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Sometime you have to modify the theory, but sometime the missing mass is really there. For example neutrinos were postulated to exist to explain missing quantities in some interactions. Then they were actually discovered experimentally .

Incidentally neutrinos are dark matter, although not of the right kind.

Slight clarification of that last sentence: neutrinos are "dark" (do not interact with electromagnetism) and "matter" (have mass, take up space), but they are not what we are looking for when we say "dark matter" (the current best explanation for why galaxies move as they do).

In particular, they are weakly-interacting massive particles, but they aren't the Weakly-Interacting Massive Particles (WIMPS) we're looking for. WIMPs have to be slow-moving, or they'd escape the galaxy, and there's no apparent way to make slow-moving neutrinos (almost no mass means very high speed), and we haven't observed any.

It's still not absolutely impossible, but it's very unlikely. Dark matter is more likely to be something else -- though we're still unclear on what, and the most likely theories are looking somewhat less likely recently.

Right, that's why I referred to them as the wrong kind. IANAP, but I believe that neutrinos are in fact sometimes referred as hot dark matter.

Still, I understand that the current best model to explain the (tiny) neutrino mass involves theoretical much more massive "sterile" neutrinos that potentially could be the right kind of dark matter if they indeed exist.

> no apparent way to make slow-moving neutrinos

Adiabatic cooling of relic neutrinos (the cosmic neutrino background, CvB).

CvB formed before the cosmic microwave background and so is cooler than the CMB. Massless bosons like CMB photons have their wavelengths stretched through the history of the metric expansion of space; massive (even if the masses are small) fermions (like CvB neutrinos) instead see their speeds drop. The drop is about 161(1+z)/m with m being the neutrino mass and z the redshift; at present times CvB neutrinos are moving nonrelativistically (a couple thousand km/s) and so are certainly cold dark matter.

CvB neutrinos are incredibly abundant and do form a small fraction of CDM in the standard cosmology.

I don't think it's fair to call them WIMPs, though -- one wants invariant masses in the GeV range to gather up sufficient energy-density to drive galaxy cluster dynamics (cf. <https://en.wikipedia.org/wiki/Light_dark_matter>). CvB neutrinos are several orders of magnitude too light (invariant masses of 50-100 meV, kinetic masses of about 250 µeV).

It's ironic that Mercury is the chosen example of a discrepancy in an existing theory requiring a revision, because as I understand it MOND being based on Newtonian gravitation can't explain Mercury's actual orbit either. So it purports to solve one problem (galaxy scale gravitation) while re-introducing one we already solved. This makes it a bit weird that the example of Mercury is so often used in arguments for MOND.

-Thanks for the correction.

From article:

>If you want to merge MOND with Einstein’s General Relativity, it is possible as well, simply by adding in scalar (and possibly vector) terms in addition to the standard metric tensor terms.

So there's no issue.

> there's no issue

There's no issue as long as you think that "adding in scalar (and possibly vector) terms" is somehow a "simpler" change than "adding a new kind of matter".

But when you look at what "adding in scalar (and possibly vector) terms" actually means in GR, it's the same thing as "adding a new kind of matter". You're just calling the new kind of matter a "scalar field" (and possibly also a "vector field", i.e., two new kinds of matter).

In other words, when you take relativity into account, "MOND" is not an alternative to "dark matter"; it's just one particular way of adding "dark matter".

IANAP.

My understanding is that MOND doesn't kick-in in the Solar System at all; the strength of gravitation from the Sun is much greater than the MOND threshold. So I'm surprised that Mercury ever comes into discussions of MOND.

I would love to stand corrected, but as far as I understand it, NP->GR modification also instantly explained many same-day and subsequential phenomena, and mostly without issues. GR->? modification still faces some obvious today’s issues like galaxies “almost without dark matter” and galaxies/regions “almost fully consisting of it”.

It doesn’t mean that GR is correct. But GR is a formula that perfectly matches a dataset of local observations. ? should at least match farther ones, but they clump randomly like some non-interacting blobs/streams and do not form a general rule. This new dataset is either still too small or has no clear formula describing it at all. That’s why ? is still ?

Is that correct?

> Is that correct?

Basically, yes. But I would add a few points:

> GR is a formula that perfectly matches a dataset of local observations.

More precisely, our best current model of the solar system, which uses GR as its law of gravity, matches our best current dataset of solar system observations.

But similarly, our best current model of the universe, which also uses GR as its law of gravity but is a different model, matches our best current dataset of universe observations--which includes galaxy rotation curves but also includes many other observations.

> they clump randomly like some non-interacting blobs/streams and do not form a general rule. This new dataset is either still too small or has no clear formula describing it at all

I'm not sure what you mean here. Our dataset of universe observations is described by a "clear formula"--our best current model of the universe, which I described above. That model includes "dark matter", i.e., matter that we cannot see, but whose presence is necessary to account for the motion of things that we can see if we use GR as our law of gravity.

MOND proponents criticize the above model because it includes matter that we can't see. But that's not the same as saying the above model doesn't account for observations. It does.

Thanks!

That model includes "dark matter"

Yeah, I meant that if we “turn a blind eye” on dark matter in GR, then no universal formula can cover it. In the same sense that universal jet aerodynamics formulas don’t account for trees and mountains.

> I meant that if we “turn a blind eye” on dark matter in GR, then no universal formula can cover it. In the same sense that universal jet aerodynamics formulas don’t account for trees and mountains.

I'm still not sure what you mean here. The "universal formula" in GR is the Einstein Field Equation, which covers everything (more precisely, everything in which quantum effects are negligible).

I thought grandparent was saying that GR is wrong, and that Vulcan exists, but it’s made of dark matter. But maybe that’s not the right interpretation ;)

> I thought grandparent was saying that GR is wrong

No. The dark matter hypothesis is part of our best current model based on GR.

That hypothesis does include the belief that, as far as galaxy rotation curves are concerned, GR corrections to Newtonian gravity are negligible. But that is not the case for other observations that dark matter also accounts for (see below).

> and that Vulcan exists, but it’s made of dark matter.

That is basically what the dark matter hypothesis says, yes: that we don't need to modify the laws of gravity to explain galaxy rotation curves, we just have matter there that we can't see.

If this hypothesis were only introduced to explain galaxy rotation curves, that would be one thing. (It still wouldn't be as easily refutable as the Vulcan hypothesis was, since it's a lot easier for us to rule out the presence of significant additional matter in the solar system than it is in distant galaxies. But that's a side issue.) But it isn't. The dark matter hypothesis also explains many other observations (for example, the amount of structure--gravitational clumping of matter into galaxies and galaxy clusters--as compared with the amount of baryonic matter present based on Big Bang nucleosynthesis (which by itself would be much too small to account for the structure that we see). MOND, OTOH, was introduced solely to explain galaxy rotation curves and still leaves all the other observations that dark matter accounts for unexplained.