Everyone is scientific circles is abuzz with the big news: there’s proof that dark matter exists! The paper from the scientists who made the discovered is [here][dark-matter-paper]; and a Sean Carroll (no relation) has [a very good explanation on his blog, Cosmic Variance][cv]. This discovery happens to work as a great example of just why good science needs good math.
As I always say, one of the ways to recognize a crackpot theory in physics is by the lack of math. For an example, you can look at the [electric universe][electric] folks. They have a theory, and they make predictions: but because there’s *no* math, the predictions are vague, and there’s no good way of *really* testing them, because there’s no quantifiable way of making a precise prediction – because there’s no math. So they can make predictions like “the stardust experiment will get bigger particles than they expect”; but they can’t tell you *how* big.
The dark matter result is a beautiful example of how to use good math in science.
Here’s the basic idea. The theory says that there are two kinds of matter: “dark” matter, and “light” matter. Dark matter only interacts with light matter via gravity; it does not interact with light matter via other forces. But dark matter and light matter generally clump in the same places – because gravity pulls them together. So it’s very difficult to really prove that dark matter exists – because you can’t see it directly, and it normally only appears with light matter, so you can’t really prove that the dark matter is there: any observed effect *might* be caused by the light matter behaving in a way different than our current theories claim it should.
But what if you could somehow sweep the light matter away?
What the scientists who did this work found is a collision of two galactic clusters. When these clusters collided, the light matter, mostly in the form of gas, interacted very strongly with one another, creating a shock wave pattern. But the *dark* matter passed through without interacting – the “collision” between the gas clouds didn’t affect the dark matter. So the gas clouds were swept back, while the dark matter continued moving. There’s a great animation illustrating this; in the animation, the blue is the dark matter; the red is the light matter. As the two clusters pass through each other, the light matter is swept away by the electromagnetic interactions between the gas clouds; the dark matter passes right through:
Here’s where the math comes in.
They used a combination of optical and X-ray telescope to produce maps of the gravitational fields of the clusters. This was done by computing the gravitational lensing effect distorting the images of other, more distant galaxies visible *behind* the collided clusters. By carefully computing the distortion caused by gravitational lensing, they were able to determine the distribution of *mass* in the collided clusters. And what they found was the bulk of the mass was *not* in the light matter. It was in the places that the center of gravities of the clusters would have been *without* the shock-wave effects of the collision. So the bulk of the mass of these two clusters do not appear on our telescope images; but it behaves exactly as the math predicts it would if it were dark matter.
The prediction and the result are both based on very careful computations based on the *mathematical* predictions of gravity and relativity. They were able to predict precisely what they would expect from the interaction using a mathematical model of the how the gas clouds would interact to be swept away; and how the dark matter would interact gravitationally to predict where the dark matter masses should be. Then they were able, via a *separate* computation to determine how much mass was in what location based on gravitational lensing. And finally, they were able to compare the two *separately computed* results to see if the reality matched the prediction.
Now *that* is both good math and good science! And the science could *not* have been done without the math.