe, but because they got “good fits using MOND” and “bad fits using the Navarro, Frenk & White halo” (an ‘elegant’ ΛCDM model). Reproducing the wiggle is only one point of an overall score that has given MOND its good empirical status.

    As explained in the section 5.2 of Gentile et al., the Burkert dark matter model uses TWO parameters (rho_0 and r_{core} in the eq. 1), whereas MOND uses ZERO parameters (see eqs. 6 and 7). For values of r_{core} = 5.6 kpc and rho_0 = 0.8×10^−24 g cm^−3, the best fit M/L ratio for the Burkert dark matter model is of 2.3. Using ZERO parameters, the best fit M/L ratio for MOND is 0.98. The reference value for the ratio obtained from stellar population analysis is 1.43.

    If you take all the points together (chi-squared plus wiggle plus ML ratio plus total number of free parameters…) you will find that MOND works better and, indeed, Gentile et al. affirm that MOND does it better than Burkert model and much much better than ΛCDM (which is empirically falsified).

    Regarding http://arxiv.org/abs/1005.5456, the authors claim that “MOND is successful” for roughly three quarters of the galaxies in a sample of 27 dwarf and low surface brightness galaxies and that “This is remarkable, given that MOND is a one parameter fit with only M/L as a free parameter.”

    MOND does not adequately explain the observed rotation curves for the remaining one quarter. The authors also emphasize that for the discrepant galaxies poor predictions were expected due to strong uncertainties in inclinations and distances.

    If you take a look to their sample, you will find that some of the galaxies (e.g. UGC 5750, UGC 6446) were already covered in the section “Galaxies for which MOND fit is dubious” of a link given in a previous post from mine (http://www.astro.umd.edu/~ssm/mond/fitroster.html). However, UGC 5750 was then listed in that section, whereas now is reported as being in good agreement with MOND predictions.

    This sample adds 8 new galaxies to the section of “Galaxies for which the MOND fit is dubious” and 14 new to the section “Galaxies well fit by MOND” and moves UGC 5750. This gives an overall score of about 98-0-18, with the 18 being associated to strong uncertainties.

  • Albert

    Juan, having heard talks about MOND since its inception in the 1980s, I can assure you that the wiggle in NGC 1560 plays a prominent role in the presentations of MOND by its advocates since the early 1990s. I have seen that plot presented quite a number of times, and Stacy singles it out in his Web presentation as well. I don’t think my sampling of MOND advocates is biased.

  • Ben

    Albert, you are probably right about overinterpretations of the wiggle of 1560, even though as I said it is much more *plausible*, I think, to explain it in mond or with HI-scaling than with a DM halo. But non-axisymmetric models in each of these paradigms are needed in order to prove this: hopefully it will come soon. Concerning showing the individual contributions of the gas and stars, it doesnt really make sense in mond as the theory is non-linear. Finally concerning the stellar M/L ratio being a free parameter, you are totally right (even though one of the strong arguments for mond is that the fitted ones follow well the trend expected from population synthesis models), but the whole point of Stacy’s paper under discussion here was to take away that free parameter by considering gas-dominated galaxies. The fact that mond still works well for these is, I think, striking. But you are right that it is not true to state that mond has, in general, zero free parameters.

  • Question Mark

    #116: So Ben, you are confirming that with MOND one does not get an improved representation over dark matter models since in MOND there are free parameters that can be chosen to improve any fit?

  • http://canonicalscience.org Juan R. González-Álvarez


    In this comment-page I have introduced six links from Stacy website. Only one part of one of the links discuss the wiggle. The other links discuss MOND predictions (all verified), samples of about a hundred of galaxies explained by MOND…

    The same about the Gentile et al paper. They discuss the wiggle and more as ML ratios and overall fits.

  • http://canonicalscience.org Juan R. González-Álvarez

    Albert, Ben, and Question Mark,

    MOND has zero parameters. It is the dark matter model which uses “free parameters that can be chosen to improve any fit” (as Question Mark says).

    I invite you to read again the section 5.2 of Gentile et al.


    Two parameters for Burkert dark matter model (central density and core radius).

    One/two parameters for the ΛCDM model of Navarro, Frenk & White (concentration and virial mass). Gentile et al. use cosmological simulations to correlate both (see eq. 3), but due to bad fit to the data they repeated the fit leaving both parameters free (read section 6) and still obtained a bad fit and related difficulties.

    Zero parameters for MOND (see equation 6).

    Regarding http://arxiv.org/abs/1005.5456, the authors use M/L as a free parameter to correlate velocity with light distribution, not because M/L was a free parameter in MOND. MOND are equations 1 and 2 in that preprint and they have zero parameters.

    If you were to repeat their analysis using dark matter models you would use one or two parameters (of the dark halo) plus the M/L ratio of the correlation to light.

    I.e. using the Burkert dark matter model you have three times more freedom (rho_0, r_{core}, and M/L) and still cannot match MOND predictions.

    Precisely, the fact that MOND has zero parameters is the reason which is so sensitive to uncertainties in distances, whereas the dark matter models can absorb distance uncertainties into the halo parameters.

  • http://canonicalscience.org Juan R. González-Álvarez

    Above I wrote that in dark matter model you have three times more freedom and still cannot match MOND predictions. A beautiful example of this is discussed in

    Extended rotation curves of spiral galaxies – Dark haloes and modified dynamics. Mon. Not. R. astr. Soc. 1991: 249, 523-537. Begeman, K. G.; Broeils, A. H.; Sanders, R. H.

    Authors compare three-parameter dark-matter fits (M/L for the visible disk, plus two parameters for the dark matter halo: the core radius and the asymptotic circular velocity of the halo) with one-parameter MOND fits (M/L for the visible disk).

    They find that MOND works well and “in some cases better than multi-parameter dark-halo fits.”

    I am sorry to say this to dark-matter enthusiasts, but MOND rocks…

  • Ben

    @question mark: No, I disagree. The M/L ratio is a “free” parameter but its best-fit obtained in mond from dynamics alone is ususally amazingly similar to what one expects from completely independent models based on stellar populations synthesis (that have nothing to do with dynamics): this has been, and still is, one of the strongest arguments for mond! In addition, this free parameter goes away when fitting gassy galaxies, and that was precisely the point of the whole press release of Stacy. Then, there is the distance, which again can sometimes be a little discrepant when set completely free, but which usually gives very good fits when constrained to lie within the range of distances obtained from various independent methods. So, yes there are free parameters (M/L and distance, and in the case of Stacy, only distance), but you wouldnt call a good fit a fit using a crazy value for these parameters, that are in the end not so free anymore… The point is that mond yields brilliant fits in most spiral galaxies with completely reasonable values of those parameters. This is neither overselling nor underselling what mond does. And again whatever the reason for it, its success should be, in my opinion, understood.

  • anand srivastava

    My problem with DM+GR is not that it does not fit the data.
    My problem is that the MOND fits the data without needing DM.
    Since this simple equation works very well at the galactic scale everywhere. The fits actually keep on improving with more data. There can only be two solutions.
    1) DM does not exist at Galactic scale.
    2) DM position in space is defined by BMs position in space. This is simply untenable if we believe DM to be separate particles. Also BM is not supposed to interact with DM except by gravitational force. This is totally non-sensible

    So the real solution is that DM does not exist at the galactic scale.
    I would have had no problem with DM, if MOND did not work so well at galactic scale.

    The fact that MOND does not work as well at cluster or higher scales makes no difference. It is probably an indication that some form of DM exists on those scales. I don’t even think that MOND can be enhanced to form a theory. TeVeS is just a toy theory that shows how to build one, but I am pretty sure the encompassing physical theory will be discovered from a totally unexpected direction. The recent Verlinde’s theory of Entropic gravity looks interesting.

    I liken MOND to an Empirical law. Any quantum theory of gravity needs to bring out MOND or it is not physical. Since GR in its present form does not predict MOND, it is not physical.

    It is as simple as that. Empirical laws must be explained by all physical theories. If Newtons gravitational theory did not explain Kepler’s laws, it would be as useless (at the solar system scale) as GR is presently (at the galactic scale).

  • http://canonicalscience.org Juan R. González-Álvarez

    anand srivastava,

    There is a third solution:

    1′) DM does not exist at all.

    “The fact that MOND does not work as well at cluster or higher scales…” This is only partially true


    and, of course, discrepancies with MOND do not imply existence of DM, (ΛCDM has also difficulties http://adsabs.harvard.edu/abs/2010ApJ…718…60L), but that MOND is being applied outside its range of empirical validity and that a more general theory beyond MOND is needed.

    As commented above (#101), MOND (and generalizations of it) can be derived from a truly general gravitational theory. You are right on that “the encompassing physical theory” was “discovered from a totally unexpected direction”!

    Our goal was to correct other known deficiencies of GR (see the FQXi Essays cited above) and, as a bonus, we discovered that MOND and its acceleration scale were natural outcomes from the new theory.

    If you look to my FQXi Essay, you will discover that the recent theory is much more general than Verlinde’s theory, which is based in a number of approximations and controversial assumptions.

  • anand srivastava

    No MOND does not work very well beyond Galactic scales so we cannot conclude that at all. It is certainly possible, but we cannot determine that from the data alone. But that is not important MOND working at Galactic Scales kills DM+GR at Galactic Scales. This means GR needs modification. We don’t know what the correct theory is going to be. I am not a physicist or a mathematics. I am just a software developer, with an interest in the MOND problem. I can only conclude if a model is good based on its applications and what it predicts. Unfortunately I did not see much effort at resolving different problems of GR in the quoted essay. Particularly MOND and Pioneer Anomaly.

  • http://canonicalscience.org Juan R. González-Álvarez

    anand srivastava,

    I agree with most of what you say. Effectively MOND “kills DM+GR at Galactic Scales” and effectively this means that “GR needs modification“.

    I did not say that MOND works very well beyond Galactic scales. I said just the contrary and even explained why one must wait discrepancies: “MOND is being applied outside its range of empirical validity“.

    I also wrote in this blog how, thanks to a new theory, we do not need DM (neither DE) to explain observations beyond the Galactic scale anymore.

    FQXi Essays are limited in size by Contest rules, therefore I could not write about all the advantages beyond GR (my first draft Essay was over the size limit and I was forced to eliminate many interesting stuff! For instance, I gave some additional technical details, on how the new canonical theory goes beyond M-theory and the rest of quantum gravity approaches, in Dr. Tejinder Pal Singh Essay).

    In despite of size limitations, details and further info are given in the cited literature and in the technical notes in my Essay. In the technical note in page 9, I explain the assumptions and approximations over the which GR is based and how we derive GR from a more fundamental theory. I explain how well-known problems of GR as “the lack of gravitational energy-momentum-stress tensor“, “spacetime singularities“, “the problem of the systems of reference“, “violation of the usual conservation laws“, and “the impossibility to obtain a consistent quantization of such [geo]metric theory” are absent in the new theory.

    Moreover, I have commented in Dr. Corda Essay how we can already go beyond MOND, PCG, TeVeS… explaining data that those theories cannot explain, and also commented I have not still studied Pioneer anomaly enough to say.

  • Phil_Osopher
  • Bob Sanders

    Let’s forget about TeVeS or Bimond or generalized Einstein-Aether theories
    or any of the complicated relativistic extensions of MOND. Instead, consider
    a minimalist definition: MOND is an algorithm (and a very simple
    algorithm) which allows one to calculate the distribution of force in an
    astronomical object from the observed distribution of baryonic matter.
    And, as evidenced by rotation curves, it works! It works extremely well,
    even explaining details in rotation curves which are clearly related to
    corresponding details in the light or gas distribution. This fact is remarkable,
    and it constitutes a severe challenge to CDM or to any dark matter that
    clusters on the scale of galaxies. How can one image that dark matter
    can reproduce this remarkable success of MOND? To think that
    it could presupposes properties of dark matter that is totally at odds
    with its perceived nature as a non-interacting (except for gravity),
    non-dissipational fluid. The dark matter fluid is very different from
    the baryonic fluid; the dm is immune from
    influences that affect baryons: the baryonic fluid can dissipate — loose energy –,
    it can be shocked, it can be removed by supernovae or stellar winds,
    it can be swept out in collisions (e.g. the famous Bullet). Why then should
    these two fluids be so intimately connected and similarly distributed
    as to subsume the existence of the MOND algorithm? In fact, the success of
    the MOND algorithm on the scale of galaxies is a falsification of CDM
    or any dark matter that clusters on the scale of galaxies. To blandly
    state that dark matter exists and accounts for the observations of
    galaxy kinematics is to turn a blind eye to a vast range of phenomena;
    to imagine that dark matter will someday, when we have more understanding
    of the complicated baryonic physics, reproduce the correspondence
    of rotation curves to the distribution of baryonic matter is a
    leap of faith that is more akin to religion than to science. This goes as
    well for the near perfect Tully-Fisher relation as pointed out by Stacy —
    so perfect that the TF by itself implies a connection with physical
    law rather than the messy details of galaxy formation. And how
    will dark matter explain the ubiquitous emergence of a0 —
    as the acceleration below which the discrepancy appears in galaxies,
    as the normalization of the Tully-Fisher and Faber-Jackson relations,
    as the internal acceleration of near isothermal systems ranging
    from globular clusters to clusters of galaxies, and, when expressed
    as surface brightness, as the characteristic (Freeman) surface brightness
    of galaxies. If the putative dark matter particles are ever found
    (and I doubt that they will be), then we have a lot of work ahead of us
    to understand how these regularities, so neatly encapsulated by MOND,
    emerge in the context of a non-interacting, dissipationless, dark matter fluid.

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About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] cosmicvariance.com .


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