> One may need to add more free parameters to a theory, but those parameters need not be finely tuned.
You're right I've been too loose with how I've been using the term "fine-tuning". Adding a parameter is not fine-tuning so much as just tuning.
The point I was trying to make is that both adding parameters to a theory to fit observations that it didn't predict, and fine-tuning it's parameters to fit should count against its plausibility, since they're both forms of tweaking the theory to match observations after the fact rather than making accurate predictions that follow naturally from the model being proposed.
Famaey & McGaugh's review <https://arxiv.org/abs/1112.3960> (Stacey McGaugh is <https://tritonstation.com/>, a frequent critic of particle dark matter) §7 is all about adding whole new fields ("parameters") to standard General Relativity in order to capture higher-order terms in post-Newtonian expansions (in 1/c^n or in the metric tensor) of theories that preserve the central characteristics of Milgrom's MOND.
Those characteristics are: no "non-luminous" or "hidden" matter sources -- the glowing, refracting, and obscuring dusts are the sole sources of gravitation -- and in circumstances where post-Newtonian corrections are vanishingly small, strong concordance with Newton and Kepler except at the lowest accelerations.
The orbits of galactic blobs of slowly-moving molecular gas that produce characteristic spectral lines amenable to Doppler redshift study are almost always in those special circumstances, and they have higher accelerations "corewards" in galaxies and low accelerations "outwards" in galaxies. These gas blobs are most interesting at the leading and trailing limbs of edge-on discoid/spiral galaxies, or face-on in large elliptical galaxies with negligible bulk rotation (the Doppler-shifting blobs move in and out, almost entirely radially), precisely where the accelerations are smallest.
The question we then ask is: what if we have a blob or some other spectrally well-defined object in a galaxy is on a very fast orbit? We can no longer ignore post-Newtonian corrections, or we lose the MONDian match with spectral lines. This is what drives §7 ibid.
If we think of the expansion as:
Total gravitation = empty flat background + MONDian matter relation + higher-order terms (h.-o.t.s. or HOTs)
the relativistically moving but still-MONDian matter is the generator of the HOTs, which has been measured (by among other people Pavel Kroupa, the author of the fine article at the top of all this discussion).
Abandoning the MONDian matter relation is easy. Just recast:
Total Einstein gravitation = empty flat background + unknown stress-energy tensor + higher-order terms
and adapt the stress-energy tensor. Nothing in the theory of gravitation has ever suggested strongly the nature of matter which generates the stress-energy, but we can get constraints from other areas of physics like the standard model of particle physics (or even classical electromagnetism, as was the case when General Relativity was new), and we can get candidates from programs seeking to expand or alter the Standard Model to solve open non-gravitational problems. Thus: various types of electrically-neutral particles like axions or supersymmetrical sparticles have been considered because "someone else" (i.e., not a relativist) hypothesized them. (Observational cosmologists can find evidence to constrain such theories, and in practice helped kill off several supersymmetry extensions of the standard model, for example). Low-mass primordial black holes were a candidate too, because there were non-galactic-dynamics reasons to suspect they could exist in significant number. But those black holes (or very dim tiny stars or isolated cold Jupiters) could maybe generate the unknown stress-energy tensor.
Retaining the MONDian approach can be done in a couple of ways. Hold to the idea that the "luminous" stuff is the only source of gravitation, and then ask whether relativistically-moving MONDian matter is coupled to an unexpected background:
(where all that's left in HOTs is basically gravitational waves from relativistically-moving MONDian matter)
or alternatively whether there is a further field or fields to which slow-moving MONDian matter couples only very weakly, but fast-moving MONDian matter experiences quite strongly. That means the HOTs imply the existence of one or more new fields.
Are these fields free parameters? Good (and open) question.
What types of fields are allowed? §7 ibid. explores this largely in terms of adding fields to the Einstein Field Equations (EFEs) of general relativity. The fields conceptually modify Einsteinian gravitation, so are written on the curvature side of the EFEs. However, as the authors of the survey note, in most cases for purely mathematical reasons the fields could be written exactly equivalently as a function on the stress-energy tensor (the matter side of the curvature = matter relation).
Why are we thinking in terms of an adaptation of the Einstein Field equation in the first place? Because it works well for length scales much shorter than ~ten kiloparsecs, and might work well for length scales much greater than megaparsecs. In particular, it works so well in the solar system that it cannot be ignored: it is the effective theory of gravitation near us. So however one might eventually write down a relativistic MOND theory, it must be possible to re-write it into a modification of the Einstein Field Equations for use in the solar system and in systems like Hulse-Taylor or triple-pulsar J0337+1715.
Additionally, analysis through tools like the Parameterized post-Newtonian formalism <https://en.wikipedia.org/wiki/Alternatives_to_general_relati...> is extremely useful if one recasts some arbitrarily-different-from-General-Relativity gravitational theory into something for which PPNF variables can be found. The discipline of submitting to PPNF by rewriting a theory for PPNF friendliness often is personally useful for the theorist keenly interested in her or his not-like-General-Relativity theory of gravitation.
One might say, aiming for neutrality, that if one adapts the EFEs in such a way that the adaptation can appear on either side of the EFEs, the "conceptual" weight of the adaptation is perhaps more aesthetic than physical.
However, that's not quite fair: outright adding extra stress-energy dark-matter-style lets one decouple the "adaptation" of the galactic relation from galaxies themselves. One could put particle dark matter in parts of the universe where there are no electrons or protons. For instance, before electroweak decoupling and big bang baryogenesis, or in the extreme distant future where we have basically isolated black holes and relic microwaves (and neutrinos) that are undetectably cold/long-wavelength. Even around "today"'s epoch, dark matter could be put willy nilly well away from clusters of galaxies.
A modified gravity theory, relativized along the lines of Famaey and McGaugh's surveyed options, might also be able to do this. Strange curvature just existing apart from any matter. (One can do this by a choice of a strange background in a post-Newtonian correction formulation of standard General Relativity too.) But to be MONDian I think that you would want attractive gravitation to appear only where there is matter that interacts electromagnetically, because far from such matter (attractive) accelerations will be very low, and the central feature of MOND is that Newtonian gravitation needs adjustment at very low accelerations.
So for a fully-relativistic MONDian theory of gravitation, although maybe mathematically we could treat the low-acceleration as a field that we could drop just about anywhere, doing so would violate MOND's spirit. There is thus no vacuum + MOND field(s) gravitational solution that is remotely physical. This is certainly not the case for particle theories of dark matter. Those basically insist that it is perfectly reasonable to drop dark matter just about anywhere. One can easily expect to simulate a vacuum + cold dark matter solution to the Einstein Field Equations, and that the simulation might accord with some part of our actual universe.
Finally, without further diving into the aesthetics or bets about what particle physics at CERN and the like might discover about mechanisms that generate stress-energy, I think the "fight" between MONDian modified gravitation and Einsteinian gravitation with dark matter is irrelevant to astrophysicists (as opposed to theorists who deal with non-astrophysical systems), even those who work on galaxy dynamics. It is almost certain that it will be possible to find an initial values formulation for either type of "final conceptual" answer to the observed Milgrom relation. It's just a question then of finding out how to populate the initial values surface, and then letting the dynamical laws go to work on those.
(The initial data and laws for each theory (MOND or GR+DM) reformulated this way will necessarily differ, perhaps by a lot, but the approach of evolving a set of initial data will be the same (this is done in many areas of physics having little/nothing to do with gravitation, after all)).
That is, the core of the MOND/particle DM fight might be more about bets on whether the single minimally-coupled metric tensor approach in General Relativity is not always suitable, or whether the Standard Model of particle physics is incomplete in relevant ways, than about whether one is really more suitable for calculations than the other. (The bet is also not strictly either/or!)
I'm honestly not sure who will really care in practice, if it's ever "finally" decided one way or another.
> So however one might eventually write down a relativistic MOND theory, it must be possible to re-write it into a modification of the Einstein Field Equations for use in the solar system and in systems like Hulse-Taylor or triple-pulsar J0337+1715.
This is the contention I have with the "fine-tune" argument against DM: there's still tuning needed from the MOND side to both make it a predictable tool across the universe and also ensure it still acts like EFE at home. Everybody's tuning/tweaking because no one has anything novel.
To bring in an interesting analogy: it's almost like the debate over functional and OO programming paradigms. MOND seeks to tune the "function" or theory to better fit all observations. DM seeks to tune the "objects" or observations to better fit the theory.
> This is the contention I have with the "fine-tune" argument against DM: there's still tuning needed from the MOND side to both make it a predictable tool across the universe and also ensure it still acts like EFE at home.
The whole point of MOND is that our gravitational theory is inadequate, and exploring what modifications are needed to match observations is the way move forward, rather than assuming GR is correct and searching for the missing mass it says should be there. We actually already know GR must be wrong because of its singularities, so this insistence on looking for DM despite the constant failures is doubly strange.
MOND's process of exploring what modifications are needed isn't "fine-tuning" in the way that DM has been tuned because MOND is not a final or complete theory, and nobody has presented it as such.
> We actually already know GR must be wrong because of its singularities
This is not why we "know" GR must be wrong.
You keep making very strong assertions that any expert -- including those not hostile to MOND, or even positively in favour of properly capturing the empirical MOND relation into some other theory (whether that's the standard one or one like Bekenstein's) -- simply would not make.
I do not know what you are trying to do here on HN, but it does not seem to be an attempt to honestly help people who are interested in dark matter but who lack expertise; it doesn't seem to be an attempt to acquire expertise you clearly lack; and it doesn't seem to be an attempt to work out how you yourself might better understand difficult concepts through a process of ELI5/ELI12. It seems, frankly, like you just enjoy being rude on hackernews.
In order to make up for the observations above that might be fairly taken as leading off with insults, I'll supply some related real, standard, uncontroversial physics discussion.
The principal problem with General Relativity is that the stress-energy tensor when generated by real matter (which we know can behave quantum mechanically) must in principle be able to encode superpositions of (at least) spin, momentum, and position. However, the Einstein Field Equations are fully classical, so how to do this encoding is not known. As a result "hacks" like taking the expectation value of the stress-energy T_{\mu\nu} -> <T_{\mu\nu}> are used to make the EFEs work at all. Unfortunately this averaging generally destroys superpositions, so one runs into problems like: if we took a fairly large molecule and put it into a superposition of position in a laboratory full of sensitive precision-stabilized accelerometers, what should we expect them to show? To which the answers are unattractive (and hopefully will be tested soon enough by
direct experiment (at e.g. <https://www.npl.washington.edu/eotwash/node/1>)). A little more detail in <https://en.wikipedia.org/wiki/Semiclassical_gravity> or for more advanced readers e.g. <https://journals.aps.org/prd/abstract/10.1103/PhysRevD.47.45...> which corresponds with <https://arxiv.org/abs/gr-qc/9304008>.
This is far far far from the strong gravity regime near gravitational singularities. It's a problem we could test in a spacecraft in deep space, or in a laboratory here on Earth. No black holes required.
Singularities, while annoying for developing Cauchy problems as one likes to do in many areas of physics, are not immediately fatal to the theory for several reasons, including the probable correctness of the cosmic censorship hypothesis and the long term stability of realistic black holes. Indeed, at least General Relativity is a complete theory that makes a prediction about what happens at its highest energy levels (measured in curvature invariants, like Kretschmann's). The Standard Model of Particle Physics is not presently "UV-complete". (More details @ <https://en.wikipedia.org/wiki/Physics_beyond_the_Standard_Mo...>, "The Standard Model is inherently an incomplete theory.") The converse is that while General Relativity is an inherently complete theory, it requires care in encoding the stress-energy tensor, any "background" curvature, boundary conditions, constraints, energy and coordinate conditions, and so forth. It is not an easy theory at all, especially when one does not understand all the mechanisms that generate the stress-energy tensor. Its successes as an effective field theory in astrophysical applications are legion, and completely contradict the remainder of your second paragraph.
All of the above equally applies to relativistic MOND (except the last sentence of the preceding paragraph: relativistic MOND generically gets the acoustic peaks of the CMB temperature power spectrum wrong, and usually badly wrong for the odd-numbered peaks, principally and importantly because of how different MOND is, by design, at assigning pressure in equations-of-state, and how that matters before the formation of the first galaxies). Milgrom's work has afaik always been in the regime where quantum weirdness has been negligible (and indeed, for most of MOND's history was even wholly in the regime where special-relativistic weirdness was negligible).
MOND has been explored for more than fifty years, and Relativistic MOND for more than twenty years, by some of the biggest brains in gravitational physics, including Mordehai Milgrom <https://arxiv.org/abs/1310.3373>. There are endless publications about MOND even today (tiny sample: <https://arxiv.org/search/advanced?advanced=&terms-0-operator...>). Nobody working in galactic astrophysics is ignorant of it, or of the phenomenological Milgrom's law. Most theorists working in gravitation have played with it so they already know:
> exploring what modifications are needed to match observations is the way forward
So I find myself wondering: do you genuinely not know that MOND "is a thing" already (and has been for decades) in the relevant academic and professional circles?
I don't at all dispute that GR is very well confirmed in many regimes, but it's still an indisputable fact is that GR is definitely wrong because of its singularities. Whether it's wrong in other regimes remains to be seen.
Some like to reframe its breakdown as GR being "incomplete", but that's just a cute euphemism for "wrong". This point couldn't be more obvious so I'm not even sure why you would dispute it.
You can of course argue that GR may only be wrong on small scales or very high energies where quantum effects become relevant, but that's just conjecture. A conjecture with good reasons given GR's empirical success so far, but still not established fact.
How GR fails may or may not impact the argument for DM, but we should acknowledge that the fact that GR is wrong actually might impact the justification for DM, which should already make us more skeptical of the core case for DM.
> So I find myself wondering: do you genuinely not know that MOND "is a thing" already (and has been for decades) in the relevant academic and professional circles?
Of course it's a thing. I'm not sure how I can be more clear on what arguing, so I'll try one last time: while I appreciate the interesting details you've put into your replies, nothing you've said changes the fact that DM's highly regarded status in this field is just undeserved, and that MOND still gets less attention than it deserves given its unexpected predictive successes [3,4].
DM was very plausible early on, but it has repeatedly failed to provide clear predictions and failed to match observations without post-hoc adjustments, where MOND has had some very surprising predictions that matched observations in ways it had no right to if DM were true. I don't believe I ever disputed that MOND also required tuning to match some results, so clearly neither theory is adequate to explain all of our observations in their current forms. At the very least we should be able to agree on that.
Other specific points:
TeVeS is one relativistic generalization of MOND, but hardly the only one possible is it? How much attention has been paid to MOND and relativistic generalizations when compared to tweaking DM theories to match results, would you say? Wouldn't you agree that all of the attention to DM, and the dogma that DM must simply exist [1], detracts from exploring other possible avenues, like questioning assumptions that underlie our theories, as in [2]?
On a final point on tone, I have no idea what you mean by me being enjoying being rude. I haven't said a single rude thing that I can see, I've only disagreed with some interpretations of the data and claimed that DM enjoys an undeserved status as preferred model, and that MOND deserves more attention, all positions with ample evidence.
You're right I've been too loose with how I've been using the term "fine-tuning". Adding a parameter is not fine-tuning so much as just tuning.
The point I was trying to make is that both adding parameters to a theory to fit observations that it didn't predict, and fine-tuning it's parameters to fit should count against its plausibility, since they're both forms of tweaking the theory to match observations after the fact rather than making accurate predictions that follow naturally from the model being proposed.