Science

This is an easier one than dark matter vs. modified gravity. As mentioned, I’m going to be on Science Friday today, and they asked me to contribute a guest blog post, which I’m cross-posting below. Old news, I’m sure, for longtime CV readers, but here you go.

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Probably the biggest single misconception I come across in popular discussions of dark matter and dark energy is the accusation that these concepts are a return to the discredited idea of the aether. They are not — in fact, they are precisely the opposite.

Back in the later years of the 19th century, physicists had put together an incredibly successful synthesis of electricity and magnetism, topped by the work of James Clerk Maxwell. They had managed to show that these two apparently distinct phenomena were different manifestations of a single underlying “electromagnetism.” One of Maxwell’s personal triumphs was to show that this new theory implied the existence of waves traveling at the speed of light — indeed, these waves are light, not to mention radio waves and X-rays and the rest of the electromagnetic radiation spectrum.

The puzzle was that waves were supposed to represent oscillations in some underlying substance, like water waves on an ocean. If light was an electromagnetic wave, what was “waving”? The proposed answer was the aether, sometimes called the “luminiferous aether” to distinguish it from the classical element. This idea had a direct implication: that Maxwell’s description of electromagnetism would be appropriate as long as we were at rest with respect to the aether, but that its predictions (for the speed of light, for example) would change as we moved through the aether. The hunt was to find experimental evidence for this idea, but attempts came up short. The Michelson-Morley experiment, in particular, implied that the speed of light did not change as the Earth moved through space, in apparent contradiction with the aether idea.

So the aether was a theoretical idea that never found experimental support. In 1905 Einstein pointed out how to preserve the symmetries of Maxwell’s equations without referring to aether at all, in the special theory of relativity, and the idea was relegated to the trash bin of scientific history.

Aether was a concept introduced by physicists for theoretical reasons, which died because its experimental predictions were ruled out by observation. Dark matter and dark energy are the opposite: they are concepts that theoretical physicists never wanted, but which are forced on us by the observations.

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Okay, sticking to my desire to blog rather than just tweet (we’ll see how it goes): here’s a great post by John Baez with the forbidding title “Information Geometry, Part 11.” But if you can stomach a few equations, there’s a great idea being explicated, which connects evolutionary biology to entropy and information theory.

There are really two points. The first is a bit of technical background you can ignore if you like, and skip to the next paragraph. It’s the idea of “relative entropy” and its equivalent “information” formulation. Information can be thought of as “minus the entropy,” or even better “the maximum entropy possible minus the actual entropy.” If you know that a system is in a low-entropy state, it’s in one of just a few possible microstates, so you know a lot about it. If it’s high-entropy, there are many states that look that way, so you don’t have much information about it. (Aside to experts: I’m kind of shamelessly mixing Boltzmann entropy and Gibbs entropy, but in this case it’s okay, and if you’re an expert you understand this anyway.) John explains that the information (and therefore also the entropy) of some probability distribution is always relative to some other probability distribution, even if we often hide that fact by taking the fiducial probability to be uniform (… in some variable). The relative information between two distributions can be thought of as how much you don’t know about one distribution if you know the other one; the relative information between a distribution and itself is zero.

The second point has to do with the evolution of populations in biology (or in analogous fields where we study the evolution of populations), following some ideas of John Maynard Smith. Make the natural assumption that the rate of change of a population is proportional to the number of organisms in that population, where the “constant” of proportionality is a function of all the other populations. That is: imagine that every member of the population breeds at some rate that depends on circumstances. Then there is something called an evolutionarily stable state, one in which the relative populations (the fraction of the total number of organisms in each species) is constant. An equilibrium configuration, we might say.

Then the take-home synthesis is this: if you are not in an evolutionarily stable state, then as your population evolves, the relative information between the actual state and the stable one decreases with time. Since information is minus entropy, this is a Second-Law-like behavior. But the interpretation is that the population is “learning” more and more about the stable state, until it achieves that state and knows all there is to know!

Okay, you can see why tweeting is seductive. Without the 140-character limit, it’s hard to stop typing, even if I try to just link and give a very terse explanation. Hopefully I managed to get all the various increasing/decreasing pointing in the right direction…

Here’s a fun thing that has been zipping around the internets this week: a collection of “back of the envelope problems” put together by Edward Purcell. Hours of fun reading if you’re the kind of person who likes to spend their leisure time doing word problems (and I mean that in the best possible way).

One of Purcell’s problems is labeled “Electromagnetic energy in your eyeball,” and it concludes with a provocative (and true) observation. The problem asks the reader to calculate the total energy in all the photons that are inside your eyes at any one moment. Roughly speaking — which is the point, since we’re doing back-of-the-envelope problems — these photons come from one of two sources: the visible light from the outside world that enters your pupil, and the infrared light that is emitted as blackbody radiation from your eye itself, since you are an object at body temperature. Purcell suggests that you compare the amount of energy from each source.

And the answer is: there is much more electromagnetic energy in your eye at any one moment from the infrared radiation you’re emitting yourself, than the pittance of visible light you get from the outside world. Between 100,000 and a million times as much. Which raises a question we may never have thought to ask: why does it get dark when we close our eyes? The amount of electromagnetic radiation hitting our retinas hardly changes!

Purcell’s last sentence gives the answer: “Only quantum mechanics can explain why that makes it dark!”

We see light when photons of an appropriate wavelength reach the photoreceptor cells in the retinas of our eyes. The energy from the photon is converted into chemical energy via phototransduction, which sets an electrochemical signal to the visual cortex. (Presumably unnecessary disclaimer: everything I know about vision I learned from Wikipedia.) In particular, the photons are absorbed by a chemical called retinal, which isomerizes from the 11-cis state to the all-trans state. (That last bit was a blatant cut and paste.)

Here’s the part I do understand: isomerization is a matter of nudging a chemical from one structural form to another, without actually changing the chemical formula. Molecules have energy levels, just like electrons in atoms, and in order to effect the change in the retinal via photoexcitation, a photon has to have enough energy to cause a transition between the isomers. That’s a matter of quantum mechanics, full stop. Molecules can’t take on just any old energy; the allowed energies are quantized. As a result, it doesn’t matter that the infrared light inside your eyeball has much more energy than the visible light from the outside world; the energy comes in the form of individual photons, none of which has enough energy to get the reaction going. It’s very analogous to the photoelectric effect in metals, for which Einstein won his Nobel prize.

We often say that quantum mechanics applies to the world of the very small, and involves mind-bending alterations of our everyday reality. Which is true as far as it goes, but the more simple truth is that quantum mechanics applies to absolutely everything. It underlies how the everyday world works, from the stability of matter to the darkness when you close your eyes.

Last month we mentioned a paper on the arxiv that made a provocative claim: evidence from the dynamics of stars above the galactic disk indicates that there is essentially no dark matter in the vicinity of the Sun. I am not an expert on galactic dynamics, but nevertheless I and others were immediately skeptical, especially since there is overwhelming evidence for the existence of dark matter from other measurements. Skeptics, of course, happily piled on. But this isn’t an area where one opinion or the other matters very much — better data and better analysis is what matters.

Now we have a better analysis, from people who are experts: Jo Bovy and Scott Tremaine have a paper in which they examine the claim closely. They find it wanting. This was pointed out here in a comment by Ben; Jester and Peter Coles also have useful blog posts up about it.

Short version: the original authors made assumptions about the distribution of velocities of the stars they were looking at, and those assumptions are known to be wrong. Using a better model (i.e., one more compatible with known data), Bovy and Tremaine show that the observations are perfectly consistent with the conventionally-assumed dark matter density. The good news is that they are actually able to use this technique to get a more precise measurement of that density than was previously available. It’s a rare scientific lemon that can’t be turned into at least a little bit of lemonade.

I’m not sure why people get so emotional about dark matter. The original paper here by Bidin et al. was accompanied by a dramatic press release from the European Southern Observatory. I am known as a “dark matter supporter,” but I have no personal investment; I think it would be much cooler if something crazy were going on with gravity. But that’s not what the data indicate. It’s just some new particle we haven’t yet made in the lab, hardly the end of the world.