A strange and interesting aspect of MOND is the External Field Effect (EFE). If physics is strictly local, it doesn’t matter what happens outside of an experimental apparatus, only inside it. Examples of gravitational experiments include an Eötvös-style apparatus in a laboratory or a dwarf galaxy in space: in each case, test masses/stars respond to each other’s gravity.
The MOND force depends on the acceleration from all sources; it is not strictly local. Consequently, the results of a gravitational experiment depend on the environment in which it happens. An Eötvös experiment sitting in a laboratory on the surface of the Earth feels the one gee of acceleration due to the Earth and remains firmly in the Newtonian regime no matter how small an inter-particle acceleration experimenters achieve within the apparatus. This is the way in which MOND breaks the strong equivalence principle (but not the weak or Einstein equivalence principle).
A dwarf galaxy in the depths of intergalactic space behaves differently from an otherwise identical dwarf that is the satellite of a giant galaxy. In the isolated case, only the dwarf’s internal acceleration matters. For the typical low surface brightness dwarf galaxy, the internal acceleration gin due to self-gravity is deep in the MOND regime (gin < a0). In contrast, a dwarf satellite with the same internal acceleration gin is also subject to an external orbital acceleration gex around the host that may be comparable to or even greater than its internal acceleration. Both of those accelerations matter, so the isolated case (gin < a0) is deeper in the MOND regime and will evince a larger acceleration discrepancy than when the same dwarf is proximate to a giant galaxy and in the EFE regime (gin < gin+gex < a0)*. This effect is observed in the dwarfs of the Local Group.
The same effect holds everywhere in the universe. There should be a minimum acceleration due to the net effect of everything: galaxies, clusters, filaments in the intergalactic medium (IGM); anything and everything add up to a nonzero acceleration everywhere. I first attempted to estimate this myself in McGaugh & de Blok (1998), obtaining ~0.026 Å s-2, which is about 2% of a0 (1.2 Å s-2). This is a tiny fraction of a tiny number, but it is practically+ never zero: it’s as low as you can go, an effective minimum acceleration experienced even in the darkest depths of intergalactic space.
One can do better nowadays. The community has invested a lot in galaxy surveys; one can use those to construct a map of the acceleration the observed baryonic mass predicts in MOND. We did this in Chae et al. (2021) using a number of surveys. This gets us more than just a mean number as I guestimated in 1998, but also a measure of its variation.
Here is a map of the expected Newtonian acceleration across the sky for different ranges of distance from us. Blue is low acceleration; yellow higher. Glossing over some minor technical details, the corresponding MONDian acceleration is basically the square root (a0 gN)1/2, so 2% of a0 corresponds to log(eN) = -3.4 in the following plots, where eN is the Newtonian environmental acceleration: what Newton would predict for the visible galaxies alone.
The EFE imposes an effect on all objects, even giant galaxies, which we were trying to estimate in Chae et al. (2021) – hence the dots in the above maps. Each of those dots is a galaxy for which we had made an estimate of the EFE from its effect on the rotation curve. This is a subtle effect that is incredibly hard to constrain, but there is a signal when all galaxies are considered statistically in aggregate. It does look like the EFE is at work, but we can’t yet judge whether its variation from place to place matches the predicted map. Still, we obtained values for the acceleration in intergalactic space that are in the same realm as my crude early estimate.
Here’s another way to look at it. The acceleration is plotted as a function of distance, with the various colors corresponding to different directions on the sky. So where above we’re looking at maps of the sky in different distance bins, here we’re looking as a function of distance but relying on the color bar to indicate different directions. There is a fair amount of variation: some places have more structure and others less with a corresponding variation in the acceleration field.
Different catalogs have been used to map the structure here, but the answer comes out pretty much the same, but for one little (big) detail: how clustered are the baryons? The locations of the galaxies have been well mapped, so we can turn that into a map of their gravitational field. But we also know that galaxies are not the majority of the baryons. So where are the rest? Are they clustered like galaxies, or spread uniformly through intergalactic space?
When we did this, we knew a lot of baryons were in the IGM, but it really wasn’t clear how clustered they might be. So we took two limiting cases by assuming (1) all the baryons were as clustered as the galaxies or (2) not clustered at all, just a uniform background. This makes a difference since a uniform background, being uniform, doesn’t contribute. There’s as much force from this direction as that, and it cancels itself out, leading to a lower overall amplitude for the environmental acceleration field.
That’s where the new result reported last time comes in. We now know that the missing baryons were all in the IGM. Indeed, the split is 1/4 clustered, 3/4 not. So something closer to (2), the “no clustering” limit above. That places the minimum acceleration in intergalactic space around log(eN) = -3.5, which is very close to the 2% of a0 that I estimated last century.
The diffuse IGM is presumably not perfectly uniform. There are large scale filaments and wall around giant voids. This structure will contribute variations in the local minimum acceleration, as visualized in this MOND structure formation simulation by Llinares (2008):
Surveys for fast radio bursts are very sensitive to variations in the free electron density along the line of sight. Consequently, they can be used to map out structure in the IGM. The trick is that we need to cover lots of the sky with them – the denser the tracers, the better. That means discovering lots of them all over the sky, a task the DSA-110 was built to do.
I sure hope NSF continues to fund it.
*I write gin < gin+gex for simplicity, but strictly speaking the acceleration is a vector quantity so it is possible for the orientation of gin and gex to oppose one another so that their vector sum cancels out. This doesn’t happen often, but in periodic orbits it will always happen at some moment, with further interesting consequences. The more basic point is that the amplitude of the discrepancy scales with the ratio a0/g: the lower the acceleration g, the bigger the discrepancy from Newton – or, equivalently, the more dark matter we appear to need. The discrepancy of the isolated case a0/gin is larger than the discrepancy of the non-isolated case a0/(gin+gex) just because gin+gex > gin.
+A test of MOND using Lyman-alpha clouds was proposed by Aguirre et al (2001). These tiny puffs of intergalactic gas have very low internal accelerations, so should evince much larger discrepancies than observed. Or at least that was their initial interpretation, until I pointed out that the EFE from large scale structures would be the dominant effect. They argued it was still a problem, albeit a much smaller one than initially estimated. I don’t think it is a problem at all, because the amplitude of the EFE is so uncertain. Indeed, they made an estimate of the EFE at the relevant redshifts that depended on the rate of structure formation being conventional, which it is not in MOND. Lyman-alpha clouds are entirely consistent with MOND when one takes into account the more rapid growth of structure.
I may have limited access to the internet for the coming week, so please be patient about replies.
Could you please comment on arXiv:211200026
The phenomenology of the external field effects in cold dark models
Abstract:
“The phenomenology of the external field effect in cold dark matter models
Aseem Paranjape (IUCAA), Ravi K. Sheth (UPenn/ICTP)
In general relativity (GR), the internal dynamics of a self-gravitating system under free-fall in an external gravitational field should not depend on the external field strength. Recent work has claimed a statistical detection of an `external field effect’ (EFE) using galaxy rotation curve data. We show that large uncertainties in rotation curve analyses and inaccuracies in published simulation-based external field estimates compromise the significance of the claimed EFE detection. We further show analytically that a qualitatively similar statistical signal is, in fact, expected in a Λ-cold dark matter (ΛCDM) universe without any violation of the strong equivalence principle. Rather, such a signal arises simply because of the inherent correlations between galaxy clustering strength and intrinsic galaxy properties. We explicitly demonstrate the effect in a baryonified mock catalog of a ΛCDM universe. Although the detection of an EFE-like signal is not, by itself, evidence for physics beyond GR, our work shows that the sign of the EFE-like correlation between the external field strength and the shape of the radial acceleration relation can be used to probe new physics: e.g., in MOND, the predicted sign is opposite to that in our ΛCDM mocks.”
These authors do not agree that an EFE has been detected in galaxy rotations; they then say that Lambda-CDM has an `effective’ EFE, and its sign is opposite to that in MOND. And that data at present are not good enough to pick up this sign.
It bothers me that supporters of DM and of MOND do not manage to agree on what the data is telling us. Will this disagreement go away with better/more data? Thanks.
Priors. What does LCDM predict? Not MOND – it doesn’t get rotation curves right in the first place. Arguing about whether it predicts a signal that mimics the EFE after you fudge it to mimic rotation curves is silly, like using a submersible to rearrange deck chairs on the Titanic. There are plenty of people who will assert that rotation curves, the RAR, etc. are fine in LCDM, but this is simply not correct. See, e.g., https://arxiv.org/abs/2004.14402. So the first issue is not so much what the data say as it is getting the advocates of LCDM to agree on a prediction and refrain from adjusting it as they do every time the data come up looking like MOND.
Dark matter became an epicycle theory a long time ago. That’s where the problem is, not with the data. It’s easy to say that whatever the data say is consistent with your theory if your theory can be modified to explain anything.
I agree with what you say about priors and epicycles in LCDM. I posed the same to a DM proponent – they replied by saying this is how science works; model the data and modify the model when new data comes. Anyways…
The following statement in their abstract questions the claimed detection of EFE predicted by MOND and rotation curves:
” We show that large uncertainties in rotation curve analyses and inaccuracies in published simulation-based external field estimates compromise the significance of the claimed EFE detection.”
Do we have a rubuttal to this above? Thanks.
The problem with the “this is how science works” line (which seems to be a fad these days) is that most of the LCDM community is ignoring the predictive successes of MOND. The way science is *supposed* to work is testing hypotheses that make different a priori predictions. We did that. LCDM predicted NFW halos with a TF-like relation for halos with a slope of 3. That’s not what we observed; we observed what MOND predicts. So what people are doing is tweaking one theory to make it look like another while ignoring that the other exists then pretending that’s somehow “how science works”. Nonsense.
I am not going to attempt to rebut other claims here. I agree that the detection of the EFE could be more convincing: it’s a subtle effect, as I said. But I’ve spent years upon years upon years rebutting such claims (when they deserved it), literally hundreds of times, and have concluded that doing so is a waste of my time. There is always a Dr. Z as in https://tritonstation.com/2022/02/08/a-script-for-every-observational-test/ ; that’s the role Paranjape & Sheth are playing here.
I’ve thought the EFE is a good place to find things out for a while – I know you’ve called people out for using MOND wrong in that area, and that you’ve predicted correctly for dwarf galaxies like Crater 2, with a velocity dispersion of 2 km/s, instead of LCDM’s 17 km/s. I have a question about the quasi-Newtonian regime, which seems to give a different prediction from my tentative interpretation for MOND from PSG (which I’d much rather falsify by hearing about the data from you, than go on believing it if it’s wrong). In the external field dominant QNR, you say MOND predicts Newtonian behaviour, but with a boost to GM of a0/g[ex].
In my interpretation it’s more like what you mention above, relating to a situation where g[in] < g[in] + g[ex] < a0. You say in a footnote that the two are really combined as vector quantities, I had that as well. In my picture, if the combined internal and external fields push the local acceleration above a0, you get Newtonian behaviour, as if it was one field. But if the two combined stays below a0 you don't get GM-boosted Newtonian behaviour, I can't see a reason for that to happen.
So one question is, are these two scenarios different on paper, as it seems to me they are. The other is, if so, has the data distinguished between them so far?
It sounds like they are different. I would think a good place to test this difference would be the Local Group dwarfs; see the data in McGaugh & Milgrom (2013a & b) (I cite 213b above).
Thank you. What you describe above makes good sense – an isolated galaxy will be deeper in the MOND regime that one near a host with a significant field, which will bring g nearer to a0.
But in what you wrote on the EFE in the MOND pages (assuming the emphasis hasn’t shifted to another version since 2007), to me the quasi-Newtonian regime (QNR) is weirder than other EFE effects. Deep in the MOND regime, MOND predicts there can be little islands of Newtonian gravity, arising when two small fields combine, even if both are below a0, and the two combined are as well, g[in] < g[in] + g[ex] > g[ex] or g[in] << g[ex]), equation 3 being for the QNR, with a different effective value for G. You say that as the two fields tend to be about equal, both estimates have been made.
So it seems that although the QNR provides a genuine difference in the predictions of two approaches, MOND and an interpretation from PSG, so far measurements haven't ruled either out.
[sorry, it posted it incomplete, with a chunk missing]
Thank you. What you describe above makes good sense – an isolated galaxy will be deeper in the MOND regime that one near a host with a significant field, which will bring g nearer to a0.
But in what you wrote on the EFE in the MOND pages (assuming the emphasis hasn’t shifted to another version since 2007), to me the quasi-Newtonian regime (QNR) is weirder than other EFE effects. Deep in the MOND regime, MOND predicts there can be little islands of Newtonian gravity, arising when two small fields combine, even if both are below a0, and the two combined are as well, g[in] < g[in] + g[ex] > g[ex] or g[in] << g[ex]), equation 3 being for the QNR, with a different effective value for G. You say that as the two fields tend to be about equal, both estimates have been made.
So it seems that although the QNR provides a genuine difference in the predictions of two approaches, MOND and an interpretation from PSG, so far measurements haven't ruled either out.
[It posted it incomplete again, here’s the last bit]
Sorry if I’ve misunderstood. I’ve read the papers you mention (also Milgrom’s explanation for the EFE), can’t tell if any instance of the QNR has been observed. It seems not, as the relative sizes of g[in] and g[ex] affect whether one uses equation 2 or 3 in the first paper (whether it’s g[in] >> g[ex] or g[in] << g[ex]), equation 3 being for the QNR, with a different effective value for G. You say that as the two fields tend to be about equal, both estimates have been made.
So it seems that although the QNR provides a genuine difference in the predictions of two approaches, MOND and an interpretation from PSG, so far measurements haven't ruled either out.
The comment that g[in] and g[ex] are roughly equal applies to the dwarfs of the Local Group, it isn’t a general expectation. That said, there is only a narrow window in which dynamical equilibrium might hold in the EFE before an object slips into the regime of tidal disruption. Been meaning to write a paper about this, but perhaps I should just outline it in a post here. Too many things to do.
So for the QNR, yes, there are many cases where objects have been observed to be in the EFE regime, but if you mean the specific aspect of the QNR in which one should see a Keplerian decline in the effective rotation curve but with a modified effective value of G, then no, I’m not aware of that having been clearly observed. I’ve seen hints of it, but nothing convincing. Part of the problem there is that to see it one must get way far out, at which point stars are subject to tidal removal – at least for the dwarfs near to us where we might hope to see it.
Dear Stacy,
Wonderful blog post. I will think about it.
One more reason to model our space better.
So far, we assume a continuum, similar to the real numbers.
But that’s not enough when space expands.
Then questions remain unanswered, like:
Is space getting more or thinner?
A continuum is also not enough to explain experiments with entangled quantum objects.
Here too, local mathematics is used to try to understand a non-local effect…
Best regards
Stefan
Thanks for this post and your blog ! The explanation put forward by the authors (self-interacting dark matter) is questionable, but according to some researchers, it would be difficult to explain this effect in Mond. Could this be the case?
“Unexpected clustering pattern in dwarf galaxies challenges formation models” arXiv:2504.03305v2
Interesting. I’m not sure how to interpret this even in the context of dark matter; it sounds like the opposite of what we found in https://arxiv.org/abs/astro-ph/9311004 (note that there are coauthors in common). I don’t really see how this is a problem for CDM that favors SIDM, let alone its relevance to MOND. I mean, I can see how it would be a problem for specific realizations of such models, like how people always seem eager to attribute galaxy diffuseness to the portion of CDM halos with large angular momentum. So I’d say this is just another reason not to believe that common oversimplification.
More generally, clustering is basically a matter of Gaussian statistics. How we interpret the relative clustering of different galaxy types depends on how we assign them to the Gaussian distribution of initial lumps from which they form. We know the power spectrum of the lumps very well, but how we assign galaxy types to a particular portion of the distribution of those lumps is model dependent. That they see a clear signal here is encouraging insofar as it implies that such an assignment may be meaningful. I can believe it excludes some extant models, but I find it harder to believe it excludes all plausible CDM models. For this sort of thing, there is not much difference between CDM and MOND: a model prescription that works for one will probably work for another, e.g., associate the most diffuse galaxies with the earliest forming objects at a given mass.
Thanks a lot for you answer. It will take some time for me to assimilate its content. Best wishes.
Thank you for this clarifying work on the EFE. It is interesting that 3/4the of the ‘lost baryons’ do indeed appear to be lost.
“Dark matter became an epicycle theory a long time ago”
One must be careful not to build a theory that cannot be falsified because the theorists allow endless ad hoc tweaks.
“… most of the LCDM community is ignoring the predictive successes of MOND.” Are any pro-MOND experts in close contact with the Tel-Aviv University Astronomy Club? What is the verdict on the following?
“MOND from a brane-world picture” by Mordehai Milgrom, 2018, revised 2019
https://arxiv.org/abs/1804.05840 — published as pages 217–242 of
“Jacob Bekenstein: The Conservative Revolutionary”, 2019, World Scientific
I would expect members of an Israeli astronomy club to be more likely than most to be aware of the achievements of an Israeli scientist, but I have no specific knowledge of their thinking.
Bekenstein was a great visionary who was lost to us too soon. One quote of his that sticks with me is that “There’s nothing sadder than an idea ahead of its time.” He was alluding to MOND and how people just aren’t ready to go there. I don’t think people will be ready to go there until dark matter is thoroughly debunked. It has been thoroughly debunked repeatedly – I wasn’t ready to go there myself until the wealth of self-contradictions within the dark matter paradigm convinced me it was unworkable – but it seems that every scientist has to figure this out on his or her own, and most are not up for making the effort.
Milgrom presents MOND as that non-relativistic modification of [Newton’s second law + inverse square law of gravitation] which obeys space-time scale invariance. MOND immediately follows then. This is highly insightful. MOND shares this symmetry with the 4D deSitter universe. This commonalty suggests there is a relativistic fifth force (whose non-relativistic limit is MOND) which also obeys space-time scale invariance. Such a fifth force should arise naturally as a beyond-standard-model physics, and should be a renormalisable quantum field theory. Ideally, the tensor product GR x fifth force should be a renormalisable quantum field theory. Symmetry breaking at the end of a deSitter phase then leaves RelMOND as the unbroken scale-invariant symmetry, with GR resulting as the symmetry broken theory. There should be a prediction of a gauge boson corresponding to the fifth force. One should also have a framework for doing cosmology with the fifth force as a source on the right hand of Einstein equations. I feel if such a relativistic setup can be achieved, it will greatly help increase attention towards MOND as a fundamental new interaction.
Since the article you refer from Milgrom is about a 5D spacetime on a spherical brane, which is quite like the Nariai spacetime in 5D I was opting for: thanks for the reference! I did not know of this article.
As to the verdict you asked Stacy, since he didn’t really give one: patience is what all scientists need most. Results cost lots of time in order to become realized. I personally believe something in the direction of Milgrom’s paper you cited is a good way forward for understanding gravity better – but who am I?
Can you comment on the original motivation and the potential effects of the Vera C. Rubin Observatory dark matter search spearheaded by Tony Tyson as described in a recent Quanta Magazine story (https://www.quantamagazine.org/the-biggest-ever-digital-camera-is-this-cosmologists-magnum-opus-20250711/) in resolving the DM-MOND controversy? The existence of DM is clearly a given there, and MOND not even mentioned…
Tyson’s thing is gravitational lensing. The Rubin Observatory should detect lots of that all over the sky. That’ll help map out the mass distribution on large scales, though I expect the ESA Euclid mission will do a better job for this particular task, having the advantage of space-based resolution. Either way, lots of new data are inbound.
As for DM-only, this is a good example of where the terminology serves us poorly. Whenever someone like Tyson says “dark matter,” he really means (whether or not he realizes it) the discrepancy that indicates a problem for which the solution could be either literal invisible mass or a modification to the force law. By calling it the “dark matter problem” as we often do, we exclude the latter possibility without consideration. As trivial a bit of epistemology this is, it is where most of the community gets hung up.
Is the External Field Effect (EFE) a form of evidence supporting the existence of MOND inertia mediated by D-branes? https://en.wikipedia.org/wiki/D-brane
What are the criticisms of the following 3 hypotheses?
1. Inertial mass-energy is equivalent to gravitational mass-energy, but there are 2 basic forms of inertia: Newton-Einstein inertia & MOND inertia.
2. MOND inertia is caused by D-brane influences from alternate universes.
3. Einstein’s field equations need to be somehow modified in order to model the empirical effects of MOND inertia.
Digressing just a little, the ‘missing baryons’ distribution modifies the EFE; but there is another budget worth considering:
A couple decades ago, I integrated Chandrasekar’s equation for a pencil beam of light across cosmic space, assuming 1 atom per cubic meter of ionized baryons. (The 1 atom/m^3 was suggested by a colleague.)
I found palpable loss of energy to the photon stream without significant loss of coherence when the ‘lost baryons’ were held at the background temperature. There needs to be a budget for -this- factored into cosmic redshifts.
The gas of the IGM was reionized at high redshift and its temperature remains much higher than the 3K CMB background. That’s why there are free electrons to scatter passing radiation, leading to the dispersion we measure to infer that one atom per cubic meter.
Question: if there is a minimum acceleration in IG space, in what direction is the minimum acceleration at a midpoint between to dwarf galaxies?
Apologies if this has been asked’n’answered already.
The directional component of the vector is complicated, as it will depends on where pretty much everything else in the universe is. In the toy picture of two equal masses, the acceleration goes to zero at the midpoint and has no direction if it has no amplitude. In practice that never happens, but it’s be very interesting if patches could be identified that approach this limit as the effects of MOND would be largest there. In the solar system, one expect this around Lagrange points, but there are so many objects that their precise location jitters around and their effective size is tiny (circa 1 meter).
Presumably the best Lagrange point in the vicinity of the solar system would be the L1 point of the Sun’s orbit around the galactic centre. I have a vague memory that someone has tried to test MOND using pairs of binary stars in eccentric orbits, but that the results were not conclusive (I think there were arguments about the selection criteria). Have there been any further developments in this area?
There are a number of tests related to this for which there are contradictory claims. One I keep meaning to write about but haven’t is the possibility that the signal suggesting the existence of Planet 9 is really a MOND effect that is a consequence of the EFE of the Galaxy on the outer solar system: https://ui.adsabs.harvard.edu/abs/2023AJ….166..168B/abstract
Guess we are slowly getting to acknowledgment that everything is connected and that looking at portions as if they were in isolation is futile. Sure, if one only wants more or less useful approximation so one could use a mathematical model of it to do something, like sending a probe to Pluto, then such approach is justified. Providing one then doesn’t falsely assume that aggregating all those bits and pieces will give us the big picture. Universe is *not* a jigsaw.
Two problems I find with your train of thought; and it could be because you wanted to keep things reasonably limited. One is the absence of the fourth dimension. Everything moves. The other is chain effect. Simplistically, a satellite of Andromeda affects Andromeda. Andromeda affects MW. So that satellite affects MW. And so on. One analogy might be path integral. Never mind how messed up whole QM is. In order for calculation to be ‘correct’ one would have to consider depressingly large number of interactions. So one does a cut off. Which is set arbitrary. So one ends up with approximation. Then one uses that approximate result and uses it in the next calculation. Sure, we jiggle around error bars and we do statistics but the deeper the hole the darker it gets. Same here. You can say, sure, we *do* know about that satellite of Andromeda but the effect is minuscule. Effect of *all* Andromeda’s satellites combined is minuscule. If one wants to get an approximate time of the merger (let’s just say there will be one) that’s fine. For anything more universal, not so much.
As for time and everything being in motion; well it’s kinda the same. 50 year survey means jack shit, pardon my French, in intergalactic terms. It’s still effectively a snapshot. Again, can be and is useful for some vague conclusions in applied astrophysics but near useless in cosmology.
I get it, we want answers. Or better said recently, write papers and accumulate prestige in order to get a better paid job. Every now and then somebody will birth the cursed phrase “We don’t know” followed immediately with how we absolutely need more research (aka approve my grant proposal please). Still calling everything science is frankly an insult to all those greats that got us to here as they truly just wanted to learn a tiny bit more and to hell with the purse. Humility went extinct and 99% of industry of science is peacocks parading the courtyard.
Cheers for being the 1%.
Yes – everything is interconnected and in motion all at once. Even the filamentary large scale structure of the universe evolves as it expands; nothing is fixed. So we make the approximation of dynamical equilibrium in hopes of making progress, but then tend to forget that it never entirely holds – a good example being for dwarfs in the EFE regime, which in MOND is knocking on the door of tidal disruption.
We do what we can.
could you focus on
Quantum modified inertia: an application to galaxy rotation curves
Authors: Jonathan Gillot
Abstract: This study explores the field of modified inertia through a novel model involving maximal and minimal acceleration bounds. A principle of dynamics is developed within special relativity and has direct implications in astrophysics, especially for galaxy rotation curves. The presence of a minimal acceleration significantly reduces the amount of dark matter required to account for these curves. The model presented here is however conceptually different from fiduciary Modified Newtonian Dynamics (MOND).
arXiv:2507.11524
could minimal gravity acceleration bounds also work
It seems to me that in a MOND world moving a test particle infinitely far away from a galaxy will cost an infinity amount of energy. For the finite, but still very long, distances in the universe, the energy is finite but a lot more than what would be in a Newtonian world. If we naïvely plug in the mass-energy relation from special relativity, then no photon can leave a gravitational field completely, and those traveling away from a galaxy will have higher redshift than expected in a Newtonian world.
Of course naïvely mixing formulas from MOND and SR doesn’t make sense, and at some point the gravity from other structures in the universe will dominate. But I’m curious whether more serious calculations have been made.
There effective potential in MOND is logarithmic, so there is no leaving it. The trick is what happens on the scales where this is relevant, which means the metric of the background cosmology, which is why we need a deeper underlying theory to address this sort of question.
Is the EFE thought to appear in globular clusters? I’ve found conflicting results on that – although you’ve shown that dwarf galaxies follow the EFE closely, some studies of GCs 15 or 20 years ago seemed to show MOND, but no EFE. Does that still apply, or has new data altered things since then – it seems the EFE used to show up only in some places where it’s expected.
In one way or another the EFE is about how fields combine (with or without the PSG interpretation, in which it’s more literal). There’s a comparatively complex set of rules, coming from both theory and observation. I’m wondering if there could be more structure within the EFE – more rules – than we know about so far. Can you see any possible pattern, or room for one, like some cutoff point relating to the relative strengths of two fields, which might decide whether or not they combine, or some directional aspect?
I should say, the MOND interpretation’s incomplete, but the solid basis of PSG isn’t – it can be tested in ten minutes, first putting numbers for two points on any orbit into an equation, the sides always agree to 16 decimal places. You then check the angle to the normal, it’s simple geometry, the rest is obvious. A link to the preprint is three posts back – on radial paths it’s a near-proof.
The vast majority of globular clusters are in the Newtonian regime. A few kinda probe the EFE, and people argue over what is seen. Perhaps the most intriguing test with globular clusters is the apparent asymmetry in their tidal streams, e.g., https://ui.adsabs.harvard.edu/abs/2024ApJ…970…94K/abstract
The EFE regime is not yet well enough probed to divine patterns beyond what is predicted by MOND, if they are there.
Are MOND’s empirical successes the first empirical evidence for non-locality in macroscopic, post-quantum-averaging physics?
I admire your commitment to observations prediction, and secondly to observations matching. Without this we are just doing math, and I am a mathematician. Matching is already more of a math riddle than physics.
And clearly MOND is true, as an approximation limit of an unknown underlying theory.
I have a few questions on the former post (comments closed).
In your old posts about baryons, the IGM was divided in Lyman alpha and WHIM. Is the new estimate an account of WHIM? Something completely new? In any case, why were the former estimates of IGM too low? Is there a reason to believe the new estimate rather than the old ones?
It is clearly a huge win for LCDM: now the missed second peak becomes a strong prediction: detecting that the bayrons were more than what was believed at the time. So going against what is known, and still getting it right.
But now that we have the ‘right’ number, what is the sociological risk we stop searching for baryons? I guess there were other possibilities for missing baryons? What if there are STILL more baryons? Even more than allowed by LCDM? What would be the most likely possibilities to accommodate such a scenario? In particular with respect to baryogenesis?
The FRB method is sensitive to all plasma along the line of sight, so includes both WHIM and the Ly-alpha forest, which are probed by different absorption lines (usually [O VI – VIII] and Ly a). Part of the issue before was the potential for double-counting: some of the detections of [O VII] might be the same as Ly-a. The dispersion measure just cares about electrons, not the ionization state of many-level atoms.
It is certainly a relief for LCDM. I wouldn’t describe it as a win for it in terms of the second peak; more like it lucked out. The no-CDM prediction is the same for the second peak for any plausible baryon density, including this one. LCDM just happens to hit on the right value now when it could have (and should have) been lots of other values.
Yes, there is absolutely the risk that we stop when we get the “right” answer. Happens all the time. I hope here people will want to reduce the still large uncertainties on the individual components like the CGM. If there are further reservoirs of baryons above the “right” value (perhaps associated with clusters of galaxies), this will hopefully become clear as the budget becomes more accurate.
Even if the global missing baryon problem is solved, the local one remains: the baryons are not fairly divided among their notional dark matter halos.
Probing the nature of gravity in the low-acceleration limit: wide binaries of extreme separations with perspective effects
Authors: Youngsub Yoon, Yong Tian, Kyu-Hyun Chae
Abstract: Recent statistical analyses of wide binaries have revealed a boost in gravitational acceleration with respect to the prediction by Newtonian gravity at low internal accelerations m\,s . This phenomenon is important because it does not permit the dark matter interpretation, unlike galaxy rotation curves.
thoughts ?
Stacy, good luck and strength for dealing with the Trump administration cuts on science! Such stupidity in governing a country is unprecedented, but it will never take away the reasons to do good science.
There’s science to be done under any government, but this one appears to be intent on repeating some of the darkest mistakes of the past.
Have any pro-MOND astronomers and astrophysicists considered creating “A MOND Study Guide for String Theorists”?
https://arxiv.org/pdf/2504.15127
Reconstructing the redshift evolution of Type Ia supernovae absolute magnitude
This paper is worth noting for three reasons: 1) They are using a Gausian/Baysian analysis to test a null hypothesis that supernova Ia magnitudes remaining constant over cosmic time. 2) Their model becomes unstable – oscillates – if they try to apply it to LCDM cosmology. If they add a couple of additional dark energy tweaks, they can produce a stable outcome that suggests supernova do not age or age only slightly.
3) They compare their results with a MONDian universe that modifies gravity and find this is compatible with their analysis.
I found it interesting that they considered the MOND solution – you do not see that a lot in the supernova community. I also find the instability that they observed using Lamda cosmology curious.
Why I see no one pointing out that the gravitational acceleration of the observable universe already amounts to a0? Is this ignored?
This is noted in the coincidence of a0 ~ c*sqrt(Lambda) so it isn’t ignored, but beyond that, what do we discuss?