Good ideas, Bad ideas, MOND, and Dark Matter

> “There’s an old saying about those who forget history. I don’t remember it, but it’s good.” -Stephen Colbert

Let me start by telling you a story about an old problem. Take a look at the planet Mercury, one of the five planets (not counting Earth) visible in our night sky to the naked eye.

And I can see some of you at home squinting at your screen, asking why I’m showing you a picture of the Moon right after sunset. Well, Mercury’s in that picture, I promise. Let me make it a little easier for you.

No less a naked-eye astronomer than Copernicus had difficulty seeing the planet Mercury, and near most cities around the world it’s completely invisible. And surprisingly, light pollution isn’t the only reason.

Because of its extremely close proximity to the Sun, Mercury never appears more than 28 degrees away from it — what astronomers call elongation — in the sky.

Which means it’s only ever visible close to the horizon, either shortly after sunset or shortly before sunrise. But if you plot the position of Mercury very accurately over time, you start to find something very unusual.

Unlike Kepler’s Laws of Planetary Motion told us, Mercury doesn’t move in a perfect ellipse with the Sun at one focus! Instead, its ellipse shifts over time, a process called precession. Now, we knew of two things that caused precession: the Earth’s equinoxes precessing (which is why the pole star shifts with a period of 26,000 years) and the gravitational forces of the other planets.

But that didn’t explain all of it. So we had our theories of planetary motion and gravitation, and they didn’t line up completely with our observations. What were our options?

1.) Maybe there was a new planet! This idea — that an extra gravitational force from an unseen planet affects the orbit of a visible planet — is how we found Neptune, the planet outer to Uranus. Well, maybe we could find one interior to Mercury! It’s a nice idea, but this hypothetical planet, named Vulcan, simply isn’t there.

2.) Maybe Newton got that exponent slightly wrong. In Newton’s law of Universal Gravitation, the gravitational force is inversely proportional to the distance squared. In other words, if you’re twice as far away, the force is only one quarter, and if you’re 10 times as far away, the force is only one one-hundredth. It was suggested that instead of a “2” in the exponent, the number should actually be “2 plus a tiny bit,” which would explain Mercury’s motion.

3.) Gravity doesn’t work according to Newton’s Laws at all, but instead works by matter and energy bending spacetime. This was Einstein’s theory of General Relativity, and it totally accounted for the discrepancy between what was predicted and observed pretty much exactly!

So which of these ideas was the right one? Any one of them is reasonable, so what you have to do is test it.

And it won’t do you any good to test it for the thing it was designed to do, you need to test it doing something new.

So in 1919, they did. (You can read the detailed story here.) One of the more bizarre predictions of Einstein’s General Relativity was that near a strong gravitational source (like the Sun), mass would bend light! And not only was it predicted, but Einstein’s theory predicted the amount that light would bend, too!

So they organized an expedition to Brazil in 1919 to watch the Total Solar Eclipse, where they prepared to watch the stars during the day, when they appeared nearest to the Sun, and compare them to where they appear during the night!

(Image credit: American Physical Society.)

And sure enough, the shift in the stars’ apparent position matched Einstein’s theory, and no one else’s!

And since then, there have been a whole suite of disconnected, but very precise observations — gravitational lensing, the gravitational redshift of light, gravitational frame dragging, the Shapiro time delay, the decay of binary pulsar orbits, etc. — that confirm it. So we think we have the correct explanation for Mercury’s perihelion shift.

But we don’t think so because of how good General Relativity is for it; we think so because of all the other things it also successfully does.

So what do you do when you look up at galaxies and galaxy clusters — like Abell 1689 as imaged by Hubble — and find that the amount of mass you find in stars isn’t enough to explain the motions that you see, consistent with the laws of physics that you know?

Well, you’ve got two options again: you can either assume there’s more matter than you can detect, or you can change the laws of gravity. Not surprisingly, both camps have strong adherents.

Dark matter — the idea there’s a new type of matter than exerts a gravitational force — has been around since the 1930s. And it has given us a whole slew of cosmic successes, including the ability to predict how large scale structure forms and matter clumps together.

(Image credit: Virgo consortium.)

Dark matter also gives us a model for how galaxy clusters collide. Note below, the discrepancy between where the normal, gaseous matter is (in pink), and where the mass is (in blue). Without dark matter, this is virtually impossible to explain.

And perhaps in its greatest success, dark matter predicts the same patterns of fluctuations we observe in the Cosmic Microwave Background!

Take dark matter away, and we can reproduce none of these things. Want more details? Check out parts 1, 2, 3, 3.5, and 4 of my series on Dark Matter.

So what about the competitor: what about modifying gravity?

Back in 1983, some scientists looked at rotating galaxies like M81 — imaged by Hubble — above. And rather than trying to add dark matter to explain their rotation curves, they made a modification to Newton’s old law of gravity.

And it worked! You can, in fact, explain the rotation curves of most (but not all) types of galaxies by making that modification. This idea of Modified Newtonian Dynamics is known as MOND, and it works very well for explaining the rotation curves of individual galaxies. In fact, arguably, this is something MOND does even better than dark matter!

But then we come to the other stuff. (Sean Carroll has a great writeup of this, BTW.) And, particularly for the Microwave Background, MOND fails spectacularly. Let’s take a look at what we observe. Not showing the fluctuations in the sky, but the data points we get if we plot temperature fluctuations vs. angular size.

(Image shamelessly stolen from Sean.)

The data points are shown as x’s with error bars, the dotted line is Dark Matter’s predictions, and the solid line is MOND’s predictions. In this case, even the painstaking relativistic version cannot match Dark Matter’s accurate predictions. The third little peak at the end is the killer; it simply isn’t strong enough with MOND under any circumstances.

Which is why it kills me every time (and it happens about twice a year) a story like this comes out.

Are you kidding me?! This time Stacy McGaugh, who I’ve met twice now, is looking at low surface brightness galaxies and declaring that MOND works and dark matter doesn’t.

MOND WAS DESIGNED TO WORK FOR ROTATING GALAXIES! The problem is it doesn’t do anything else. And its adherents never point to anything other than rotating galaxies to support it.

I wrote about this, angrily, over a year ago, and it doesn’t seem to change. So maybe I need to be a little clearer.

If you want to be taken seriously as a theory, you need to do more than just the one thing you were designed to do. Otherwise, you’re in the “Vulcan” category.

All of this isn’t to say that MOND isn’t an interesting idea, or that the people working on it are frauds. But what’s being reported is grossly misleading at best, and blatantly dishonest at worst. General Relativity could still need fixing, and there could be something else going on with gravity beyond dark matter. But we still need dark matter — or something heretofore indistinguishable from it — to explain all our large-scale observations.

And definitively, however you slice it, whether there’s any validity to it or not, MOND certainly isn’t an alternative to dark matter. And everyone, even Stacy McGaugh, knows it.

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