**A Philosophical Approach to MOND: Assessing the Milgromian Research Program in Cosmology**

*By David Merritt*

Cambridge University Press (April 30, 2020)

Don’t get put off by the title of the book! Really it should have been called “A Scientific Approach To MOND,” and I am

*so*glad someone wrote it. MOND, to remind you, stands for Modified Newtonian Dynamics, which is the competing hypothesis to dark matter. Dark matter explains a whole bunch of astrophysical observations by positing a new type of matter that makes itself noticeable only through its gravitational pull. MOND instead postulates that the laws of gravity change on galactic scales.

The vast majority of astrophysicists today think erroneously that dark matter has better support in observational evidence, but Merritt cleans up with this myth. Let me emphasize that Merritt is not originally a philosopher by training. He worked for decades in astrophysics before his interest turned to the philosophy of science in recent years. His book is not a verbose pamphlet, as – excuse me – philosophical treatises tend to be, but it’s an in-depth scientific analysis.

What makes Merritt’s book special is that he evaluates the evidence, both for MOND and the standard model of cosmology, according to the most widely accepted criteria put forward by Popper, Zahar, Musgrave, and Carrier. The physicists among you need not despair: Merritt’s book has an excellent (and blissfully short) introduction into the philosophy of science that contains everything you need to know to follow along.

The book is extremely well structured. Merritt first analyses MOND as a phenomenological idea, largely formulated in words, then MOND in the non-relativistic case, then relativistic completions, and then the hybrid theory of dark matter and modified gravity that can be interpreted as a type of superfluid dark matter. In each step, Merritt examines how the theory fares with respect to confirmed predictions and corroboration, which he summarizes in handy tables.

Along the way he cleans up with quite a number of mistakes that you encounter all over the published literature. Yes, this is hugely troubling, and it should indeed trouble you. There is for example the idea that MOND cannot explain the CMB power spectrum when indeed it made a correct prediction for the second peak, whereas dark matter did not. In fact, astrophysicists had to twiddle with the dark matter idea after the measurement to accommodate the new data. Another wrong but wide-spread conviction is that modified gravity has somehow been ruled out by observation on galaxy clusters.

Having said that, Merritt clearly points out that MOND (or its relativistic generalizations) has certain problems, notably the third peak of the CMB is a headache.

The most interesting part of the book, though, is that Merritt demonstrates by many quotations that astrophysicists who prefer dark matter are confusing the predictive power of a theory with the ability of the theory to accommodate new evidence.

I have found this book tremendously useful, though I want to warn you that this is clearly not a popular science book. The book is full with technical detail. However, I believe that the biggest part of it should be understandable for anyone who has an interest in the topic. There are some parts which will be incomprehensible if you don’t at least have an undergrad degree in physics, eg when Merritt goes on about the Lagrangian formulation of the relativistic completions. But I don’t think that these parts are really essential to understand Merritt’s argument.

But. Of course I have a “but”!

I think that Merritt does not pay enough attention to the problem that MOND, because it is non-relativistic, is incompatible with an extremely well-confirmed theory – General Relativity –, and that we have to date no relativistic completion that does not run into other problems with evidence. This means that MOND, simply put, does not live up to the current scientific standard in the field.

Let me be clear that this does not mean that MOND – as an approximation – is wrong. But I believe the lack of a controlled limit to recover General Relativity is the major reason why so many physicists presently reject MOND. I find it somewhat unfair to simply disregard the scientific standard. The standard is there for a reason, and that reason itself is based on evidence, namely: Certain types of theories have proved successful. MOND is not that type of theory, and no one has yet managed to improve it. It only reproduces General Relativity in the cases where we have precision tests by postulating that it does so, not because there is an actual derivation that demonstrates this is consistently possible. This is an extremely non-trivial problem.

This problem is solved by the hybrid version that can be interpreted as superfluid dark matter. In Merritt’s evaluation this option receives mediocre grades. But of course this is because he does not appreciate the need to remove the tension between MOND and general relativity to begin with. Superfluid dark matter does this.

In summary, I think that everyone who has a research interest in astrophysics and cosmology will benefit from reading this book. And I think that physics would much benefit from a similar analysis of inflation and other hypotheses for the early universe, quantum gravity, theories of everything and grand unification, and quantum foundations.

*Disclaimer: Free review copy*

You write

ReplyDelete"it is incompatible with an extremely well-confirmed theory - General Relativity"

But e.g. the equivalence principle is not broken by the MOND, or?

Personally, I don't understand why the equivalence principle has to apply to long distances or low densities. Since the equivalence principle is only a “local theory”?

If the inertial mass becomes smaller, but the gravitational force does not, then the acceleration would be greater.

If the gravitational and inertial masses would differ at long distances and low density, then MOND would not be incompatible with general relativity, or?

Delete"But e.g. the equivalence principle is not broken by the MOND, or?"Depends on how you define equivalence principle. If I take the equivalence principle to mean general covariance, then MOND trivially violates it.

This sounds like a really good book, not to mention that I am a fan of MOND to begin with. With our endless, dreary weather in the northeast US there's plenty of time for reading.

ReplyDeleteViolates or Enhance it?

ReplyDeleteThis is the question that I would like to understand.

Wot? Can't follow, sorry.

DeleteI have a very naive, maybe even stupid, question. What is the problem with GR reducing to Newton in the (intermediate) weak-field limit; and then Newton reducing to MOND in the extremely weak field limit? Why do you need to go all the way from GR to MOND in one step, as it were?

ReplyDeleteNewtonian gravity just does not reduce to MOND. I don't know why you think so. I guess Milgrom would be thrilled if it did, but then if it did that would be in conflict with loads of evidence, so it's not going to happen.

DeleteNobody asked me, but I think you are using different concepts of "reduces to". In mathematical physics, I think that means you have a general set of equations (General Relativity) and in some circumstances some terms of those equations become negligible, and when you drop them out you have a reduced set of equations (Newton's Gravity) which work usefully some of the time.

DeleteIn Mond, you have Newton's equations, and then you materially alter them under certain conditions, without any reason for saying the difference in calculations between them is negligible (it isn't).

As an analogy, you have water which obeys equations of fluid dynamics, and then you have a phase transition to ice, which obeys rigid-body (plus Theory of Elasticity) equations. Those sets of equations are incompatible and do not reduce one to the other as physicists/mathematicians use that term, since one assumes a crystalline structure and the other does not. (For glass, on the other hand ..)

Hi susskind — and you do know that’s a famous name in string theory, yes?

DeleteWhat I

thinkyou were trying to ask is this: What’s wrong with simply using GR for intense gravity fields, Newtonian for average gravity fields, and MOND for very weak gravity fields? Can’t the math be set up to allow the three to fade into each other, with GR at one end handling black holes, Newtonian in the middle handling solar systems, and MOND at the other end handling galaxies?The answer, alas, is no.

You

canset up a smooth transition between Newtonian and MOND. That is precisely why it’s calledmodifiedNewtonian dynamics! However, in terms of your question, the “fade in” is the other way around: Newtonian gravity pops out ofMONDin cases wheredistances(not field strengthper se) are modest, e.g. on the scale of our solar system. For the scale of galaxy clusters and galaxies, though, there simply is no scenario where unaided Newtonian gravity gives result anything remotely like what is actually seen in observations. MOND is just a weird, unique, very arbitrary-seeming addition to Newtonian equations that has gained interest for one reason and one reason only: It works remarkably well for predictingmanyaspects of what is actually seen. But it’s not perfect, and it definitely does not work for everything.Einstein’s GR has a similar relationship with Newtonian gravity, except that in this case the “fade in” depends more on field strength, not distance. The black hole extremum in particular results in vastly different predictions Also, some of the predictions of Newtonian gravity are just flat-out wrong, such as how much gravity bends light paths. Still, it’s not too inaccurate to assert that GR “fades into” Newtonian gravity as field strength (again, versus distance) gets weaker.

What you have, then, is a classic love triangle: Both GR and MOND are “competing” for the fade-in love of Newtonian gravity… and the competition flatly does not work well, either conceptually or mathematically, though I gather lots of folks have tried. For more on that the Merritt book would be a great resource.

I hope that helps a bit.

But, what is the type of evidence that precludes Newtonian gravity reducing to MOND in the very weak-field limit?

ReplyDeleteAnd if you are convinced that a MOND-type theory cannot be obtained as an extremely weak-field of Newtonian gravity , in which sense do you expect it could stand as a dynamical theory describing the dynamical evolution of galaxies?

Newtonian gravity just does not reduce to MOND. How do you want to do that? Do you seriously think people wouldn't have noticed if Newtonian gravity gave you an 1/r force instead of a 1/r^2 force? What are you even talking about?

DeleteIf there is something about mond that is right, then somewhere at the 'edge' of the solar system (~0.1 light year.) There would be a transition region... from ~Newtonian to ~'mond' gravity.

Delete(where the ~ sign is to indicate that these are (hopefully) approximations to some unifying underlying theory.)

Sabine,

ReplyDeleteI bought and downloaded the Kindle version of this excellent book, and can honestly say I've viewed every page... for about 1/4 second each for most.

But that was enough to get a feel for the contents. It does indeed start off very philosophically, but then rather abruptly shifts to full science mode. I

lovethe precise details, tables, and especially curve-fit data point charts later in the book. Also, little details such as the discussion of the cosmogenesis and star history of lithium-7 are just the kinds of details I delight in finding in a good science book.Without mathematical support it's easy for our minds to estimate poorly the levels of improbability associated with various types of data-to-prediction curve fits. Straight-line fits, meh... but complex curves with considerable detail, such as I recall seeing even decades ago (drat... I cannot find the article!) in the first round of renewed interest in Milgrom's idea? Those quickly become astronomically unlikely. So when such curves are generated by

extremely minimal hypotheses, attention should be paid, indeed.And precisely as you have stated in your review, poor attention to the implications of unexpected complex curve fitting is exactly the misperception that this book is trying to correct. Dark matter theory has for decades been extraordinarily weak on prediction. Far from predicting anything, it has instead seemed as if every time a new observation comes along, the data once again "breaks" the dark matter model in some way. Folks then say hey, no problem, we'll just tweak the software

againto make it fit the new data fitagain.Bleh! If Kepler had taken that approach we'd

stillbe using angels to push planets around, just with more sophisticated software to track how the angels like to dance. In a worst-case version this approach to modeling theory becomes not much more than a lookup function for a nicely organized database of observations. That in fact would often be the more honest ways to explain such theories. Sure, they describe the data -- theyarethe data! -- but such data-capture models tell you next to nothing about what's really going on at a deeper level.The real message is always hidden in the Kolmogorov complexity of the data, in the ability to reduce all of it as if by magic to some insanely compact set of equations (Kepler! and Newton, and Maxwell). Making some rather loopy but very simple modifying assertion -- Milgrom's idea that gravity falls off too slowly, which even he initially thought was a pretty wild idea -- that nonetheless ends up predicting remarkably good curves for phenomena for which there was not yet any data back in 1986 definitely falls into this category, even if it does so in a very strange fashion.

I have no idea what to make of MOND and its relationship to one of my favorite theories of all time, general relativity... and I love that! It tells me that Mystery still exists, that there is something deep and likely profound that everyone is still missing. Those are the kinds of conundrums that can give rise to entirely new ways of understanding physics, just as happened in the emergence of quantum mechanics from a few nominally "simple" loose ends related to atom electromagnetic emission and absorption.

P.S.: A side effect of scanning the entire book is that I now know why Sabine took a sudden interest in the Raven Paradox.

Ha, yes, you are right, it was Merritt's book that reminded me of the Raven paradox :)

DeleteSabine,

ReplyDeleteCan I clarify something? Is it right to say that MOND can be formulated in a way that is compatible with SR, but not with GR?

David,

DeleteNo, by definition. MOND is a non-relativistic limit which means exactly that it's not relativistically invariant and thus incompatible with both GR and SR.

But someone developed a relativistically invariant version of MOND, didn't they? That is what I meant.

DeleteThere are relativistic completions which have MOND as limiting cases, but, as I said, all the known ones have problems. Why not read the book?

DeleteIs there only ONE reasonable MOND so far? And if so, why?

ReplyDeleteSabine,

ReplyDeleteI completely agree with David Merrit and your enthusiasm, but not with your critic: "MOND, because it is not relativistic, is incompatible with an extremely well confirmed theory - general relativity -, and that to date we have no relativistic completion which does not come up against other problems of proof. This means that MOND, in simple terms, does not live up to the current scientific standard in the field "

IMO, one should not oppose GR to MOND because MOND is not a theory but a marvelous empirical rule which explains itself several empirical laws of the galaxies, and which remains to be explained by a theory, which indeed will have to integrate the effects of GR, either by modifying GR or by supplementing it with some cosmological effect, or both. It is also the job of this future explanation to theoretically deduce an interpolation rule between the Newtonian and worldly regimes. Not the job of the MOND rule.

Currently, the MOND rule (from which several empirical rules observed in astronomy are deduced) has somewhat the same status as the Bohr quantization rule for the angular momentum of atomic electrons, which explained Balmer's empirical formula so well but also expected d 'be explained by the MQ (which is itself still awaiting explanation). At that time Bohr's rule contradicted known physics, but had for it to integrate h, the fundamental element of new physics. Likewise MOND, but less clearly, flirts with this incongruous element which calls for a new cosmology: the acceleration of expansion.

At that time, physicists did not reject Bohr's rule as most of them rejected MOND, sometimes with incredible violence. This is where there is a degradation of the standards of science.

MOND is a “sorta maybe” that I keep on a back burner. To be honest developments do not appear to be leaning in its favor.

ReplyDeleteThere seem to be some questions people are asking that illustrate some problems. An elementary form of MOND has a modification of gravitation with a potential Φ = -GM/r – gM ln(r). The first of these U = -GM/r is the standard Newtonian potential. The term V = -gM ln(r)is a modifying term and g is the gravity coupling constant associated with that term. The force is given by F = -∇Φ. These potentials can be computed, but in different dimensions of space. The force defines a charge, or in the case of gravitation mass, given by

q = ∫F∙dA

where the area A is a Gaussian surface. Appealing to spherical symmetry we can see this is q = 4πGM for the force F ∝ 1/r^2 that divides the r^2 in the area of the Gaussian surface. In 2 spatial dimensions the Gaussian surface is a circle and this requires the force be F ∝ 1/r. It is then not hard to see the potentials.

If MOND were due to this log potential, where would this have come from? That is where things are odd. Hossenfelder’s suggestion there is a type of phase change between this type of potential and matter is interesting. This suggests maybe something similar to a holographic principle. The phase with the potential might then be a sort of trapped phase, such as seen with pure water that can be liquid below freezing. These fields trapped on the horizon might have been on the horizon of the inflationary cosmos, and with the rapid phase change of reheating it is them plausible a small part of the gravitational field is “trapped” in this inflationary phase on a surface of two dimensions.

Other questions appear to revolve around general relativity. One can have 2-space plus time general relativity. The BTZ black hole and AdS_3/BTZ-BH correspondence is an example of this sort of physics. With low mass, energy etc the 2-space plus time GR will recover a form of gravity with the F ∝ 1/r for of potential. If gravitation or general relativity has a small aspect of this 2-space plus time phase, then the low energy gravity would be this sort of modified gravitation.

There are other aspects to MOND, and there are sorts of “form factor” terms people insert. These terms to model galactic structure more fully I can’t comment on too much. At this time I would say that MOND appears to be a bit on a defensive strategy. ΛCDM pretty much dominates the subject of dark matter. If I were to put the contest between ΛCDM and MOND in analogous war history terms, I would say with the American Civil War it is a bit like the siege of Atlanta 1864, where the Confederacy was in trouble, or maybe Napoleon at Leipzig in 1813, yeah he was in trouble. Without some sort of shot in the arm I am not sure if MOND will make much further impact.

Sabine,

ReplyDeleteMaybe for the sake of us non-physicists you could comment on where the wiggle comes from that would a theory to make predictions different from the standard model without violating GR. Doesn't GR itself predict the orbital speeds? If so, how could MOND predict different speeds without contradicting GR?

Andrew,

DeleteI am not sure I understand the question. First, MOND is a non-relativistic limit. It will never reproduce GR because it isn't generally covariant. What you are looking for is a theory that in the non-relativistic limit reduces to MOND but at acceleration reduces to GR. Finding such a theory that, in addition, isn't incompatible with evidence already, turns out to be extremely difficult. Despite almost 30 years of trying, no one has found one.

(1) MOND is a empirical rule which cannot reproduce GR (or any theory) just as Bohr's condition could not reproduce classical electrodynamics

Delete(2) Perhaps the explanation of this rule is not a new gravitational theory but a new cosmological model. A departure of relativistic cosmology (FLRW) which would follow from another GR's interpretation, not from a modified gravity (i have worked in that way but i am just a "philosophe"). In this way the theory which support MOND is not just a modified theory of gravity but a result of a new cosmological effect in another vision of GR.

I was responding to Sabine's apparent major objection to MOND: it "is incompatible with an extremely well-confirmed theory – General Relativity". I was making the simple-minded rejoinder that of course it is incompatible with GR - how else could it make different predictions?

DeletePerhaps the problem is not that MOND is merely incompatible with GR, but that the incompatibility is too profound?

When I say the two imcompatible, I don't mean that MOND makes different predictions in some parameter ranges, which it obviously does, I mean that we already know that there is no limiting case of MOND in which we will recover General Relativity.

Delete"...there is no limiting case of MOND in which we will recover General Relativity. "

DeleteSo in certain domains MOND makes predictions which are known to be wrong? Because it conflicts there with GR which is known to be right?

Andrew,

DeleteBasically, yes, though that's a weird way to put it. It's more that MOND does not make predictions for certain cases because we already know it doesn't apply. Simple example: No one is going to correctly predict the emission of gravitational waves from binary systems with MOND because MOND is a non-relativistic limit. Now you can insist on using it and then say "it makes a wrong prediction" but that would be silly because we already know you should not use it.

It's the same as proclaiming that "Newtonian gravity is wrong" because you tried to use it to predict time dilation. It's wrong not because the theory itself is wrong, but because you have used it in a regime in which we know it is not a good approximation.

And now I ask you: why are you assuming that I want to reduce anything to MOND, what gave you such an idea? I am just trying to understand the problem from someone who thought hard about it. And I said at the outset that my questioning is naive. I was also assuming that if you write that such a reduction would conflict with loads of other evidence, you would then give us a couple of examples instead of pointlessly ask me back another rhetorical question.

ReplyDeleteYou don't want to reply, don't publish my comment. It's not a problem; but if you wish to reply do it seriously.

Delete"And now I ask you: why are you assuming that I want to reduce anything to MOND, what gave you such an idea?"You did. You first wrote:

"What is the problem with GR reducing to Newton in the (intermediate) weak-field limit; and then Newton reducing to MOND in the extremely weak field limit?"And then again:

"And if you are convinced that a MOND-type theory cannot be obtained as an extremely weak-field of Newtonian gravity"Now you write:

"You don't want to reply, don't publish my comment. It's not a problem; but if you wish to reply do it seriously."I have responded to your questions twice already, which I frankly think is enough.

Jean-Paul errata :"between the Newtonian and worldly regimes" read Mondian regime.

ReplyDeleteAnd of course, ACDM cannot predict DM effect because in his frame any explanation of discrepancy with GR is a "discovery" of DM object. As Terry Bollinger says : "[such "theories"] describe the data -- they are the data!"

I wonder if we fell back into kindergarten...

ReplyDeleteOK, I see your level of understanding.

I have spent time trying to understand and politely respond to your ill-informed and badly phrased questions. In response, you insult me. I have no patience for shitty behavior like this. You need not bother submitting further comments, I will no longer approve them. Good bye.

Delete

ReplyDelete"There is for example the idea that MOND cannot explain the CMB power spectrum when indeed it made a correct prediction for the second peak, whereas dark matter did not."Not really. This refers to Stacy McGaugh's prediction of the height of the second peak. Stacy, of course, is a proponent of MOND, but there is no MOND in that prediction in any way, shape, or form. All he assumed was that there is no dark matter. The prediction otherwise uses standard CMB physics, no MOND at all. Of course standard cosmology can explain the CMB spectrum; this is probably the best success story of modern science. But there are 6 or so free parameters (many of which are constrained by non-CMB stuff). The default values for some of the parameters used by some people didn't get the height of the second peak right. Big deal.

In retrospect, it's a coincidence that McGaugh got the height of the second peak right. However, his simple model goes vastly wrong on the third peak, as he is the first to admit. So, now that we've seen more than two---about seven---peaks, MOND definitely cannot explain the power spectrum of the CMB. Not only that, but a) no-one knows how to so such a calculation in MOND, and b) the one thing one can say is that if one naively extends MOND to handle structure formation, structure forms way too quickly, which even the MOND people see as a problem.

Maybe Stacy will weigh in here.

I haven't read this book yet, but have read a

similar articleby Merritt from a few years ago. The main problem I see is that he attacks a straw-man version of standard cosmology. You didn't mention that; maybe he has toned it down in the book compared to the article. Also, he doesn't apply the same standards. For example, in the article he criticizes dark matter and dark energy as ad-hoc ideas, whereas Milgrom's idea of a change in gravitational attraction below some acceleration is almost the textbook example of an ad-hoc explanation, i.e. one invented solely to fit the data with no theoretical motivation whatsoever (though in the meantime people have tried to come up with explanations for MOND).I actually think that there is something to MOND phenomenology, thought it is not clear what the explanation is. It is a problem that the mainstream cosmology community is not as aware of this as they should be (though to be fair most MOND phenomenology has nothing to do with cosmology). However, I fear that they will be put off by strawman attacks, since they are usually an indication that one has no better arguments, though that is definitely not the case with MOND.

I'm looking forward to reading the book and am interested in seeing whether it is more balanced than his article.

Phillip Helbig:

DeleteSome of the papers on MOND that I’ve read are quite technical, and were hard for me to understand, but I gather the model doesn’t have a ‘seed’ mechanism equivalent to Dark Matter that can produce density variations in the early Universe, that eventually coalesce into galaxies and larger structures. Googling a minute ago, I was quite surprised to see a Discover magazine article from February describing a computer model that claims that structure formation can proceed without Dark Matter, which I’ve linked below.

https://www.discovermagazine.com/the-sciences/does-the-universe-need-dark-matter-to-form-galaxies-a-controversial-model

Phillip Helbig

ReplyDeleteI know that MOND cannot explain all DM effects, but i was not aware of that : " the one thing one can say is that if one naively extends MOND to handle structure formation, structure forms way too quickly, which even the MOND people see as a problem". Could you give a reference ? Thank you

What is your opinion about TeVeS and STVG? What was the impact of GW170817 episode in MOND theories?

ReplyDeleteRead the book?

DeleteI will for sure as I did for your "Lost in Math"...

ReplyDeleteIs the "extra" gravity needed to explain the various observations that don't agree with "linearised" GR, uniform or not?

ReplyDeleteE.g. do the stars orbiting on the edge of 2 very similar galaxies orbit at similar speeds?

If so then one would expect a modified gravity solution. If not then one would expect a mixed dark matter and modified gravity solution or possibly just dark matter and GR. Would one not?

One of the problems that I see with dark matter in general is the feeling as the matter is entrained in a Black hole it ought to be producing a signal identifiable as distinct from baryonic matter.

ReplyDeleteI wonder if the author addresses dark matter /black hole encounters.

Hi Sabine,

ReplyDeleteI came across the interesting work of M. E. McCulloch where there he compares the results of Newton, General Relativity and MoND vs his Quantised Inertia for the wide binaries. The work is named "Testing Newton/GR, MoND and quantised inertia on wide binaries" (Link: https://link.springer.com/article/10.1007/s10509-019-3615-z).

I do not know (I am new on this Blog) if you have ever written an article or comment about McCulloch's Quantised Inertia before, therefore I would like to ask about your opinion. After MoND, a theory that appears today to receive significant attention (maybe I am wrong) is that of McCulloch.

What is your view?

Now the Bullet Cluster, and like structures, seem to be impossible to explain in MOND, or any other model, without Dark Matter. Yet, I seem to recall that Sabine stated somewhere, though not on this particular post, that MOND can handle the Bullet Cluster. Or maybe it was on Stacey McGaugh’s website that I read that the Bullet Cluster’s dynamics can be accommodated in MOND. I will have to do some searching. In the meantime, from reading a Forbes article on the Bullet Cluster by Ethan Siegel, I see that there is a modified gravity model that can account for the displacement of the gravitation potential in the Bullet cluster away from the center-of-mass of the system represented by the hot gases in the collision zone. I’m going to read that soon to see how they solve this seemingly intractable problem in a non-dark-Matter framework.

ReplyDeleteModified gravity has no problem handling the bullet cluster. Instead, the Bullet Cluster is a problem for LCDM. I explained this here.

DeleteSabine, thanks for pointing me to your 2017 write-up on the Bullet Cluster, where you emphasize that the actual center of mass of a system can be dislocated from the baryonic mass center in modified gravity models. This is the situation in galactic structures where the radius corresponding to the mean mass center is shifted outward due to the deviation from Newton in the outer galactic burbs. And, it’s in galaxies that MOND has it best track record. Looking at the composite red/blue image of the Bullet Cluster it’s apparent that the bulk of the ionized gas clouds are butted up against their respective galactic clusters where the mass is centered. So, while there is center-of-mass displacement from the Newtonian expectation, it’s perhaps no worse than seen in galaxies.

ReplyDeleteI meant to mention the name of the modified gravity model referred to in the Forbes article in my earlier comment. There were actually two papers, which I just noticed this morning. One was authored by John Moffat and Victor Toth, titled “Cosmological Observations in a Modified Theory of Gravity (MOG)”, dated 2013. It was a tour-de-force of mathematical complexity, which I won’t even pretend to say I understood. I did wonder if perhaps they were introducing too many adjustable parameters to make things fit. In my mind the MONDian framework is better with just one parameter. The other paper dealt with MOG’s compatibility with the neutron star merger data from LIGO event GW170817 and the coincident gamma ray burst.