Dark matter remains undetected in the laboratory. This has been true for forever, so I don’t know what drives the timing of the recent spate of articles encouraging us to keep the faith, that dark matter is still a better idea than anything else. This depends on how we define “better.”
There is a long-standing debate in the philosophy of science about the relative merits of accommodation and prediction. A scientific theory should have predictive power. It should also explain all the relevant data. To do the latter almost inevitably requires some flexibility in order to accommodate things that didn’t turn out exactly as predicted. What is the right mix? Do we lean more towards prediction, or accommodation? The answer to that defines “better” in this context.
One of the recent articles is titled “The dark matter hypothesis isn’t perfect, but the alternatives are worse” by Paul Sutter. This perfectly encapsulates the choice one has to make in what is unavoidably a value judgement. Is it better to accommodate, or to predict (see the Spergel Principle)? Dr. Sutter comes down on the side of accommodation. He notes a couple of failed predictions of dark matter, but mentions no specific predictions of MOND (successful or not) while concluding that dark matter is better because it explains more.
One important principle in science is objectivity. We should be even-handed in the evaluation of evidence for and against a theory. In practice, that is very difficult. As I’ve written before, it made me angry when the predictions of MOND came true in my data for low surface brightness galaxies. I wanted dark matter to be right. I felt sure that it had to be. So why did this stupid MOND theory have any of its predictions come true?
One way to check your objectivity is to look at it from both sides. If I put on a dark matter hat, then I largely agree with what Dr. Sutter says. To quote one example:
The dark matter hypothesis isn’t perfect. But then again, no scientific hypothesis is. When evaluating competing hypotheses, scientists can’t just go with their guts, or pick one that sounds cooler or seems simpler. We have to follow the evidence, wherever it leads. In almost 50 years, nobody has come up with a MOND-like theory that can explain the wealth of data we have about the universe. That doesn’t make MOND wrong, but it does make it a far weaker alternative to dark matter.Paul Sutter
OK, so now let’s put on a MOND hat. Can I make the same statement?
The MOND hypothesis isn’t perfect. But then again, no scientific hypothesis is. When evaluating competing hypotheses, scientists can’t just go with their guts, or pick one that sounds cooler or seems simpler. We have to follow the evidence, wherever it leads. In almost 50 years, nobody has detected dark matter, nor come up with a dark matter-based theory with the predictive power of MOND. That doesn’t make dark matter wrong, but it does make it a far weaker alternative to MOND.
So, which of these statements is true? Well, both of them. How do we weigh the various lines of evidence? Is it more important to explain a large variety of the data, or to be able to predict some of it? This is one of the great challenges when comparing dark matter and MOND. They are incommensurate: the set of relevant data is not the same for both. MOND makes no pretense to provide a theory of cosmology, so it doesn’t even attempt to explain much of the data so beloved by cosmologists. Dark matter explains everything, but, broadly defined, it is not a theory so much as an inference – assuming gravitational dynamics are inviolate, we need more mass than meets the eye. It’s a classic case of comparing apples and oranges.
While dark matter is a vague concept in general, one can build specific theories of dark matter that are predictive. Simulations with generic cold dark matter particles predict cuspy dark matter halos. Galaxies are thought to reside in these halos, which dominate their dynamics. This overlaps with the predictions of MOND, which follow from the observed distribution of normal matter. So, do galaxies look like tracer particles orbiting in cuspy halos? Or do their dynamics follow from the observed distribution of light via Milgrom’s strange formula? The relevant subset of the data very clearly indicate the latter. When head-to-head comparisons like this can be made, the a priori predictions of MOND win, hands down, over and over again. [If this statement sounds wrong, try reading the relevant scientific literature. Being an expert on dark matter does not automatically make one an expert on MOND. To be qualified to comment, one should know what predictive successes MOND has had. People who say variations of “MOND only fits rotation curves” are proudly proclaiming that they lack this knowledge.]
It boils down to this: if you want to explain extragalactic phenomena, use dark matter. If you want to make a prediction – in advance! – that will come true, use MOND.
A lot of the debate comes down to claims that anything MOND can do, dark matter can do better. Or at least as well. Or, if not as well, good enough. This is why conventionalists are always harping about feedback: it is the deus ex machina they invoke in any situation where they need to explain why their prediction failed. This does nothing to explain why MOND succeeded where they failed.
This post-hoc reasoning is profoundly unsatisfactory. Dark matter, being invisible, allows us lots of freedom to cook up an explanation for pretty much anything. My long-standing concern for the dark matter paradigm is not the failure of any particular prediction, but that, like epicycles, it has too much explanatory power. We could use it to explain pretty much anything. Rotation curves flat when they should be falling? Add some dark matter. No such need? No dark matter. Rising rotation curves? Sure, we could explain that too: add more dark matter. Only we don’t, because that situation doesn’t arise in nature. But we could if we had to. (See, e.g., Fig. 6 of de Blok & McGaugh 1998.)
There is no requirement in dark matter that rotation curves be as flat as they are. If we start from the prior knowledge that they are, then of course that’s what we get. If instead we independently try to build models of galactic disks in dark matter halos, very few of them wind up with realistic looking rotation curves. This shouldn’t be surprising: there are, in principle, an uncountably infinite number of combinations of galaxies and dark matter halos. Even if we impose some sensible restrictions (e.g., scaling the mass of one component with that of the other), we still don’t get it right. That’s one reason that we have to add feedback, which suffices according to some, and not according to others.
In contrast, the predictions of MOND are unique. The kinematics of an object follow from its observed mass distribution. The two are tied together by the hypothesized force law. There is a one-to-one relation between what you see and what you get.
This was not expected in dark matter. It makes no sense that this should be so. The baryonic tail should not wag the dark matter dog.
From the perspective of building dark matter models, it’s like the proverbial needle in the haystack: the haystack is the volume of possible baryonic disk plus dark matter halo combinations; the one that “looks like” MOND is the needle. Somehow nature plucks the MOND-like needle out of the dark matter haystack every time it makes a galaxy.
Dr. Sutter says that we shouldn’t go with our gut. That’s exactly what I wanted to do, long ago, to maintain my preference for dark matter. I’d love to do that now so that I could stop having this argument with otherwise reasonable people.
Instead of going with my gut, I’m making a probabilistic statement. In Bayesian terms, the odds of observing MONDian behavior given the prior that we live in a universe made of dark matter are practically zero. In MOND, observing MONDian behavior is the only thing that can happen. That’s what we observe in galaxies, over and over again. Any information criterion shows a strong quantitative preference for MOND when dynamical evidence is considered. That does not happen when cosmological data are considered because MOND makes no prediction there. Concluding that dark matter is better overlooks the practical impossibility that MOND-like phenomenolgy is observed at all. Of course, once one knows this is what the data show, it seems a lot more likely, and I can see that effect in the literature over the long arc of scientific history. This is why, to me, predictive power is more important than accommodation: what we predict before we know the answer is more important than whatever we make up once the answer is known.
The successes of MOND are sometimes minimized by lumping all galaxies into a single category. That’s not correct. Every galaxy has a unique mass distribution; each one is an independent test. The data for galaxies extend over a large dynamic range, from dwarfs to giants, from low to high surface brightness, from gas to star dominated cases. Dismissing this by saying “MOND only explains rotation curves” is like dismissing Newton for only explaining planets – as if every planet, moon, comet, and asteroid aren’t independent tests of Newton’s inverse square law.
MOND does explain more that rotation curves. That was the first thing I checked. I spent several years looking at all of the data, and have reviewed the situation many times since. What I found surprising is how much MOND explains, if you let it. More disturbing was how often I came across claims in the literature that MOND was falsified by X only to try the analysis myself and find that, no, if you bother to do it right, that’s pretty much just what it predicts. Not in every case, of course – no hypothesis is perfect – but I stopped bothering after several hundred cases. Literally hundreds. I can’t keep up with every new claim, and it isn’t my job to do so. My experience has been that as the data improve, so too does its agreement with MOND.
Dr. Sutter’s article goes farther, repeating a common misconception that “the tweaking of gravity under MOND is explicitly designed to explain the motions of stars within galaxies.” This is an overstatement so strong as to be factually wrong. MOND was explicitly designed to produce flat rotation curves – as was dark matter. However, there is a lot more to it than that. Once we write down the force law, we’re stuck with it. It has lots of other unavoidable consequences that lead to genuine predictions. Milgrom explicitly laid out what these consequences would be, and basically all of them have subsequently been observed. I include a partial table in my last review; it only ends where it does because I had to stop somewhere. These were genuine, successful, a priori predictions – the gold standard in science. Some of them can be explained with dark matter, but many cannot: they make no sense, and dark matter can only accommodate them thanks to its epic flexibility.
Dr. Sutter makes a number of other interesting points. He says we shouldn’t “pick [a hypothesis] that sounds cooler or seems simpler.” I’m not sure which seems cooler here – a universe pervaded by a mysterious invisible mass that we can’t [yet] detect in the laboratory but nevertheless controls most of what goes on out there seems pretty cool to me. That there might also be some fundamental aspect of the basic theory of gravitational dynamics that we’re missing also seems like a pretty cool possibility. Those are purely value judgments.
Simplicity, however, is a scientific value known as Occam’s razor. The simpler of competing theories is to be preferred. That’s clearly MOND: we make one adjustment to the force law, and that’s it. What we lack is a widely accepted, more general theory that encapsulates both MOND and General Relativity.
In dark matter, we multiply entities unnecessarily – there is extra mass composed of unknown particles that have no place in the Standard Model of particle physics (which is quite full up) so we have to imagine physics beyond the standard model and perhaps an entire dark sector because why just one particle when 85% of the mass is dark? and there could also be dark photons to exchange forces that are only active in the dark sector as well as entire hierarchies of dark particles that maybe have their own ecosystem of dark stars, dark planets, and maybe even dark people. We, being part of the “normal” matter, are just a minority constituent of this dark universe; a negligible bit of flotsam compared to the dark sector. Doesn’t it make sense to imagine that the dark sector has as rich and diverse a set of phenomena as the “normal” sector? Sure – if you don’t mind abandoning Occam’s razor. Note that I didn’t make any of this stuff up; everything I said in that breathless run-on sentence I’ve heard said by earnest scientists enthusiastic about how cool the dark sector could be. Bugger Occam.
There is also the matter of timescales. Dr. Sutter mentions that “In almost 50 years, nobody has come up with a MOND-like theory” that does all that we need it to do. That’s true, but for the typo. Next year (2023) will mark the 40th anniversary of Milgrom’s first publications on MOND, so it hasn’t been half a century yet. But I’ve heard recurring complaints to this effect before, that finding the deeper theory is taking too long. Let’s examine that, shall we?
First, remember some history. When Newton introduced his inverse square law of universal gravity, it was promptly criticized as a form of magical thinking: How, Sir, can you have action at a distance? The conception at the time was that you had to be in physical contact with an object to exert a force on it. For the sun to exert a force on the earth, or the earth on the moon, seemed outright magical. Leibnitz famously accused Newton of introducing ‘occult’ forces. As a consequence, Newton was careful to preface his description of universal gravity as everything happening as if the force was his famous inverse square law. The “as if” is doing a lot of work here, basically saying, in modern parlance “OK, I don’t get how this is possible, I know it seems really weird, but that’s what it looks like.” I say the same about MOND: galaxies behave as if MOND is the effective force law. The question is why.
As near as I can tell from reading the history around this, and I don’t know how clear this is, but it looks like it took about 20 years for Newton to realize that there was a good geometric reason for the inverse square law. We expect our freshman physics students to see that immediately. Obviously Newton was smarter than the average freshman, so why’d it take so long? Was he, perhaps, preoccupied with the legitimate-seeming criticisms of action at a distance? It is hard to see past a fundamental stumbling block like that, and I wonder if the situation now is analogous. Perhaps we are missing something now that will seems obvious in retrospect, distracted by criticisms that will seem absurd in the future.
Many famous scientists built on the dynamics introduced by Newton. The Poisson equation isn’t named the Newton equation because Newton didn’t come up with it even though it is fundamental to Newtonian dynamics. Same for the Lagrangian. And the classical Hamiltonian. These developments came many decades after Newton himself, and required the efforts of many brilliant scientists integrated over a lot of time. By that standard, forty years seems pretty short: one doesn’t arrive at a theory of everything overnight.
What is the right measure? The integrated effort of the scientific community is more relevant than absolute time. Over the past forty years, I’ve seen a lot of push back against even considering MOND as a legitimate theory. Don’t talk about that! This isn’t exactly encouraging, so not many people have worked on it. I can count on my fingers the number of people who have made important contributions to the theoretical development of MOND. (I am not one of them. I am an observer following the evidence, wherever it leads, even against my gut feeling and to the manifest detriment of my career.) It is hard to make progress without a critical mass of people working on a problem.
Of course, people have been looking for dark matter for those same 40 years. More, really – if you want to go back to Oort and Zwicky, it has been 90 years. But for the first half century of dark matter, no one was looking hard for it – it took that long to gel as a serious problem. These things take time.
Nevertheless, for several decades now there has been an enormous amount of effort put into all aspects of the search for dark matter: experimental, observational, and theoretical. There is and has been a critical mass of people working on it for a long time. There have been thousands of talented scientists who have contributed to direct detection experiments in dozens of vast underground laboratories, who have combed through data from X-ray and gamma-ray observatories looking for the telltale signs of dark matter decay or annihilation, who have checked for the direct production of dark matter particles in the LHC; even theorists who continue to hypothesize what the heck the dark matter could be and how we might go about detecting it. This research has been well funded, with billions of dollars having been spent in the quest for dark matter. And what do we have to show for it?
Zero. Nada. Zilch. Squat. A whole lot of nothing.
This is equal to the amount of funding that goes to support research on MOND. There is no faster way to get a grant proposal rejected than to say nice things about MOND. So one the one hand, we have a small number of people working on the proverbial shoestring, while on the other, we have a huge community that has poured vast resources into the attempt to detect dark matter. If we really believe it is taking too long, perhaps we should try funding MOND as generously as we do dark matter.