Last time, we started talking about the data in the recent paper The Baryonic Mass-Halo Mass Relation of Extragalactic Systems. Here, we’ll put on our dark matter hat, and use the data to make an accounting of the mass – both the dark matter and the baryons in all their various forms. From this conventional perspective we will obtain a method for relating what we see to what we don’t. In the context of LCDM cosmology, this provides an alternative approach to abundance matching. It also provides a test: are the two consistent?
The conventional picture we have in mind is a baryonic galaxy residing in a dark matter halo bathed in a background of intergalactic matter.
Fig. 1 of McGaugh et al. (2026): Conceptual elements of a galaxy: the stars (yellow/blue) and atomic gas (green) of NGC 6946 (Spitzer 3.6Β΅ and 21 cm data: F. Walter et al. 2008) are shown embedded in an extended dark matter halo (black). The dark matter density decreases continuously with radius so the halo has no hard edge, but for convenience we adopt the common convention that the radius r200 marks the boundary of the dark matter halo and the dividing line between the circumgalactic medium (CGM) and the intergalactic medium (IGM; orange). The stars and atomic gas illustrated here appear within r < 20 kpc while r200 β 220 kpc (not shown to scale).
I’ve talked here about the stars and gas a lot because that’s what we see. These are the essential components that define a galaxy and comprise the mass that correlates with rotation velocity to make the baryonic Tully-Fisher relation (BTFR). I’ve talked a bit about the stuff between the galaxies, the intergalactic medium (IGM), but I don’t think I’ve previously had cause to talk much about the circumgalactic medium (CGM). As the name implies, this is gas in the vicinity of a galaxy, but not in the galaxy itself – at least not the part we can readily see. In the notional picture above, the distinction between the CGM and the IGM is the boundary of the dark matter halo that nominally demarcates gravitationally bound from unbound material.
Notional is doing a lot of work here. There’s a lot of gas in the IGM, and some of it is certainly in the vicinity of galaxies, so in that regard counts as circum-galactic. But there’s no hard and fast distinction between these components just as there’s no hard edge to a dark matter halo. Our brains don’t like that, so we impose notional boundaries and proceed as if these are meaningful.
Proceeding thus, we expect our dark matter halo* to contain its fair share of the cosmic baryon fraction, fb = Mb/M200 = 0.157 according to the Planck flavor of LCDM cosmology. We can test this by adding up all the baryons and comparing that to the total mass enclosed by r200. This is straightforward for the stars and gas we see, but not for the stuff we don’t see – both dark matter and the gas in the CGM.
There are some measurements of the CGM, but these tend to be statistical in nature (if we stack data for a bunch of galaxies, we sorta see something), not the precise, individual, galaxy-by-galaxy measurements that we have for the stars and atomic gas. The stars and atomic gas are the mass in the extended Tully-Fisher relations we discussed previously, and are the bulk of the normal material in the galaxies we see. The bulk of the CGM lies at much larger radii, beyond the stars and atomic gas, but within the notional edge of the dark matter halo, as depicted above. Since we don’t measure it directly in individual galaxies, we’re gonna leave the mass of the CGM as an open question rather than something to be included in the sum of known baryonic mass.
The situation is even murkier for the dark matter, which we don’t see at all, so we don’t have a good way to measure the “total” mass of dark matter halos. This isn’t even a well-defined quantity in principle since halos are not expected to have a hard edge. Conventionally, we adopt the mass within a radius that contains a density two hundred times the cosmic critical density, r200, as the notional edge. There are obscure historical reasons for this choice that I do not have the patience to describe. One could make other choices, arguably better choices, but r200 is the most common choice used in the literature so we’ll stick with it here. The halo mass is the mass enclosed by this radius, M200. If one goes through the math, it turns out that the circular speed of a test particle, V200, orbiting at r200 scales with the Hubble parameter [h = H0/(100 km/s/Mpc)] such that V200 = h r200 when V200 is in km/s and r200 is in kpc. The dynamical mass (rV2/G) can then be written
That is a lot of huffing and puffing to get a way to relate the halo mass to something we can (kinda sorta) measure. The flat rotation velocity Vf has always been taken as the signature of the dark matter halo. One therefore expects V200 ~ Vf. Indeed, these quantities cannot differ by much if dark matter is what explains flat rotation curves. However, the notional radius of the dark matter halo where V200 occurs is much larger, by roughly an order of magnitude or more, than the radius where Vf is measured. So they need not be identical, depending on the halo model. So to relate what we measure to what we’d like to know we define a little ol’ fudge factor, fv, such that:
If a rotation curve stays flat indefinitely (as our empirical experience suggests), fv = 1. If instead dark matter halos behave as they should in LCDM, then the rotation speed should gradually decline as we approach the halo’s edge so that fv > 1. How much greater?
One way to estimate the fudge factor fv is to fit dark matter halo models to data. This process does not directly measure V200, but it does provide an estimate of that quantity based on the data available a smaller radii. One can do this for as many halo models as one has the patience to consider. For example, here are the results for two common halo models, the traditional pseudo-isothermal halo first adopted to explain flat rotation curves and the CDM-expected NFW halo:
The result for pseudo-isothermal halos is consistent with fv = 1, as expected – this model was adopted to make flat rotation curves. There is nevertheless some scatter. This typically happens because the observed rotation is not observed to be flat over a large enough range of radii to enforce flatness further out (as often happens in dwarf galaxies) or because the stars account for so much of the mass over the observed range that the inferred dark matter component is still rising (as often happens in bright, high surface brightness galaxies). This sort of haziness is inevitable when one only measures the inner few percent of the notional virial radius.
The result for NFW halos is approximately fv = 1.4, albeit with a lot more scatter. This happens for the same reasons as above, with the additional problem that the dark matter profile in real galaxies rarely looks like NFW. Of all the many halo models considered by Li et al. (2020), NFW consistently performs the worst. One is forcing a fit of a function that would rather not. One signature of this misfit is the occurrence of very large V200 for dwarf galaxies with small Vf. Taken literally, this would mean that some of the smallest dwarf galaxies reside in dark matter halos that outweigh those of giants like the Milky Way. This seems absurd, and it is. For example, by this approach, the dwarf galaxy NGC 3109 residing just outside the Local Group outweighs the Local Group and both its giants, Andromeda and the Milky Way, put together. But it is pretty clear from the local velocity field that the entire Local Group is not orbiting this little dwarf.
The estimation of huge V200 for galaxies with small Vf happens because of the cusp-core problem. The density cusp predicted by NFW expects a curved shape for the inner rotation curve while the data show a more gradual, quasi-linear rise. Any decent fitting program will realize that it can make a curve look like a straight line if it stretches it out enough, so it does exactly this by making the halo very large. That sorta fits the data, but it makes no physical sense. Between this systematic effect and the large scatter induced by the other effects discussed above, one is better off inferring V200 from Vf with a fixed fudge factor. So we’ll do that, leaving the exact value of fv as an open question, but noting that for most objects it almost certainly resides in the narrow range
That’s a lot of words to say the observed flat rotation speed gives us our best kinematic estimator or the dark matter halo mass. In this context, bear in mind the small scatter in the extended Tully-Fisher relations. This contrasts with the large scatter seen in the fits above. This strongly implies that Vf is more closely tied to the underlying mass^ than are the model-specific halo fits to the entire rotation curve. That might seem counterintuitive given that Vf is only a portion of the rotation curve (albeit a well-defined portion). However, it makes more sense when one considers that rotation curve fits must consider the contribution of stars as well as dark matter. Since the stellar mass-to-light ratio is never perfectly known, there is a degeneracy between the two that contributes to the scatter seen above. That variation is not real, it’s just an artifact of the fitting procedure. But when we get to large radii, beyond the confounding effects of the stellar population, the signature of the dominant mass becomes apparent in the flat rotation speed.
We saw above that we expect the halo mass M200 to correlate with V200. We observe that baryonic mass Mb correlates with the flat rotation velocity Vf. The natural assumption is that the stuff we see is proportional to the total (mostly dark) mass while the observed flat velocity is a property of the halo. Hence Mb ~ M200 and Vf ~ V200. This simple argument has been the basis for many papers claiming to explain the Tully-Fisher relation over the course of many years. This would be entirely satisfactory if it weren’t so completely wrong.
Here we need to introduce another fudge factor, mb, that relates the mass we see to the halo that spawned each galaxy:
The obvious assumption is that mb is a constant for all galaxies, in which case Tully-Fisher follows because Mb ~ M200 ~ V2003 and V200 ~ Vf. The wee problem is that this predicts a Tully-Fisher relation with slope 3: Mb ~ Vf3 when we observe one with slope 4: Mb ~ Vf4. In order to reconcile these two, our new fudge factor cannot be a constant. Worse, we need to fine tune it to transform the predicted power law into the observed one: mb ~ Vf. That… doesn’t make any sense.
We can refrain from thinking and plunge ahead to simply plot the baryon fraction. While we’re at it, let’s also plot the stellar mass fraction m* = M*/M200 because that is more commonly discussed in the literature. (Often stellar masses are available for galaxies without the corresponding gas mass measurements.) These fractions have to be increasing functions of circular velocity, or equivalently, mass (mb ~ Vf ~ Mb1/4):
To be specific, I’ve computed the halo mass assuming fv = 1. Different assumptions just slide the data up and down; the trend persists. This is discussed more in the paper if you’re interested in such details.
This gives a nifty way to relate what we can see to what we can’t. There’s a simple formula:
where fb = 0.157 is the cosmic baryon fraction and and M0 = 5 x 1013 Mβ is the scale where the function bends, transitioning from the Mb ~ Vf4 of the BTFR that holds over most of the mass range to the mb = fb of rich galaxy clusters. The precise value of the turnover mass is not well constrained, as it happens in the one place that is not well sampled by the available data. Indeed, there is nothing special about the functional form; it is simply a choice that transitions nicely from one regime to the other. There’s no physics in it&. Still, this is a useful way to estimate the halo mass of pretty much any extragalactic object just by summing up its observed baryonic mass.
Indeed, this kinematic mass-matching relation is better than the widely used abundance matching relations in that it has less scatter. Abundance matching generally relies on stellar mass; that results in more scatter for the same reasons discussed for Tully-Fisher. This is particularly apparent at the low mass end of the top panel above, where galaxies of the same circular velocity (halo mass) have very different stellar masses. This goes away when baryonic mass is used instead.
There is reasonable agreement between abundance matching and kinematics at intermediate masses. The lines representing various abundance matching relations parallel the kinematic data. The offsets that are apparent can be cured by an appropriate choice of fv. Always a free parameter to the rescue there is.
At the high mass end, things go amiss again. Partly this is because abundance matching relations reference the stellar mass of the “central” galaxy. The picture is that each halo contains one central galaxy with many satellite galaxies in subhalos, so what matters is the stellar mass of the central. This is overly simplistic: galaxy clusters are messy, the brightest galaxy isn’t necessarily at the center, and most have substructure with multiple groups rather than a single hierarchy. Besides that, the stellar mass tells you little about the halo mass without further environmental context: a galaxy with M* ~ 4 x 1011 Mβ could reside in halo masses spanning a couple of orders of magnitude.
Setting aside the issue of centrals, there is a serious tension for individual high mass galaxies. The stellar mass fraction suggested by kinematics keeps going up where that of abundance matching turns over. This is due to the linearity of the Tully-Fisher relation compared to the knee in the Schechter function shape of the stellar mass function. The two don’t match up, as discussed previously. This same tension has long been with us; in the ’90s we were concerned with the difference between “the luminosity function normalization” and “the Tully-Fisher normalization.” This tension never went away. Still, the tension between abundance matching and kinematics doesn’t seem tragic, and might be remedied with some appropriate finagling of both the baryon fraction and the velocity fudge factor.
But where are all the baryons? They’re all accounted for in clusters, which reach the cosmic baryon fraction. But in no other system is the checksum complete. There is a missing baryon problem locally in each and every dark matter halo below the cluster scale. To confound matters further, there is a fine-tuning problem: the amount of missing baryons scales precisely with the amount of observed baryons.
The logarithmic plot above may understate the magnitude of the problem. To clarify this, we can plot the ratio of missing-to-observed baryons on a linear scale, at least in part:
The scatter blows up when we plot linear ratios; this is an artifact of error propagation. Nevertheless, it is helpful to see that the local missing baryon problem is not subtle. It is already a factor of ~2 for groups and ~3 for bright galaxies. It’s not as if we’ve misplaced a few percent of the baryons. Most of the baryons that should be associated with galaxy dark matter halos are not in evidence.
This problem has been known for a while, but doesn’t seem to be acknowledged to be a problem. Not all baryons need condense down into the central galaxy; some might be left behind, still mixed in with the dark matter halo. The widespread assumption seems to be that the missing baryons are probably in the CGM.
Accounting for the missing baryons with gas in the CGM almost works in bright galaxies like the Milky Way where we need “only” a factor of a few. Recent estimates suggest that the CGM is comparable in mass to the stars, or even somewhat more. These are very uncertain, as this mass is dispersed in diffuse gas over an enormous volume, and the total mass estimates often involve large extrapolations: the CGM is detected most readily nearby the central galaxy, but most of its implied mass is way far out near r200. Accepting these estimates at face value leads to the star symbols in the plot above. This makes the checksum complete provided the halo is not too massive, as happens if fv β 1.4. This is what we expect for NFW halos, so it might work out if those were viable. However, there is a bigger issue.
The local missing baryon problem gets progressively worse for lower mass galaxies. For 1010 Mβ galaxies – not all that much smaller than the Milky Way (Mb = 7 x 1010 Mβ), the problem isn’t a factor of two or three: there are ~6 baryons missing for every one that is observed. For 109 Mβ galaxies, the deficit is an order of magnitude. For even lower mass galaxies, the difference is so large we have to abandon the linear plot lest the interesting parts for bright galaxies get scrunched into invisibility. By the time we get to small dwarf galaxies of 106 Mβ, the ratio of missing-to-observed baryons approaches 100:1. It is not plausible to imagine that the CGM of dwarf galaxies explains this deficit. (And yes, we’ve looked.)
A common explanation for this variation is that low mass dark matter halos have shallower potential wells, so have a harder time holding onto their baryons. Supernova can drive material out of galaxies; these go off with the same energy regardless of the galaxy they’re in so they may be more effective at blowing baryons out of lower mass systems. There is sufficient energy (IF properly% distributed) to completely unbind the baryons, so they might wind up in the IGM, defeating any hope of completing the checksum. This is the sort of argument that sounds clever but fails to address the real problem. The difficulty isn’t just ridding ourselves of these meddlesome baryons, it is getting rid of exactly the right amount each and every time.
As awkward as it is to realize that most of the baryons that should be in low mass halos are not in evidence, it is not difficult to imagine ways in which this might happen, like the aforementioned supernova-driven galactic winds. The more dire aspect of the problem is the fine-tuning. Galaxies of the same observed baryonic mass are always missing the same amount of baryons, whether that’s a factor of 2 or 10 or 100. If the visible parts of a dwarf galaxy are only 1% of the available baryons, you’d expect a lot of scatter. Sometimes a halo of that mass might have 2% or even 3% of its baryons condense to the parts we see. That would show up in the scatter in a way it does not: galaxies of the same circular velocity (halo mass) have the same baryonic mass every time. They don’t vary by factors of two (or more). So while we can build models that makes the baryon fraction just so, the fact that we can write a simple equation for it with practically zero scatter is profoundly uncomfortable.
An extra bit of weirdness is that in LCDM, galaxies are built hierarchically by merging small objects into large ones. This poses a teleological problem. Consider a small halo at high redshift. If it remains alone, then it it will contain a dwarf galaxy at low redshift that has a low baryon fraction. But if it mergers into a larger system, then by the current time that larger system has to have a larger baryon fraction. In effect, a low mass halo has to know where it will end up some billions of years in the future. Will it remain alone and unmerged? Better blow out all those baryons! Will it merge into a larger system? Better hang on to the right amount of baryons. Does that system merge into a still larger object? Hope it held onto even more baryons, in exactly the right amount at every step along dozens of mergers.
I can imagine all this happening in a stochastic fashion with the net result being that more massive systems wind up with a higher baryon fraction, at least on average. I cannot give credence to this process resulting in the small observed scatter. As people are always telling me, “galaxies are complicated.” Indeed, they should be – in LCDM. But in reality they’re not! They obey simple scaling laws, laws that do not follow naturally from LCDM.
The local missing baryon problem encapsulates one of the fine-tuning problems that has never been satisfactorily explained. This alone would be considered fatal for most theories. For LCDM, it is just another problem to be addressed through the eternal tweaking of models and simulations.
*Strictly speaking, M200 refers to all mass within r200, baryons as well as dark matter. I’m going to call it halo mass anyway, because that’s what we mean, the baryons are a small fraction of the total, and because that’s what everybody does in the literature. If we make some other choice for the definition of the mass of the halo, MΞ, then the inferred baryon fraction of an objects scales by M200/MΞ. The cosmic baryon fraction does not care what choice we make, so the implicit assumption is that one asymptotes to the cosmic fraction if one gets far enough out, irrespective of what rΞ we adopt. While this is a sensible assumption – individual objects must merge into the larger cosmos at some point – there is no guarantee that the universe cooperates. For example, the baryon fraction in galaxies declines with increasing radius, but that in galaxy clusters increases with radius. I’ve seen hints that it doesn’t really settle down to the cosmic (or any particular) value. These are only hints – considerable extrapolation is involved – so we’ll ignore this inconvenience and assume that the baryon fractions of individual objects do in fact converge to the cosmic value far enough out.
^It makes the most sense if the underlying total mass is the observed baryonic mass.
&I made a very similar fit in McGaugh et al. (2010) but didn’t publish it because there was no physics in it. Since then the field has been awash in abundance matching relations that were similarly fit sans physics. There has been much ink spilled justifying it post-facto with feedback, but I have refrained from this exercise in intellectual onanism.
%It is common to assume in simulations that a large fraction (50 – 100%) of the energy from supernovae is returned to the surrounding gas. This process is not resolved in cosmological simulations, all the energy return happens as part of the “subgrid” physics, so the feedback efficiency is set, in practice, to make things work out as well as possible.
Observationally, most of the SN energy finds its way out along the path of least resistance where the density of the surrounding gas is smallest (“chimneys”). This process couples to the surrounding gas with only a few percent efficiency.
this is compelling. essentially you are saying that only in the extreme radiative environment of galaxy clusters, does the visible matter component (plasma) approach the 15% : 85% ratio – in virtually ALL other environments, the plasma component (plus some gas) is closer to the 1-5% range. Why have folks not engaged with this obvious discrepancy
I couldn’t speak to what other people think, but I think the underlying presumption is that LCDM is correct so the checksum must work out and no further thought is required.
Of course, some people do engage with the issue – Joel Bregman has spent much of his career trying to detect and make a proper accounting of the CGM. But if he says “we detect some but it still falls short” and someone else says “it adds up (close enough!)” there is a bias to hear the latter story if that’s what you want to hear.
There also seems to be a bias towards bright galaxies where the discrepancy is “only” a factor of a few, while neglecting what dwarfs are telling us / believing anything is OK for those little things. I once heard a prominent – and usually sensible – cosmologist ascribe it all to galactic winds. It was such an obvious failure to engage with the issue (exactly as you say) that I asked a single question about how that would work in different environments (it wouldn’t) and he immediately saw the glaring hole in his argument so refused to answer and hasn’t spoken to me since.
Thanks – wow – this feels more like sociology than physics – scientists as humans are as susceptible to pouting and denial as anyone else. Back to physics – I am still fixated on your figure 7 – the killer chart – what if one plotted the core temperature of the structure versus the observed baryon fraction in that structure – would that show a high correlation – cluster cores are far hotter than galaxy cores and within galaxies, HSB cores are far hotter than LSB and dwarf cores – what if DM itself is baryonic and hotter temps ionize greater fractions of total matter, βrevealingβ more matter. What if the right demarcation is ionized/neutral, not baryonic/non-baryonic? Then Fig 7 would make sense
Oh my yes – this subject has been swamped by sociology over science for ages.
As for temperatures, do you mean the virial temperature? Certainly deeper potential wells are hotter in this sense, but the emissivity is a complicated function of temperature so I don’t think the linear relation we see could follow from that.
makes sense on the temperature. I feel somehow that even if LCDM CDM folks dismiss MOND, they need to take the almost scale-free predictions of MOND seriously, just to learn more about the nature of dark matter and its interplay with visible matter – approximating it with feedback recipes makes no sense, and the fits are so flexible with parameters given multi-dex amplitude excursion freedom, that they predict absolutely nothing. DM and baryonic mass distribution MUST go hand in hand (the disk halo conspiracy) for any of this to make sense – I do not see how spherical or near-spherical fits could EVER predict the BTFR and individual RCs versus merely fitting them. DM had to have been collisional at some point and become disk like. that would make sense dynamically
I think the ionized/neutral distinction is a useful clue, but maybe the deeper issue is not simply what matter is visible. It is what matter is dynamically coupled to the observed baryonic system.
The striking thing about the BTFR and Fig. 7 is the low scatter. If feedback, gas loss, ionization state, CGM accounting, and halo assembly history were all loosely coupled processes, the result should be messy. Instead the observed baryonic mass and the asymptotic kinematic scale behave almost as if they are two readouts of one causal record.
So I agree that spherical halo fits feel backwards here. They can be made to fit, but they do not explain why the disk baryons know the halo velocity scale so precisely. Whether the missing component is hot, ionized, weakly visible, or something else, the hard requirement is that it be causally locked to the baryonic distribution in a way that naturally yields the BTFR and individual rotation curves.
In that sense, the βdisk-halo conspiracyβ may be telling us that the usual baryonic/non-baryonic accounting boundary is not the right primitive distinction. The more basic distinction may be between material that is locally visible and material/medium response that remains dynamically coupled through the systemβs history.
exactly
If there’s DM in any form, it knows what the baryons are doing. It’s hard to do without DM at all scales, and there’s evidence for a collisionless material in clusters. But whether for a hybrid theory or whatever, we hit this major conceptual clue – there’s a close causal connection between dark and visible matter.
This is crying out for an idea to address it, but it might need a radical one. Is there a list of ideas – do you think DM used to be collisional in the past and is now collisionless?
In PSG the visible matter emits ‘DM’, it’s not matter but a collisionless small-scale medium of vibration in space itself. It creates the field by dissipating (matter is refracted on helical paths at a very small scale). Light gets lensed round objects via basic refraction, as has been known to work since Eddington, and picks up an excess that builds up at larger scales.
So DM knows what the baryons are doing, but once emitted it hardly interacts with them, and the connection is not obvious. This means DM can be in a disk shape, it follows the baryons. It allows the very thin galaxies we discussed a while ago, and a range of other things.
Incidentally, for an update on attempts to interpret MOND (from one part of the underfunded conceptual department), a recent idea doesn’t seem to work. I looked again at the far better fleshed out and cross-corroborated idea published in ’23, and much preferred it, that the field is effectively ‘compressed’ at any point beyond a0 by r/r[M]. Accelerations are boosted by the same factor, which is a perfectly good way of taking MOND, because the rate of change of the dissipation of the medium speeds up at the MOND radius, and that rate of change creates accelerations for matter (given matter’s relationship to the field) and is proportional to them, hence the 1/r^2.
Yes – exactly – DM used to be collisional post-BBN and pre-recombination – and became collisionless before recombination – the whole potential is disk like, not spherical NFW profiles. that simplifies a lot. I am preparing a paper with that very logic – so far so good, fingers crossed
Years ago I had a somewhat similar idea. The thinking was agitated matter (ionized hydrogen and helium in stars and gas clouds) was a source of bi-energy gravitons βequal numbers of both. The positive energy gravitons would enhance the gravity in galaxies and galaxy clusters, while the negative-energy gravitons would want to βget out of Dodgeβ, so to speak, since they would repel matter, pushing it apart. At first it seemed like a tidy idea, accounting for the extra gravity in large astronomical structures and Dark Energy accelerating the expansion of the Universe. But then it dawned on me that Dark Matter in the form of gravitons would be massless and moving at c, thus being quite βhot dynamically’; not the mass range needed to be dynamically cold to stick around Dodge. Also, I wasnβt sure if negative-energy gravitons would violate the Null or Weak energy conditions. And, on top of that, it didnβt seem likely that it could be modeled so that it would mimic Mondian behavior. So, unfortunately, it was a flash in the pan idea.
An interesting point here is that the Baryonic Tully-Fisher Relation links the visible baryonic mass of galaxies directly to their dynamical behavior, much as Newton’s law links the masses of a two-body system to its dynamics.
While the original luminosity Tully-Fisher relation already existed before MOND, since 1977. What MOND predicted in 1983 was that the fundamental relation should be between asymptotic rotation speed and baryonic mass, not luminosity, MOND predicted this relation before its modern observational confirmation.
The broader lesson may have little to do with dark matter itself or missing mass in general.
General Relativity was developed and calibrated in relatively simple gravitational systems, assuming specific redundancies,symmetries. Extending a framework far beyond the contexts where it has been empirically validated and the assumed redundancies not longer valid is always risky, tensions will inevitably appear.
Computer science encountered a remarkably similar situation. Early AI researchers assumed that methods successful in symbolic reasoning would naturally extend to embodied intelligence. Instead, they discovered that walking is vastly harder than playing chess. This became known as Moravec’s paradox.
The reason is straightforward. Methods that work well in highly constrained contexts, rich in symmetry and redundancy, often fail when those simplifying structures disappear.
Perhaps the real issue is not missing mass.
Perhaps it is the assumption that a framework validated in simple contexts must remain effective in increasingly complex ones.
Computer scientists could not explain the failure of symbolic AI by invoking a hidden ghost in the machine.
Cosmology has spent decades invoking hidden mass, facing a Moravec’s wall.
The fine-tuning problem described here deserves to be recognized for what it structurally is.
Fine-tuning is not a design principle. It is usually a symptom that a framework is being stretched beyond the regime where its internal structure naturally generates the observed behavior. In a robust theory, key relations emerge from the theory itself. They do not require case-by-case adjustment. When galaxies spanning six orders of magnitude in mass must each acquire exactly the right missing baryon fraction to preserve a tight relation with near-zero scatter, that is not an explanation. It is a calibration problem.
As you note, the missing baryon fraction cannot simply be constant without breaking the observed scaling relations. It must systematically vary with rotational velocity. Yet the framework provides no compelling physical reason for why it should do so. The adjustment tracks the data, but it does not arise naturally from the underlying dynamics. That is why the situation feels contrived.
Historically, this is the role epicycles play. Epicycles are not arbitrary errors. They are structurally necessary additions introduced when a framework is committed to preserving assumptions that reality is no longer supporting. Each new adjustment improves the fit. None explains why the fit is needed. The local missing baryon problem, with a simple empirical tanh relation standing in for a physical mechanism, has much of this character.
The teleological difficulty exposes the problem even more clearly. A low-mass halo at high redshift appears to require knowledge of its eventual merger history in order to retain precisely the right fraction of baryons today. This is not merely a challenging simulation problem. It is a sign that information about the collective system is being reconstructed indirectly through tuning of the components.
The remarkable lack of scatter is therefore the central fact. If the observed relation were the outcome of numerous independent stochastic processes, substantial scatter would be expected. Instead, the baryonic component alone appears to contain most of the dynamical information. A clear attractor state.
The persistent fine-tuning is then not a solution. It is evidence that the framework is compensating for a missing level of description.
This is a very sharp way to frame the problem. To me, the most uncomfortable part is not simply that baryons are βmissing,β but that the missing fraction behaves as though it is causally coordinated with the observed baryons.
If the visible baryonic mass, the flat rotation speed, and the inferred missing baryon fraction all track one another with such small scatter, then maybe the wrong assumption is that these are three loosely connected quantities: baryons formed stochastically, feedback removed some fraction, and a halo later supplies the velocity scale.
The low scatter seems to say something stronger: the observed baryonic system and the asymptotic kinematic field are two readouts of the same causal history. In that case, the βteleologyβ problem is exactly the warning sign. A low-mass system should not have to know whether it will merge later in order to choose the right baryon retention fraction today.
I wonder if the more natural interpretation is that $r_{200}$ and the cosmic baryon fraction are being used as accounting conventions where no local causal boundary exists. The flat velocity may be telling us about the causal closure of the system, not about a notional halo edge whose baryon checksum must be completed. On that reading, the missing-baryon problem is not merely a census problem. It is evidence that the inferred halo bookkeeping is not the causal bookkeeping.
It’s very good to see people extracting real physical clues out of the relationship between visible matter and DM – like the lack of scatter showing it isn’t a loose coupling between a number of components, but some kind of direct coupling. Or the fact that spherical halos would never have predicted the BTFR. It shows that for those who believe in DM, adjusting DM to fit observations (as versatile as clay to a sculptor), is not the only way. MOND is far less adjustable than DM, but both provide clues.
If you look at any puzzle – QM is a good example – a good question to ask is ‘does it suggest missing concepts – are the concepts we have enough to fill the hole in the jigsaw, or do we need more?’. If we need more, we’re stuck until we find them. Many nowadays are rearranging the concepts and mathematics we have, trying to make them fit the holes. 20th century attitudes taught us that we have all the concepts already, but we need to look outside that. If you start throwing conceptual ideas at things, even if the first ones are wrong, it gets the process going.
“The local missing baryon problem encapsulates one of the fine-tuning problems that has never been satisfactorily explained. This alone would be considered fatal for most theories. For LCDM, it is just another problem to be addressed through the eternal tweaking of models and simulations.” Without special relativity theory, there would be luminiferous aether. HYPOTHESIS: Without FUNDAMOND string theory, there would be dark matter particles.
Is there now overwhelming empirical evidence supporting FUNDAMOND string theory?
Consider 7 hypotheses: (1) The Weizmann Institute’s Prof. Milgrom is the Kepler of contemporary cosmology β on the basis of MOND’s (approximately) correct predictions. (2) BGU’s Prof. Guendelman (author of “Dynamical String Tension Theories with target space scale invariance SSB and restorationβ) has revolutionized string theory β by providing a highly plausible mathematical approach for FUNDAMOND string theory. (3) There are 3 types of inertia, namely, Newton-Einstein inertia, FUNDAMOND inertia (or Milgrom inertia), and Guendelman-Guth inertia. (4) There are 2 inertial uncertainty principles: the uncertainty principle for Milgrom inertia and the uncertainty principle for Guendelman-Guth inertia. (5) What explains the dark matter phenomenon? Gravitational geodesics have a classical stability (FUNDAMOND inertia) & a quantum instability (probabilistic tendency to overcome FUNDAMOND inertia). (6) What explains the dark energy phenomenon? Black holes emit both Hawking radiation & waves of inflatons. Event horizons have a classical stability (Guendelman-Guth inertia) & a quantum instability (probabilistic tendency to overcome Guendelman-Guth inertia). (7) Each big bang has 3 phases: pre-inflation, inflation, and post-inflation. Pre-inflation is governed by the group SO(64). Then fermions & bosons emerge to generate a matter-dominated universe & an antimatter-matter universe. The 2 universes are both governed by the group SO(32) & have an inflation phase. In the post-inflation phase, there is FUNDAMOND with MOND as the non-relativistic approximation. Am I wrong here? Please google “fundamond string theory fundamond inertia”.
This post is going to take me a good while to noodle all the gems that are in there! Unfortunately by the time I get around to knowing what question I want to ask is, you will possibly have closed the comments, lol. That’s my fault for being slow on conceptualizing.
I do finally have a question though from one of your earlier posts about wide binaries as a test for MOND.
I was under the impression that highly conflicting results were obtained between Banik and Chae.
Can you please give an update on the status of this supposed conflict?
Is it true that one method confirms MOND with high confidence, while another method refutes it with high confidence?
Yes, those are the competing claims about wide binaries. People have been working to improve the data, but I’m not in a position to give an update here.
I ask this question somewhat in reaction to your statement that galaxies should be complicated in LCDM, but do not appear so. Presumably wide binaries don’t have this LCDM complexity.
If the competing claims each have high statistical significance, than is MOND effectively being turned on or off depending on the analysis? And what exactly is different in those analyses?
Correct – wide binaries should be simple test particles.
The differences between the analyses that claim different answers are not easily described: there are many devils in the details. To give just one example, some fraction of them should have a third partner. Since they’re already far apart, this can be hard to discern, so a statistical correction is made. How that is done is apparently one of the big issues, so some have focused on measuring triples to measure their effect directly. But then the sample for which one knows everything very well becomes tiny.
I do not have the patience to adjudicate that mess. The evidence from galaxies is already conclusive; the community just chooses to ignore it. Wide binaries should be able to falsify dark matter but it is not possible to falsify invisible mass. For MOND, they can at best inform what flavor of MOND is not possible via theoretical details like screening effects.
I really must not be understanding something big here, because it seems to me it would be much easier if the discrepencies that we observe were not taken to be locally real effects in those observed systems, but projections of our own locally real effects, like observational entropy.
Why are these discrepencies not virtual effects, i.e “virtual dark matter”, or behaves “as if MOND”, or “virtual big bang”, do you know what I mean?
Turok has mathematically described the big bang as a mirror, so that is kind of in the virtual direction that I am talking about, but why not describe this mirror symmetry as ocurring at the observer? What am I missing about this?
For example, I was reading about the “naked” black holes in the early universe, and now we have to explain how the got so big. Why not take this observation as, we did something here to make galaxies appear as if substantially dominated by a black hole? Why not at least treat that view with equal consideration? Otherwise aren’t we just asking for unfalsifiable claims?
“An extra bit of weirdness is that in LCDM, galaxies are built hierarchically by merging small objects into large ones. This poses a teleological problem. Consider a small halo at high redshift.” According to Pavel Kroupa, empirical evidence now rules out LCDM with its dark matter particles & dark matter halos. Consider 3 ideas: (1) Those who understand the importance of MOND need to focus on the search for FUNDAMOND (whatever that is) instead of focusing on the empirical successes of MOND. (2) String theorists need to realize that Milgrom is the Kepler of contemporary cosmology β without this realization their failure is guaranteed. (3) String theorists need to replace their focus on supersymmetry with a focus on the search for FUNDAMOND. Does anyone agree with me on the preceding 3 ideas? What is FUNDAMOND string theory?
Consider: “Biggest Mysteries in Physics: Antimatter, Dark Energy & ToE – Don Lincoln | Lex Fridman Podcast #497”
https://www.youtube.com/watch?v=1MV3dl6DRkU
Don Lincoln thinks that the Bullet Cluster is a good argument against MOND β I say that the Bullet Cluster merely indicates that MOND needs to be replaced by FUNDAMOND β the replacement is obviously needed with or without considering
the Bullet Cluster.
You may be correct. People who invoke the bullet cluster in response to queries about MOND are usually doing so to deflect from the need to engage with it. It has become the scientific equivalent of “LA LA LA not listening!” being the one weird trick that dismisses all other evidence.
Ironically, the bullet cluster falsifies LCDM too if its collision speed is taken at face value. This never seems to get mentioned for some reason. If queried about it, most of the people who are sure the bullet cluster falsifies MOND are unaware that it also poses a problem for LCDM. The rest, who are aware, simply deny that it is a problem. There is a convoluted story about hydrodynamics that the latter folks invoke. Which, sure, maybe (and only maybe) that works out, but then sure, maybe there is still undetected normal mass in clusters that would solve this problem in MOND. Right now, they both have the status of lame excuses.
At any rate, people who are quick to invoke “bullet cluster” are generally looking to shut down the scientific discussion, not engage with it.
Or…and bear with me here…some people actually find the Bullet Cluster (and the DF2/DF4 situation) to be persuasive.
FWIW, I’m a physicist, working in the field. And my views have changed over the years. In the early 1990s, I was pretty sure that dark matter was MACHOs. When MACHO, OGLE and all them disproved that conjecture, I then strongly favored MOND (broadly defined…not necessarily Milgrom’s conjecture, but rather the much vaguer paradigm that inertia or gravity needed some improved understanding). However, in the modern day, Bullet and Dragon Fly have again changed my leaning.
Yes, yes, the Bullet Cluster is moving awfully fast. Yes, yes, it’s a problem for LCDM. But this isn’t the same level of problem as it poses for modified physics. For LCDM, it is simply an unusual entry on the tail of a known velocity distribution, while the problems it poses for MOND-ish issues is more central.
Now, this is your page and you are allowed to have an echo chamber and sycophants…no problem. But to characterize those who disagree with you as somehow not being thoughtful is just…sloppy. And dismissive. And patronizing.
The broad community might be wrong. But, you know what? So could you.
FWIW, it will be difficult to convince me of >>ANY<< solution without DM being produced in particle accelerators. Indirect measurements are background-prone. And direct measurements, while super helpful, will tell us where to look in accelerators. (Think the DAMA debacle.)
My fear is that dark matter is real, but it only interacts gravitationally or far weaker than the weak force. If that's the case, our grandkids will be having this argument.
Of course I could be wrong. It started with the realization that I had been wrong to be so certain CDM was correct. I changed my mind, and have stated criteria by which I would change it again. What would it take for you to change yours?
Two relevant questions:
1. How could we falsify dark matter?
2. If DM is correct, why does MOND get so many predictions right?
In trying to defend MOND against LCDM, and avoid the stalemate we sometimes get into, the EFE is underrated. Wide binaries need time to do it, but in some of the work you’ve done on dwarf galaxies, the EFE does it now. With Crater II, with the EFE contributing, the velocity dispersion was 2 km/sec (predicted upfront then measured). LCDM had something like 17 km/sec with no EFE. The EFE is out of the question in LCDM – it shouldn’t exist. Does anyone ever discuss this while supporting LCDM?
Yes, the EFE is important, and Crater II is a good example. I’ve seen papers claiming to explain Crater II in the context of LCDM, but I’ve not seen any that seriously engage with MOND having predicted it in the first place. This true for other observations as well: every case that is problematic for LCDM is treated as a minor puzzle to be solved in that context; it is never seen as necessary to acknowledge (let alone explain) why MOND predicted it right first. Or to be aware of it, apparently.
The arguments are very strong that we need a hybrid theory – MOND at the galaxy scale, DM at larger scales. If so, our grandchildren will know about that. But LCDM is dead already, it has been falsified in the early universe (long before any of us were born). And one part of LCDM, called GR, looks like it’s being falsified by the external field effect, which shows clearly that gravity fields combine differently from the predictions of GR and curvature. Instead they combine as they would with a collisionless refractive medium. Whatever happens at the transition point (MOND, DM, you name it), the acceleration at which it happens can be reached by two fields blending together – the contribution of the background field is taken into account, and the two fields are found to combine in a specific, predictable way.
I’ve been looking into this, GR could certainly be falsified by better measurements of the EFE in the future. But we may need to think more about interpretations for the EFE. They seem to have got a near null result for the effect of the MW on Saturn’s orbit, published this year. Where we are in the galaxy is just inside a0, and on the face of it, if the EFE as predicted by MOND works, that could mean MOND cuts in sharply, at a point some way further out.
But your 2016 interpolation equation, from the ‘universal curve’ paper, works well in galaxies, and it has a smooth transition, not a sharp one. And it works in the MW as well. In your post on ‘has dark matter been detected in the milky way’, you mentioned that the stars and gas we know about would make g = 1.45e-10, but due to either DM or MOND, what we get is actually 2.17e-10. I posted at the time that I’d put g[bar] = 1.45e-10 into your equation, and got that exact number out, g[obs] = 2.17e-10. So that equation works, and suggests a smooth transition in the MW.
So it’s strange that attempts to measure the EFE via Saturn’s orbit found nothing. I looked into it further, and rather than standard EFE, what they were trying to measure seems to be an effect that applies in some versions of MOND but not in others. With the EFE in general, there are results that push both ways, and perhaps it’s more like wide binaries than I thought – early days. What do you think about these questions on the EFE?
Yes, exactly. The EFE in dwarf satellites is pretty clear IMO and has to be active in wide binaries or the signal there would be huge (which everybody agrees it is not). But it also seems to be absent in the solar system according to some analyses, but active according to others (e.g., Brown & Mathur). So ???
A minor note about the interpolation function – the transition around a0 is fairly well constrained to be what you describe as gradual. But it can be equally well fit by the “simple function” x/(1+x) or the function I came up with 1/(1-exp(-sqrt(y))) where x = a/a0 and y = g/gN. They’re basically indistinguishable around a0. On solar system scales, the simple function predicts departures of one part in 10^8; this is unacceptable for the Earth’s very well known orbit. That’s why I came up with the other function, which predicts departures of one part in e^(10^8). So they approach Newton very differently. That said, the effects that people are talking about near Saturn and in the outer solar system are from the quadrupole moment of the external field. That doesn’t care much about the shape of the interpolation function, but it does care about the flavor of MOND. AQUAL/QUMOND flunk the Cassini test, but not modified inertia. I have no idea what to make of wide binaries.
In case it’s of interest, I’m getting order of magnitude estimates for the quadrupole from PSG, it seems to be Q2 = around 10^-31 for Saturn’s orbit, and around 10^-48 for issue of the KBO orbit clustering. This means neither would be measured, so K Brown and Mathur would have been looking at something else. The basic EFE really only arises in PSG when there’s a question of whether a field reaches a0 – fields of different ‘densities’ combine easily, and the result is only low enough to reach a0 if the total, including any background, gets there.
…or rather 10^-43 for Saturn’s orbit.
In PSG the fields combine in a nearly linear way, hence the low Q2. I see why the external field dominant quasi-Newtonian regime makes a roughly Keplerian curve, but with G effectively boosted – because the external field remains basically constant, and so does a0. But we’re technically not in the quasi zone, the external field is above a0, 2.17e-10, this must complicate the wide binary results, as we’re near the border, and not clearly in either regime.
Sorry, I’ve been looking into interpolation functions, which you mentioned – perhaps you can help with a question. I’ve known about IFs as part of MOND, but looking into the EFE trying to work out what PSG predicts, I found they can take the role of restoring Newtonian gravity, or translating between Newton and Milgrom. In the interpretation I use (acceleration-based, but emphasis on radial distances), this is done via r/rM, where the MOND radius is sqrt (GM/a0), it seems that’s an IF? (There’s also an effective radius r’ that does exactly the same, restoring Newonian gravity in the outer ‘compressed’ part of the field, πβ² = (πππ)^1/2 = (πΊππ^2/π0)^1/4. )
I’m taking the galaxy to behave like a point mass, while other IFs allow for the mass being spread out. But point mass simplifications have been used in other contexts with gravity, do you have any idea how this IF does with any of the data, if it’s different enough to be noticeable? Thank you.
I do not have a sense for how viable that would be. I went through a whole bunch of conceivable IFs in https://arxiv.org/abs/0804.1314; certainly not all are viable. But I don’t recognize the fcn you suggest so don’t know how it would do.
Thanks. It may be a working approximation, but it seems to give the same results as the standard interpolation function? what I get is nu (x) = 1 / sqrt(1 + x^2), where x = rM/r. Is this a geometrical way to get to the standard IF?
(that’s nu rather than mu)
That’s a bit sharper than present day suggest, but within the realm of uncertainty in stellar population mass-to-light ratios.
Sycophants are defined as insincerely flattering a person. I’m happy to suffer that insult in order to make science progress. I hope for you that you will also make the right choices to boost scientific progress.
As a mechanism for explaining the data you present, one could imagine that there is an error that propagates in the determination of the baryon rotational velocity (or more precisely the molecular partition function of the kinematic and thermodynamic energy levels) arising from the spectroscopic analysis.
The partition functions are determined experimentally in the Earth-based laboratory, and I don’t know how from there we approximate flat spacetime – is it by assumption or correction?
I find it ironic that where we start to see the this deviation from Newtonian gravity in the rotation curves of other galaxies in spacetime that becomes increasing different from where Earth is located.
I found a paper here,
The Effect of Spacetime Curvature on Statistical Distributions
https://arxiv.org/abs/2104.09019, and it got me thinking. How are our measured values of partition functions actually reduced to the “classical limit” of flat spacetime?
Could this be a source of error propagation?
The transition from Newtonian to GR spacetime around galaxies embedded in the expanding universe is an interesting issue. It is not a source of error that concerns me.
This may seem either obvious or crazy, but the telescope is not looking at the past, until after we process the data. The nature of the sensor at the quantum level is to be in a state of expectation towards the future. We process this quantum information in an effort to arm ourselves with knowledge of the now local future in order to reconstruct the global past. So the entropy from one process may transform into the other in a complementary way. We just have to find out how.
“… people who are quick to invoke “bullet cluster” are generally looking to shut down the scientific discussion, not engage with it.” It seems to me that there should be a wide-ranging discussion about Guendelman’s new version of string theory. In “Dynamical String Tension Theories with target space scale invariance SSB and restoration” , Guendelman’s abstract concludes with “These models suggest the swampland constraints could be avoided.” I interpret this to mean, “I, Guendelman, believe that I have solved string theory’s swampland problem β if so, that means that, in the history of science, the 3 greatest theoretical physicists are Newton, Einstein, & guess who.” My guess is that Guendelman really has revolutionized string theory & provided a mathematical basis for FUNDAMOND string theory. Are FUNDAMOND & quantum entanglement closely related? Consider 7 hypotheses: (1) Stringy, multiverse information supports FUNDAMOND string theory, which can explain quantum entanglement with a network of stringy, multiverse information. (2) The multiverse has 2 main components: multiverse boundary where all of the alternate universes occur & multiverse interior where stringy, multiverse information is propagated at a non-measurable speed vastly greater than the speed of light. (3) During each Planck-time interval, quantum information in each of the alternate universes is updated. (4) The updating of quantum information occurs at gravitational geodesics & at event horizons. (5) There are 3 forms of inertia, namely, Newton-Einstein inertia, Milgrom inertia, and Guendelman-Guth inertia. There 3 different types of string tension supporting the 3 different types of inertia. (6) Quantum fluctuations strengthen gravitational geodesics, resulting in FUNDAMOND with MOND as a non-relativistic approximation. (7) Event horizons emit both Hawking radiation & waves of inflatons. The waves of inflatons can be explained in relation to Guendelman-Guth inertia, and such waves of inflatons cause the dark energy phenomenon. Are the preceding 7 hypotheses little more than speculative nonsense? Either I have greatly overestimated Milgrom & Guendelman, or thousands of scientists have greatly underestimated Milgrom & Guendelman.
I’m afraid that just goes to prove your point really. You could kick people like me out for saying things you don’t agree with, but you don’t.
I watched a video some years back of Lenny Susskind trying to convince Edward Witten that his holographic description held a deep insight about the universe.
He was describing a Nariai spacetime, and was trying to show how the smaller of the Nariai or cosmic horizon eventually evolves into the other, because the solution where they are equal wouldn’t be stable under perturbation.
According to Lenny it was going to take some ridiculous amount of time for our universe to appear in this process, like waiting for a quantum fluctuation the size of the universe or about 10^100 years or something (I lost interest in the exact number).
So here again I see a wonderful idea that becomes strangled by taking it too literally – needing it to be too physically real.
Virtual horizons could be swapped in moment, not 10^100 years. This kind of approach leads to a possible paradox,
Braun’s Paradox:
The closer we look at the early universe, the more it looks our own age.
Resolution?:
Cosmic time is measured by a clock comoving with the expansion of the universe, and determined by applying General Relativity to the FLRW metric, with the boundary conditions where the universe is homogeneous and isotropic on large scales.
We find the age of our local patch of the universe to be about 13.8 Gyr by rewinding the expansion and cosmic clock, and this age is supported by local measurements of structure and evolution of galaxies and stars. At the other end of the scale from our local patch of the universe we expect to see the origin (or at least up to the cosmic horizon).
Now consider that when making measurements of the inhomogeneous and anisotropic structures of galaxies close to our cosmic horizon (as with JWST for example), we must remove all influence on the measurements of our local patch in spacetime, such that what was our locally evolving structure becomes essentially a homogeneous and isotropic background.
Therefore, in order to look closely at the early universe, our local patch should take on the character of the cosmic horizon. As a result, our cosmic clock time (or age) should be reset to the age of the horizon.
The extremely distant galaxies and structures that we then resolve with the oldest light now appear to be about 13.8 Gyr old, as if the scale was flipped the other way.
“1. How could we falsify dark matter? 2. If DM is correct, why does MOND get so many predictions right?”
The sorcerer’s apprentice might be controlling dark matter halos. It seems to me that anyone who has spent 200 hours or more studying MOND’s predictions should realize how important MOND is.
Prof. Milgrom made the statement: “I have argued on many occasions … that understanding and formulating MOND in a relativistic framework may require completely new concepts that are, at present, beyond our ken. For example, the βcoincidenceβ of the MOND constant, a0, with cosmologically significant accelerations, makes cosmology the only strong-gravity relativistic system in the MOND regime. This may point to MOND having to be understood together with cosmology as inseparable aspects of the same FUNDAMOND, and not as some relativistic meta-theory for which cosmology is only a special solution.” β page 2 of
“The deep-MOND limit — a study in Primary vs secondary predictions”, 2025
https://arxiv.org/abs/2510.16520
If we assume that gravitation energy is conserved, all gravitons have spin 2, and Einstein’s field equations are the correct mathematical formulation of the equivalence principle, then the best bet might a FUNDAMOND string theory in which supersymmetry is significant only in the very early universe, the cosmological constant needs to be replaced by a very slowly decreasing cosmological function, and the β1/2 in the field equations should be replaced by β1/2 + FUNDAMOND+data-function. In any case, the MOND fan club should try to convince the younger string theorists that they need to work on the FUNDAMOND problem.
In a happenstance of timing, an interview I did for NPR back in late March appeared today: https://www.wvxu.org/podcast/looking-up/2026-06-05/is-most-of-the-universe-actually-invisible-with-dr-stacy-mcgaugh
From the Cincinnati Public Radio interview, “… dark matter … it’s not just a new particle waiting to be discovered. It’s new physics. It’s really got to be something beyond anything we’ve experienced so far.” If we postulate a FUNDAMOND 5th force, such as putting MOND charges on gravitons & gravitons, there are problems involving group theory & hypothetical tachyons. In making a choice between FUNDAMOND string theory & FUNDAMOND non-string theory, it seems that that the string theorists have far more mathematical punching power than the non-string theorists working on quantum gravity. I urge pro-MOND scientists to study the ideas of BGU’s Eduardo Guendelman.
Guendelman, E. I. “Dynamical string tension theories with target space scale invariance leading to 4D.” The European Physical Journal C 85, no. 6 (2025): 615.
https://link.springer.com/article/10.1140/epjc/s10052-025-14296-6
https://arxiv.org/html/2508.17333v2
From the Cincinnati Public Radio interview, “… dark matter … it’s not just a new particle waiting to be discovered. It’s new physics. It’s really got to be something beyond anything we’ve experienced so far.” If we postulate a FUNDAMOND 5th force, such as putting MOND charges on gravitons & gravitons, there are problems involving group theory & hypothetical tachyons. In making a choice between FUNDAMOND string theory & FUNDAMOND non-string theory, it seems that that the string theorists have far more mathematical punching power than the non-string theorists working on quantum gravity. I urge pro-MOND scientists to study the ideas of BGU’s Eduardo Guendelman.
Guendelman, E. I. “Dynamical string tension theories with target space scale invariance leading to 4D.” The European Physical Journal C 85, no. 6 (2025): 615.
https://link.springer.com/article/10.1140/epjc/s10052-025-14296-6
https://arxiv.org/html/2508.17333v2