I just got into Triton station, and there's loads of interesting posts on it about MOND and dark matter.
This post is really just saying errr, no there is no problem:
"That sounds normal for this type of galaxy, but I guess if you disliked MOND without understanding it, you might misinterpret that title to mean there was no mass discrepancy at all, hence a problem for MOND. I guess. I’m an expert on the subject; I don’t know where non-experts get their delusions."
As an unashamed fanboy of MOND since the early 2000s, I'm very pleased to see any sort of active discourse on the subject.
Over the last 20 years it appears to have moved slightly from "complete tinfoil hat" to "likely wrong longshot, but hard to trivially dismiss". I'm not an astrophysicist, I formed the above observation by asking astrophysicist friends what they think. :)
Exactly. And the well-posed gravitational theory that has MOND as a limit has not yet been found. So why is MOND considered as anything but an effective model?
Fluid dynamics is not a fundamental theory, but an effective model, as you said. The point here is that MOND can't explain something that GR has been able to explain for 100 years (precession of Mercury). So any serious gravitational theory needs to at least that for serious consideration.
If you're claiming that dark matter is superior because it is a fundamental theory, I fail to see why a fundamental theory that's empirically wrong is supposed to be better than an effective model. Rather than propping up dark matter, astrophysicists should be focusing on novel ideas that reproduce MOND, like superfluid dark matter, or at GR modifications in the MOND regime.
I never mentioned dark matter. My only point is that any modern gravitational theory needs to do at least as well as general relativity. That means (among others): explaining the precession or Mercury; describe black holes; predict gravitational waves. So if MOND is to be taken seriously, it needs to do all of that. That's all, really.
That's a really bad bar, beacuse it creates a bootstrapping problem: There's a lot of very difficult math that you have to do to get to that point.
And if you say "don't take it seriously until it explains all those things" then why should anyone bother to do the heavy lifting for all that math?
Let me make a different suggestion: As soon as you have one or two very interesting observations that modern GR can't explain that are apparently gravitational, then you should start encouraging people to take it seriously and start working on the hard math.
There is no misconception. The only class of theories that I'm aware of that have MOND as their non-relativistic limit are TeVeS, and these have been ruled out by experiments. If you have something else in mind, please provide a paper reference.
You asked a good question. Forgive me if my answer is aimed a little bit at the level of some of the other commenters in this thread (and discussion topic). I can do an ELI if someone wants.
General relativity simply equates the local density of the stress-energy tensor with the Einstein tensor (and possible scalar multipliers like the cosmological constant) at every point in the whole spacetime. If we measure curvature with e.g. Einstein lensing, we know what the stress-energy tensor must be. The stress-energy tensor encodes all moving matter, including internal non-gravitational degrees of freedom (DOFs). The ~seventeen fields of the Standard Model of particle physics fill all spacetime too, and contribute to the stress-energy tensor. Notably, invisible (in the sense that they do not couple to electromagnetism) DOFs exist in those fields and how they couple to each other; these standard-model mechanisms happily generate non-negligible stress-energy but nothing that we can see at a fine-grained level in any of our telescopes. Gluons' complicated self-interactions are the paradigmatic example: their whizzing about is most of the proton invariant mass, and so most of the mass of visible matter, and so most of the stress-energy in stars (gluon-gluon interactions is especially important in neutron stars, and neutron stars are an important diagnostic of any theory of gravitation) and molecular gas and dust; but gluons themselves are invisible and massless.
Dark matter, in a nutshell, says that "empty space" (ignoring the thin, cold relic fields of the cosmological microwave background and its neutrino equivalent) has some unknown internal degrees of freedom whose action generates stress-energy. Very broadly we call the generator(s) of that stress-energy dark matter.
The distribution of luminous matter (and different species thereof, and how it interacts (e.g. pressure, like ram pressure, can be important in galactic dynamics)) within a galaxy or cluster varies from galaxy to galaxy. Why shouldn't the distribution of dark matter?
So,
> possibly there is a deeper theory of gravity that explains both mercury's precession and galactic rotation
it's just General Relativity. The difference is that we know the distribution of stress energy within our solar system much better than we know the distribution of stress energy in much more distant, or much more complicated, systems (like galaxies or clusters of thousands of galaxies).
Alternatives to General Relativity broadly can take the approach that "empty space" (again ignoring the cosmic microwave background) is just that: there are no hidden non-gravitational degrees of freedom to discover there. Instead, stress-energy of the Standard Model as it is understood today generates the measured curvature seen in lensing by galaxy clusters like "El Gordo" (ACT-CL J0102-4915). Typically this is done by a redefinition of curvature to include auxiliary gravitational fields beyond the Einstein tensor, thus we get families of theories like tensor-scalar gravity, tensor-vector-scalar gravity, and so on. These fields couple with each other, so that the Newton-Einstein-like coupling in the bright parts of galaxies persists but the dynamics of that coupling generates auxiliary curvature in empty space outside the bright parts of the same galaxies. One often hears this described as introducing a new force or a "new fifth-force" produced by matter comparable to Newtonian's force of gravity; the new "force" has a different fall-off at a distance from the source matter than the 1/r^2 of Newtonian gravity or electromagnetism, and that fall-off is designed to produce Milgrom's low-acceleration relation. However (and in the spirit of a thread that started off with the words "generally covariant", MOND-compatible relativistic gravitation is still just gravitational fields being sourced by matter, but with more gravitational fields and interactions and self-in...
You seem to be saying that there is no way for DM theories to reproduce mondian dynamics naturally, it's all just about the distribution of DM.
It seems obvious that DM theories have to get the distribution (and how it interacts with itself and/or other things) right to account for the motions we observe in all cases. This seems to be difficult with our current theories, at least to my layman's eye. I see things like superfluid DM proposed, etc.
An ELI would be good to confirm my understanding, if you have time.
I don't know what level to pitch an ELI at; below is my best guess, and it's probably uneven. I did't want to aim for a reader who is perfectly capable of picking up a textbook and reading the academic literature starting with Famaey & McGaugh 2012. I also don't want to aim so low that it's basically slogans; there are enough of those in forums like this, and they're often inconsistent or outright wrong. I'm also conscious that we are not the only two participants in this particular discussion.
I'm not sure what I can do to improve your understanding and I'm not about to examine you to assess it; as I said there are textbook treatments (any decent galaxy dynamics or galactic astronomy text updated in the last twenty years will touch on the empirical MOND relation, and the standard grad textbook by Binney & Tremaine goes quite deep on MOND) and more cutting-edge literature that has developed since the 1980s. Likewise, I'm not here to help you choose between MOND or dark matter as ways of resolving observed acceleration anomalies, only to try to describe the two approaches and offer some contrasts to the extent that these very different approaches can be contrasted (IIRC McGaugh, of triton station at the top of the discussion here, calls this the theoretical "incommensurateness problem"). There are plenty of blogs by partisans.
I also don't do galactic dynamics; it has little appeal for me. However, MOND vs Newton/Einstein is a debate that arises almost exclusively because of galactic dynamics. I do do weak field General Relativity, which is rarely used in galaxy astrophysics since more tractable approximations are available, and more still are forthcoming. That colours some of what's below, as it is those approximations which are compared with MOND (which one will want to think of as an approximation of some yet unknown alternative to General Relativity).
> naturally
Don't get hung up on that; nature is what selects the distribution. Nature also selects the distribution of stars in our sky, the particles in the standard model zoo, their masses, spins, couplings, dimensionless constants, and so forth. It's not human scientists who decided to make Mizar a double double-star system with their particular orbits. Newtonian gravitation, invented by humans, can describe those orbits well enough, but you must first measure some initial positions and velocities for those four bodies. Heck, only recently (about 1997) did we discover (through such measurement) that Mizar is a four-body system!
(In fact, Mizar is possibly a test of one aspect of MOND as an adaptation of Newtonian gravitation: the External Field Effect ought to produce marginally different orbits compared to Newtonian Kepler orbits because of the system's immersion in the Galaxy's MOND field. General Relativity agrees completely with Newtonian gravitation because of the former's strong equivalence principle and because dark matter, if it exists, is such a small part of the local stress-energy tensor around Mizar that its generation of curvature is negligible. Maybe Mizar ends up as evidence in favour of MOND-like post-Newtonian gravitation because of the external field effect, who knows?)
We don't choose the matter-energy distribution of the moon, but as we've gotten better at measuring it we can now describe very precisely its orbit millions of years in the future, as long as nobody blows it up or feeds Earth to a giant space goat.
> it's all about the distribution of DM
It's all about the initial position and velocity of every teensy mote of matter however you want to think about matter (e.g. as excitations in a dozen or more quantum matter fields, or as individual interacting particles or whatever). That's the case in every one of these classical field theories be it Newton (in the Newton-Poisson sense), modified Newton (ditto, e.g. Bekenste...
I think you nailed it mostly. I can handle concepts, but my math isn't really up to it. I might have a look at the textbooks you cite.
> Likewise, I'm not here to help you choose between MOND or dark matter as ways of resolving observed acceleration anomalies, only to try to describe the two approaches
That is all I want; I am not qualified to make that choice anyway.
> DM theories have to get the distribution ([and dynamics]) right
>> yes But equivalently
>> Modified gravity theories need to get the (distribution) and dynamics right
True.
The main differences as I see it is that MOND only requires standard model matter that we can already observe, and it makes some predictions. DM requires additional matter and doesn't seem to predict anything, as we can always find a particular distribution that explains each case. But MOND is not compatible with relativity (so far) whereas DM is.
Fascinating stuff, and the truth to the extent we can determine it, will no doubt be surprising and different to what we currently think.
Thanks for taking the time to explain our current state of knowledge to an interested layman.
I'll take three things out of order, then let you get on with your other reading.
> we can always find a particular distribution that explains each case.
This is hardly a weakness, nor is it unique to one theory or the other. In order to explain the MOND rotation curve, one needs a specific distribution of luminous matter. The luminous matter is not always straightforward to measure; weighing galaxies is hard (there is lots of obscuring dust and gas and so no hope of counting, much less tracking the orbits of, a trillion or so stars in a galaxy). Nobody's confident of even Andromeda's mass. See for example the excellent <https://aasnova.org/2020/06/09/how-do-you-weigh-a-galaxy/>. So when you read, hey, MOND gets the rotation curve right, remember that both MOND and non-MOND galaxy astronomers can only estimate galaxy masses, and there are big error bars. Rotation is easier to estimate, because astronomers can use interferometry at different wavelengths (e.g. to track particular types of molecular gas cland that ouds, or particular types of stars, by looking at spectral doppler shifts e.g. between the leading edge and the trailling edge of an edge-on disc galaxy).
> ... doesn't seem to predict anything ...
On the contrary, it predicts that free bodies in galaxies, which includes stars and gas clouds, follow free-falling trajectories that are entirely predictable given the free bodies' position and momentum at any moment. It also makes predictions about the aggregation of free bodies (e.g. into Bok globules) due to gravitational collapse, and that the centre of momentum of the aggregate body itself moves as a free body. The predictability is not affected by cold dark matter, which is too sparse and collisionless. MOND-mimicking DM theories, like the superfluid DM model you mentioned, preserve all of these features of Newton-Einstein gravitation except that they tend to add actual collisions involving dark matter and so strictly speaking the collided-with stars are not free bodies. More on pseudo-MOND below.
MOND as a MOdified-Newton gravity theory predicts that given two identical free bodies (two isolated stars each with the same mass, for example) follow trajectories which depend on their position, momentum, and distance from the centre of mass of the host galaxy at any given moment. So such orbits are not entirely predictable unless you know exactly the distribution of mass in the host galaxy. More generally MOND predicts that all sufficiently wide orbits at all mass scales and mass ratios are deformed compared to Kepler's laws, so e.g. wide orbits of black holes would work differently. As a non-relativistic theory MOND says nothing about gravitational waves but it is hard to imagine a relativistic completion of modified-gravity MOND that would produce the waveforms detected at LIGO/Virgo/KAGRA and in pulsar timing arrays: gravitational radiation is determined by the orbital properties, so if the orbital properties differ (widely-orbiting black holes should complete orbits more quickly in MOND, just a star at the edge of a spiral galaxy will orbit more quickly in MOND than in Newton-without-dark-matter) then gravitational waves should too (the frequency should be higher; gravitational wave frequency is directly proportional to the orbital period of the source binary).
Distinguishing the two is presently awfully difficult because precisely tracking the orbits of stars is hard, although there is ongoing progress thanks to the ESA Gaia surveys among others. What makes it hard? Obscured (dust, gas, other stars, ...) views, difficulties in determining the angle the orbital plane makes to our line of sight, tiny tiny tiny angular sizes, and on and on. Also, the relevant orbital periods are many years long, so it also requires patience and ...
Justin Khoury's version is a Bose-Einstein condensate (BEC) of axion-like particles. The BEC forms a halo and is fluid, like a gas, in most of the halo. In the halo's central regions the BEC undergoes a phase change and becomes superfluid, and in that region interactions with baryons are produced which bubble up to the thin nonsuperfluid phase, where they interact with baryons again as a "fifth force" where one would want to understand that as viscosity. Viscosity vanishes in a superfluid. Here the idea is that the superfluid phase does not interact much with baryons except to generate vortex-like ring-perturbations which rise (and I think magnify) from the core, where the sticky-viscosity of the non-superfluid phase deposits energy into baryons, with a bias driven by galaxy's bulk angular momentum (the kicks being more in the direction of rotation and radially outward, generating the flat velocity curve). It's very much a particle dark matter theory, and a somewhat complicated one. It shows that a more than one particle dark matter theory can reproduce empirical results from MOND. And yes, as with any field theory, one would want to take a Hamiltonian approach and consider the dynamic canonical variables (x, p) [position, momentum], so you will need to specify all (x, p) at some time t, and because that's intractable, one coarse-grains.
Axions have yet to be directly detected in astronomical or laboratory settings, and nobody knows how they behave at ultracold temperatures and ultrasparse densities. Do they even BEC?
However, if they did exist and have the properties to form a Bose gas etc etc, and their cosmological participation isn't forbidden by higher-energy completions of the standard model, then there is a nice property here: it's just relativistic quantum fields on curved spacetime. Relativity (specifically in the sense that we can relate physical coincidences in arbitrary systems of coordinates) is baked in from the start. And you would get the empirical MOND relation in galaxy dynamics. But it's certianly not a MONDian theory in spirit. There is no modified gravity to be seen here.
> And you would get the empirical MOND relation in galaxy dynamics. But it's certianly not a MONDian theory in spirit. There is no modified gravity to be seen here.
There is no such thing as "purity" in physics. The whole reason most people work on MOND is because it provides a simple effective theory for not only describing observations with fewer parameters than cold dark matter, but predicting them more effectively. Every MONDian paper I've read has effectively been saying, "stop ignoring this obvious relation in preference to unnecessarily complicated and ad-hoc DM that provides no predictive power". If a superfluid or other dark matter theory derived MONDian dynamics, then pretty much everyone would be happy with that.
There was a lot of detail in your posts, which is appreciated, but also, I think, some mistaken assumptions about MOND or those pursuing alternative avenues to LCDM. For instance, it's a common misconception that MOND researchers are asking anyone to abandon GR, when really it just needs you to abandon the strong equivalence principle:
Precisely. They way I see it, MOND is a useful effective theory. But it is beyond me how people still think of it as a fundamental theory when the closest that anyone ever came up of a general-relativistic version of it is a total mess. As it is, MOND fails solar system tests. So at best, it's a useful effective model for some galactic-scale phenomenology, which would need some fundamental explanation.
The year is 3000AD. A 1 million cubic kilometer xenon detector cooled to 2K orbiting Neptune has not detected any WIMPs. Not to worry, the next one will be ten times bigger and at 0.5K.
Modified Newtonian dynamics (MOND) is a hypothesis that proposes a modification of Newton's law of universal gravitation to account for observed properties of galaxies. It is an alternative to the hypothesis of dark matter in terms of explaining why galaxies do not appear to obey the currently understood laws of physics.
NGC1277: The galaxy is unique in that it is considered a relic of what galaxies were like in the early universe. The galaxy is composed exclusively of aging stars that were born 10 billion years ago. But unlike other galaxies in the local universe, it has not undergone any further star formation. Astronomers nickname such galaxies as "red and dead," because the stars are aging and there aren't any successive generations of younger stars.
On a recent Sean Carroll podcast he said the galaxy/dark matter problem is the easy one to solve. There is another one, much harder - acoustic oscillation immediately after the Big Bang, visible in the microwave background, which MOND can't account for.
Basically normal matter goes both ways, back-and-forth, compresses and expands, but dark matter goes only one-way, only expands. And this can be seen in the microwave background.
Explaining the baryon acoustic oscillation with LCDM presumes that the phenomenon must have the same causal explanation as galaxy rotation curves. That's not necessarily the case.
It should be considered "a nice feature" that LCDM explains this but when you have a mass distribution that can be arbitrarily assigned in space, it feels like there are a lot of "nice things you could explain".
For example, they tried to explain the precession of mercury with a hunk of dm orbiting the sun called "Vulcan" (we now know you don't need dark matter to explain this). I believe the Vulcan steps in SF are named after this hypothetical dark matter planet. It's in the same neighborhood as mars, Venus, and Saturn and built around the same time
Have you listened to Carroll on the subject? As someone who knows next to nothing on this subject, he seems to me to be claiming that dark matter explains a lot of things in the universe and is very established, whereas MOND is very fringe. The claims in this post, that NGC 1277 is not a particular issue for MOND, seem to ignore the general consensus on MOND vs dark matter. The post seems to be focused on a very specific thing which doesn't seem unreasonable to me, but doesn't change the wider context that dark matter is very established and mainstream, and MOND is not, and this single issue doesn't change the big picture. Is this a flawed reading?
It is not controversial that dark matter is the orthodoxy and MOND is more on the fringe. That says nothing about how true either is.
Both DM and MOND have problems explaining various data and do well at others. DM in particular seems to require a lot of parameters and tuning to make it work.
I don't doubt that the consensus is that MOND is whack but the fact is that MOND has made some stunning predictions that have come true.
For example, Korean scientists went looking to disprove MOND by showing there isn't something called the External Field Effect, which they found as a result of their studies.
MOND predicted that JWST would see old galaxies, which mainstream astronomers are now flipping out over.
MOND predicts that binary stars that are far apart would enter the MOND regime. Two studies confirm this observation. A third refutes it but there appears to be methodological problems in this third study.
Having been a scientist, I have little faith that the median practicing scientists have any concept of discernment in terns of following the scientific method.
You're supposed to flip your opinion on models when predictive data shows up. As far as I can tell LCDM can explain a lot of stuff but it hasn't predicted much.
Think of it this way. When you train a ML model if you have a ton of parameters you run the risk of over fitting unless you have a regularization scheme. LCDM easily has at least one parameter per galaxy, and the only regularization is "can we come up with some explanation for this?" Over fitting is a huge risk for LCDM.
By contrast, MOND has one (maybe two or three, if you believe in relativistic MOND) parameters for the whole universe.
Which is why it's making a priori predictions versus a posteriori explanations, it's very hard to make a priori predictions when your parameter for any given galaxy could be anything.
It should say something that "why don't we have a picture of it: is the center of the milky way a blob of dark matter and not a black hole" (paraphrased of ciurse) was a real publication in between the time that we "took a picture" of a black hole in one galaxy and before we had done so for Sagittarius X-1
I think something like the bullet cluster, where you have gravitational lensing consistent with a collision-less fluid, leading a baryonic colliding gas (which we know is present from X-ray emissions), was a prediction of CDM. So it hasn’t predicted nothing, but yeah, I want to see more.
I don't recall that to be the case. Bullet cluster was a post hoc explanation, not a prediction. Can you find me a citation where they say "we should see matter detached from dark matter" before the bullet observation? I'll happily change my memory on this. I do recall finding something that LCDM predicted though (can't remember off the top of my head it was)
In fact LCDM shouldn't predict the bullet cluster, a collision that fast between galaxies is extremely rare in LCDM models.
> when you have a mass distribution that can be arbitrarily assigned in space, it feels like there are a lot of "nice things you could explain"
Like an eight-planet star system, or a star system with a hot Jupiter, or a multi-star system with no planets, all arising within the same giant molecular cloud (GMC)? Even though the cloud-elements behave sanely, even small arbitrary changes in initial values can produce dramatically different later arrangements. Replace the galactic GMC with a dark matter filament in the cosmic web, and why be surprised that all sorts of galaxies form within?
I don't think there is reason to fear arbitrary mass distributions so long as they obey constraints (if you're interested in the maths, the Einstein constraint equations are a good starting point you'll find in textbooks -- Robert Wald's chapter 10 is good and mathy, Alcubierre's or Baumgarte and Shapiro's numerical relativity textbooks are good alternatives for people who think computationally -- and lecture materials). We know empirical constraints and lots of solutions at many scales in the known universe already, and that constraint equations can be found for many other classical field theories; Dirac and successors (Regge et al., Rothe & Rothe et al.) are good resources wrt quantum field theories.
Roughly the slogan is to lay down some arbitrary but plausibly generic configuration and see how it evolves. Do it often enough and you should get familiar structures, or you're back to the drawing board. Large cosmological dark matter simulations that do exactly this are new hat. Standard cosmology solutions often get compared in the same project with alternative theories, sometimes following the spirit of the Standard Model Extension in parametrizing everything possible and plugging in different coefficient values, sometimes simply trying to trace cosmological implementations of an IV formalism on some published alternative to general relativity. For example, Vogelsberger et al., <https://www.nature.com/articles/s42254-019-0127-2>, <https://arxiv.org/abs/1909.07976v6> in which §5.3 has a brief literature review.
TL/DR: compact galaxies rotate fast enough that their centripetal acceleration limit for MOND. Therefore it should look Newtonian, therefore You expect to "not see dark matter" in them.
FTA: Eyeballing/back of the envelope the NGC 1277 data suggests it falls into that category (me: probably a more careful calculation is warranted). Usually galaxies that fit this are dense elliptical; 1277 is ultramassive lenticular, though to be fair lenticular ~elliptical.
I don't believe that's entirely accurate (I am not a cosmologist).
It says that because of the acceleration, MOND predicts Newtonian motion.
It does not say that you expect not to see dark matter, just that dark matter is not needed to explain that motion.
However, this is a problem for dark matter theories precisely because we expect galaxies to form in concentrations of dark matter:
"The infall of baryons acts to further concentrate the central dark matter. So the nominal expectation is that there should be plenty of dark matter near the centers of galaxies rather than none at all. That’s not what we see here, so nominally NGC 1277 presents more of a challenge for the dark matter paradigm than it does for MOND"
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[ 3.1 ms ] story [ 77.4 ms ] thread"That sounds normal for this type of galaxy, but I guess if you disliked MOND without understanding it, you might misinterpret that title to mean there was no mass discrepancy at all, hence a problem for MOND. I guess. I’m an expert on the subject; I don’t know where non-experts get their delusions."
Still fun to read though.
Over the last 20 years it appears to have moved slightly from "complete tinfoil hat" to "likely wrong longshot, but hard to trivially dismiss". I'm not an astrophysicist, I formed the above observation by asking astrophysicist friends what they think. :)
For that matter, how is QM considered to be an effective model when we can't even reconcile it with gravity?
And if you say "don't take it seriously until it explains all those things" then why should anyone bother to do the heavy lifting for all that math?
Let me make a different suggestion: As soon as you have one or two very interesting observations that modern GR can't explain that are apparently gravitational, then you should start encouraging people to take it seriously and start working on the hard math.
It's a misconception that MOND involves abandoning GR:
https://tritonstation.com/2023/02/27/take-it-where/
Fluid dynamics is a field of study, not any kind of model. Navier-Stokes is just what you get when you apply F=ma to Newtonian fluids.
Or that doesn't count as MOND because it effectively adds another source of gravity and thus dark matter in disguise?
[1] https://journals.aps.org/prx/pdf/10.1103/PhysRevX.11.041050
[2] https://arxiv.org/abs/1710.06168
A question for me is how dark matter theories can reproduce mondian dynamics naturally without each case requiring special tuning.
Or possibly there is a deeper theory of gravity that explains both mercury's precession and galactic rotation.
General relativity simply equates the local density of the stress-energy tensor with the Einstein tensor (and possible scalar multipliers like the cosmological constant) at every point in the whole spacetime. If we measure curvature with e.g. Einstein lensing, we know what the stress-energy tensor must be. The stress-energy tensor encodes all moving matter, including internal non-gravitational degrees of freedom (DOFs). The ~seventeen fields of the Standard Model of particle physics fill all spacetime too, and contribute to the stress-energy tensor. Notably, invisible (in the sense that they do not couple to electromagnetism) DOFs exist in those fields and how they couple to each other; these standard-model mechanisms happily generate non-negligible stress-energy but nothing that we can see at a fine-grained level in any of our telescopes. Gluons' complicated self-interactions are the paradigmatic example: their whizzing about is most of the proton invariant mass, and so most of the mass of visible matter, and so most of the stress-energy in stars (gluon-gluon interactions is especially important in neutron stars, and neutron stars are an important diagnostic of any theory of gravitation) and molecular gas and dust; but gluons themselves are invisible and massless.
Dark matter, in a nutshell, says that "empty space" (ignoring the thin, cold relic fields of the cosmological microwave background and its neutrino equivalent) has some unknown internal degrees of freedom whose action generates stress-energy. Very broadly we call the generator(s) of that stress-energy dark matter.
The distribution of luminous matter (and different species thereof, and how it interacts (e.g. pressure, like ram pressure, can be important in galactic dynamics)) within a galaxy or cluster varies from galaxy to galaxy. Why shouldn't the distribution of dark matter?
So,
> possibly there is a deeper theory of gravity that explains both mercury's precession and galactic rotation
it's just General Relativity. The difference is that we know the distribution of stress energy within our solar system much better than we know the distribution of stress energy in much more distant, or much more complicated, systems (like galaxies or clusters of thousands of galaxies).
Alternatives to General Relativity broadly can take the approach that "empty space" (again ignoring the cosmic microwave background) is just that: there are no hidden non-gravitational degrees of freedom to discover there. Instead, stress-energy of the Standard Model as it is understood today generates the measured curvature seen in lensing by galaxy clusters like "El Gordo" (ACT-CL J0102-4915). Typically this is done by a redefinition of curvature to include auxiliary gravitational fields beyond the Einstein tensor, thus we get families of theories like tensor-scalar gravity, tensor-vector-scalar gravity, and so on. These fields couple with each other, so that the Newton-Einstein-like coupling in the bright parts of galaxies persists but the dynamics of that coupling generates auxiliary curvature in empty space outside the bright parts of the same galaxies. One often hears this described as introducing a new force or a "new fifth-force" produced by matter comparable to Newtonian's force of gravity; the new "force" has a different fall-off at a distance from the source matter than the 1/r^2 of Newtonian gravity or electromagnetism, and that fall-off is designed to produce Milgrom's low-acceleration relation. However (and in the spirit of a thread that started off with the words "generally covariant", MOND-compatible relativistic gravitation is still just gravitational fields being sourced by matter, but with more gravitational fields and interactions and self-in...
You seem to be saying that there is no way for DM theories to reproduce mondian dynamics naturally, it's all just about the distribution of DM.
It seems obvious that DM theories have to get the distribution (and how it interacts with itself and/or other things) right to account for the motions we observe in all cases. This seems to be difficult with our current theories, at least to my layman's eye. I see things like superfluid DM proposed, etc.
An ELI would be good to confirm my understanding, if you have time.
> ELI ... my understanding
I don't know what level to pitch an ELI at; below is my best guess, and it's probably uneven. I did't want to aim for a reader who is perfectly capable of picking up a textbook and reading the academic literature starting with Famaey & McGaugh 2012. I also don't want to aim so low that it's basically slogans; there are enough of those in forums like this, and they're often inconsistent or outright wrong. I'm also conscious that we are not the only two participants in this particular discussion.
I'm not sure what I can do to improve your understanding and I'm not about to examine you to assess it; as I said there are textbook treatments (any decent galaxy dynamics or galactic astronomy text updated in the last twenty years will touch on the empirical MOND relation, and the standard grad textbook by Binney & Tremaine goes quite deep on MOND) and more cutting-edge literature that has developed since the 1980s. Likewise, I'm not here to help you choose between MOND or dark matter as ways of resolving observed acceleration anomalies, only to try to describe the two approaches and offer some contrasts to the extent that these very different approaches can be contrasted (IIRC McGaugh, of triton station at the top of the discussion here, calls this the theoretical "incommensurateness problem"). There are plenty of blogs by partisans.
I also don't do galactic dynamics; it has little appeal for me. However, MOND vs Newton/Einstein is a debate that arises almost exclusively because of galactic dynamics. I do do weak field General Relativity, which is rarely used in galaxy astrophysics since more tractable approximations are available, and more still are forthcoming. That colours some of what's below, as it is those approximations which are compared with MOND (which one will want to think of as an approximation of some yet unknown alternative to General Relativity).
> naturally
Don't get hung up on that; nature is what selects the distribution. Nature also selects the distribution of stars in our sky, the particles in the standard model zoo, their masses, spins, couplings, dimensionless constants, and so forth. It's not human scientists who decided to make Mizar a double double-star system with their particular orbits. Newtonian gravitation, invented by humans, can describe those orbits well enough, but you must first measure some initial positions and velocities for those four bodies. Heck, only recently (about 1997) did we discover (through such measurement) that Mizar is a four-body system!
(In fact, Mizar is possibly a test of one aspect of MOND as an adaptation of Newtonian gravitation: the External Field Effect ought to produce marginally different orbits compared to Newtonian Kepler orbits because of the system's immersion in the Galaxy's MOND field. General Relativity agrees completely with Newtonian gravitation because of the former's strong equivalence principle and because dark matter, if it exists, is such a small part of the local stress-energy tensor around Mizar that its generation of curvature is negligible. Maybe Mizar ends up as evidence in favour of MOND-like post-Newtonian gravitation because of the external field effect, who knows?)
We don't choose the matter-energy distribution of the moon, but as we've gotten better at measuring it we can now describe very precisely its orbit millions of years in the future, as long as nobody blows it up or feeds Earth to a giant space goat.
> it's all about the distribution of DM
It's all about the initial position and velocity of every teensy mote of matter however you want to think about matter (e.g. as excitations in a dozen or more quantum matter fields, or as individual interacting particles or whatever). That's the case in every one of these classical field theories be it Newton (in the Newton-Poisson sense), modified Newton (ditto, e.g. Bekenste...
> I don't know what level to pitch an ELI at
I think you nailed it mostly. I can handle concepts, but my math isn't really up to it. I might have a look at the textbooks you cite.
> Likewise, I'm not here to help you choose between MOND or dark matter as ways of resolving observed acceleration anomalies, only to try to describe the two approaches
That is all I want; I am not qualified to make that choice anyway.
> DM theories have to get the distribution ([and dynamics]) right >> yes But equivalently >> Modified gravity theories need to get the (distribution) and dynamics right
True.
The main differences as I see it is that MOND only requires standard model matter that we can already observe, and it makes some predictions. DM requires additional matter and doesn't seem to predict anything, as we can always find a particular distribution that explains each case. But MOND is not compatible with relativity (so far) whereas DM is.
Fascinating stuff, and the truth to the extent we can determine it, will no doubt be surprising and different to what we currently think.
Thanks for taking the time to explain our current state of knowledge to an interested layman.
> we can always find a particular distribution that explains each case.
This is hardly a weakness, nor is it unique to one theory or the other. In order to explain the MOND rotation curve, one needs a specific distribution of luminous matter. The luminous matter is not always straightforward to measure; weighing galaxies is hard (there is lots of obscuring dust and gas and so no hope of counting, much less tracking the orbits of, a trillion or so stars in a galaxy). Nobody's confident of even Andromeda's mass. See for example the excellent <https://aasnova.org/2020/06/09/how-do-you-weigh-a-galaxy/>. So when you read, hey, MOND gets the rotation curve right, remember that both MOND and non-MOND galaxy astronomers can only estimate galaxy masses, and there are big error bars. Rotation is easier to estimate, because astronomers can use interferometry at different wavelengths (e.g. to track particular types of molecular gas cland that ouds, or particular types of stars, by looking at spectral doppler shifts e.g. between the leading edge and the trailling edge of an edge-on disc galaxy).
> ... doesn't seem to predict anything ...
On the contrary, it predicts that free bodies in galaxies, which includes stars and gas clouds, follow free-falling trajectories that are entirely predictable given the free bodies' position and momentum at any moment. It also makes predictions about the aggregation of free bodies (e.g. into Bok globules) due to gravitational collapse, and that the centre of momentum of the aggregate body itself moves as a free body. The predictability is not affected by cold dark matter, which is too sparse and collisionless. MOND-mimicking DM theories, like the superfluid DM model you mentioned, preserve all of these features of Newton-Einstein gravitation except that they tend to add actual collisions involving dark matter and so strictly speaking the collided-with stars are not free bodies. More on pseudo-MOND below.
MOND as a MOdified-Newton gravity theory predicts that given two identical free bodies (two isolated stars each with the same mass, for example) follow trajectories which depend on their position, momentum, and distance from the centre of mass of the host galaxy at any given moment. So such orbits are not entirely predictable unless you know exactly the distribution of mass in the host galaxy. More generally MOND predicts that all sufficiently wide orbits at all mass scales and mass ratios are deformed compared to Kepler's laws, so e.g. wide orbits of black holes would work differently. As a non-relativistic theory MOND says nothing about gravitational waves but it is hard to imagine a relativistic completion of modified-gravity MOND that would produce the waveforms detected at LIGO/Virgo/KAGRA and in pulsar timing arrays: gravitational radiation is determined by the orbital properties, so if the orbital properties differ (widely-orbiting black holes should complete orbits more quickly in MOND, just a star at the edge of a spiral galaxy will orbit more quickly in MOND than in Newton-without-dark-matter) then gravitational waves should too (the frequency should be higher; gravitational wave frequency is directly proportional to the orbital period of the source binary).
Distinguishing the two is presently awfully difficult because precisely tracking the orbits of stars is hard, although there is ongoing progress thanks to the ESA Gaia surveys among others. What makes it hard? Obscured (dust, gas, other stars, ...) views, difficulties in determining the angle the orbital plane makes to our line of sight, tiny tiny tiny angular sizes, and on and on. Also, the relevant orbital periods are many years long, so it also requires patience and ...
> superfluid DM proposed
Justin Khoury's version is a Bose-Einstein condensate (BEC) of axion-like particles. The BEC forms a halo and is fluid, like a gas, in most of the halo. In the halo's central regions the BEC undergoes a phase change and becomes superfluid, and in that region interactions with baryons are produced which bubble up to the thin nonsuperfluid phase, where they interact with baryons again as a "fifth force" where one would want to understand that as viscosity. Viscosity vanishes in a superfluid. Here the idea is that the superfluid phase does not interact much with baryons except to generate vortex-like ring-perturbations which rise (and I think magnify) from the core, where the sticky-viscosity of the non-superfluid phase deposits energy into baryons, with a bias driven by galaxy's bulk angular momentum (the kicks being more in the direction of rotation and radially outward, generating the flat velocity curve). It's very much a particle dark matter theory, and a somewhat complicated one. It shows that a more than one particle dark matter theory can reproduce empirical results from MOND. And yes, as with any field theory, one would want to take a Hamiltonian approach and consider the dynamic canonical variables (x, p) [position, momentum], so you will need to specify all (x, p) at some time t, and because that's intractable, one coarse-grains.
Axions have yet to be directly detected in astronomical or laboratory settings, and nobody knows how they behave at ultracold temperatures and ultrasparse densities. Do they even BEC?
However, if they did exist and have the properties to form a Bose gas etc etc, and their cosmological participation isn't forbidden by higher-energy completions of the standard model, then there is a nice property here: it's just relativistic quantum fields on curved spacetime. Relativity (specifically in the sense that we can relate physical coincidences in arbitrary systems of coordinates) is baked in from the start. And you would get the empirical MOND relation in galaxy dynamics. But it's certianly not a MONDian theory in spirit. There is no modified gravity to be seen here.
There is no such thing as "purity" in physics. The whole reason most people work on MOND is because it provides a simple effective theory for not only describing observations with fewer parameters than cold dark matter, but predicting them more effectively. Every MONDian paper I've read has effectively been saying, "stop ignoring this obvious relation in preference to unnecessarily complicated and ad-hoc DM that provides no predictive power". If a superfluid or other dark matter theory derived MONDian dynamics, then pretty much everyone would be happy with that.
https://tritonstation.com/2023/02/27/take-it-where/
Modified Newtonian dynamics (MOND) is a hypothesis that proposes a modification of Newton's law of universal gravitation to account for observed properties of galaxies. It is an alternative to the hypothesis of dark matter in terms of explaining why galaxies do not appear to obey the currently understood laws of physics.
NGC1277: The galaxy is unique in that it is considered a relic of what galaxies were like in the early universe. The galaxy is composed exclusively of aging stars that were born 10 billion years ago. But unlike other galaxies in the local universe, it has not undergone any further star formation. Astronomers nickname such galaxies as "red and dead," because the stars are aging and there aren't any successive generations of younger stars.
Basically normal matter goes both ways, back-and-forth, compresses and expands, but dark matter goes only one-way, only expands. And this can be seen in the microwave background.
It should be considered "a nice feature" that LCDM explains this but when you have a mass distribution that can be arbitrarily assigned in space, it feels like there are a lot of "nice things you could explain".
For example, they tried to explain the precession of mercury with a hunk of dm orbiting the sun called "Vulcan" (we now know you don't need dark matter to explain this). I believe the Vulcan steps in SF are named after this hypothetical dark matter planet. It's in the same neighborhood as mars, Venus, and Saturn and built around the same time
Both DM and MOND have problems explaining various data and do well at others. DM in particular seems to require a lot of parameters and tuning to make it work.
For example, Korean scientists went looking to disprove MOND by showing there isn't something called the External Field Effect, which they found as a result of their studies.
MOND predicted that JWST would see old galaxies, which mainstream astronomers are now flipping out over.
MOND predicts that binary stars that are far apart would enter the MOND regime. Two studies confirm this observation. A third refutes it but there appears to be methodological problems in this third study.
Having been a scientist, I have little faith that the median practicing scientists have any concept of discernment in terns of following the scientific method.
You're supposed to flip your opinion on models when predictive data shows up. As far as I can tell LCDM can explain a lot of stuff but it hasn't predicted much.
Think of it this way. When you train a ML model if you have a ton of parameters you run the risk of over fitting unless you have a regularization scheme. LCDM easily has at least one parameter per galaxy, and the only regularization is "can we come up with some explanation for this?" Over fitting is a huge risk for LCDM.
By contrast, MOND has one (maybe two or three, if you believe in relativistic MOND) parameters for the whole universe.
Which is why it's making a priori predictions versus a posteriori explanations, it's very hard to make a priori predictions when your parameter for any given galaxy could be anything.
It should say something that "why don't we have a picture of it: is the center of the milky way a blob of dark matter and not a black hole" (paraphrased of ciurse) was a real publication in between the time that we "took a picture" of a black hole in one galaxy and before we had done so for Sagittarius X-1
In fact LCDM shouldn't predict the bullet cluster, a collision that fast between galaxies is extremely rare in LCDM models.
Do you know of any studies that try to combine them?
Like an eight-planet star system, or a star system with a hot Jupiter, or a multi-star system with no planets, all arising within the same giant molecular cloud (GMC)? Even though the cloud-elements behave sanely, even small arbitrary changes in initial values can produce dramatically different later arrangements. Replace the galactic GMC with a dark matter filament in the cosmic web, and why be surprised that all sorts of galaxies form within?
I don't think there is reason to fear arbitrary mass distributions so long as they obey constraints (if you're interested in the maths, the Einstein constraint equations are a good starting point you'll find in textbooks -- Robert Wald's chapter 10 is good and mathy, Alcubierre's or Baumgarte and Shapiro's numerical relativity textbooks are good alternatives for people who think computationally -- and lecture materials). We know empirical constraints and lots of solutions at many scales in the known universe already, and that constraint equations can be found for many other classical field theories; Dirac and successors (Regge et al., Rothe & Rothe et al.) are good resources wrt quantum field theories.
Roughly the slogan is to lay down some arbitrary but plausibly generic configuration and see how it evolves. Do it often enough and you should get familiar structures, or you're back to the drawing board. Large cosmological dark matter simulations that do exactly this are new hat. Standard cosmology solutions often get compared in the same project with alternative theories, sometimes following the spirit of the Standard Model Extension in parametrizing everything possible and plugging in different coefficient values, sometimes simply trying to trace cosmological implementations of an IV formalism on some published alternative to general relativity. For example, Vogelsberger et al., <https://www.nature.com/articles/s42254-019-0127-2>, <https://arxiv.org/abs/1909.07976v6> in which §5.3 has a brief literature review.
FTA: Eyeballing/back of the envelope the NGC 1277 data suggests it falls into that category (me: probably a more careful calculation is warranted). Usually galaxies that fit this are dense elliptical; 1277 is ultramassive lenticular, though to be fair lenticular ~elliptical.
It says that because of the acceleration, MOND predicts Newtonian motion.
It does not say that you expect not to see dark matter, just that dark matter is not needed to explain that motion.
However, this is a problem for dark matter theories precisely because we expect galaxies to form in concentrations of dark matter:
"The infall of baryons acts to further concentrate the central dark matter. So the nominal expectation is that there should be plenty of dark matter near the centers of galaxies rather than none at all. That’s not what we see here, so nominally NGC 1277 presents more of a challenge for the dark matter paradigm than it does for MOND"