| Thanks, that helps develop my understanding. > 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 some care as newer instruments replace ones that become obsolete over the course of a tracked orbit.
Finally, non-relativistic MOND says nothing about tight orbits of black holes, and it is the detection of final inspirals that give us the best signals. Worse, the MOND modification to Newton falls off with greater mutual acceleration, so it will fall off as inspiralling black holes move closer together (in MOND stars near the core of a spiral galaxy move on essentially Newton-Kepler orbits).
To summarize part of the above:
> MOND is not compatible with relativity (so far)
MOND as a modified gravity theory cannot be compatible with general relativity, and that's quite deliberate.
Pseudo-MOND (e.g. a MOND-mimicking dark matter theory comparable to the superfluid DM you brought up, in which orbits are still Newtonian but there are additional tiny "m"s in the F = GMm/r^2, or some small fifth force F = Gmm/r^2 + f) can be built and even made fully general-relativistic, but it would be really weird (and really really disingenuous) to call that MOND given what the initials stand for and given MOND's origins with Milgrom. At the risk of "no true scotsman" catcalls, real MOND requires V^4 = GMa_0 so F = m (v^2/r)^2/a_0 in the "deep-MOND regime". It just doesn't in a pseudo-MOND, at best you can come pretty close (think along the lines of a long Taylor expansion of 1 + (x^2 + x'^n + ...) where the non-leading terms are corrections from shells of (interacting so not strictly dark "super-dim") matter concentric upon the host galaxy's core and with a long enough "..." you get a decent approximation of 1 + (a_0/a) like how one might try to get a good approximation of π; deep-MOND regime's "standard interpolating function" is strictly sqrt(1/(1+(a_0/a)^2)). Pseudo-MOND DM mimicry will always introduce additional small accelerations in random directions along with a biased acceleration that's the heart of the mimicry.
More succinctly, in pseudo-MOND, Newton is more fundamental than the mimicked MOND, such that everything including the stuff doing the mimicry orbits according to Newton.
> DM requires additional matter
Yes. The matter can be a mix of things already known in the Standard Model (of Particle Physics) and things which aren't. Since the Standard Model is a concordance model that dates from the 1970s (to concord with experimental data confirming the existence of quarks) and has been updated within the past ten years (notably to concord with the experimental data confirming the existence of a Higgs boson), the Standard Model is hardly frozen in time.
There are a number of open issues in the Standard Model that drive the hunt for new particles (you can start at wikipedia, <https://en.wikipedia.org/wiki/Physics_beyond_the_Standard_Mo...>) for wholly non-gravitational reasons. Whatever these new particles are, they will be Lorentz-invariant by the nature of the Standard Model as a relativistic quantum field theory. It is straightforward to couple a non-gravitational Lorentz-invariant field theory to General Relativity up to some limits, but the dynamics of galactic spin are very much well within those limits. So if Beyond-the-Standard-Model physics searches discovers one or more new particles, those particles will both feel and source gravitation. If those particles can congregate in galaxy clusters without clumping into molecules and collapsing gravitationally in timescales that are short compared to the age of the universe, those particles would be good candidates to be part of the cold dark matter in the standard model of cosmology (which is also a concordance theory which gets updated when evidence requires that).
It wouldn't surprise many people if suitable new particles were demonstrated. However, it is certainly possible that the there won't be any found, perhaps because there aren't any to be found.
Because of the highly-tested equivalences between acceleration and gravitation and covariant physics in freely-falling and inertial coordinate systems, it would be surprising to find some feature of Standard Model of Particle Physics matter that generates gravitational fields that break these equivalences. Nobody serious would ignore that if it were demonstrated.
> it will no doubt be surprising and different to what we currently think
I would love that, but I am not that optimistic. I expect to be un-surprised (cf. the Higgs boson confirmation, and many tests of the equivalence principles and Lorentz invariance) by yet another confirmation of General Relativity rather than something which might provide usefully different yet correct descriptions of high-energy gravitational physics.