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.

It’s well known that all of our evidence for dark matter (and dark energy too, but that’s not the subject here) at the present time is indirect: it comes from observing the gravitational influence of the hypothetical stuff, not from detecting it “directly” (i.e., using some interaction other than gravitational). So it’s natural to ask whether we can do away with dark matter by positing some modification of the behavior of gravity; I’ve certainly wondered that myself.

And it may very well turn out that the behavior of gravity on large scales does not precisely match the prediction of ordinary general relativity. Nevertheless, I think that by now we’ve accumulated enough data to conclude that the universe cannot be explained solely by modifying gravity; there is ample evidence of gravitational forces pointing in directions where there isn’t any (ordinary) “stuff” to create them, leading us to accept the existence of some form of dark matter. About a year ago I put up a post that explained this point of view, and took aim in particular at the popular framework known as MOND.

This led to some good discussion in the comments, and also to a behind-the-scenes email exchange between Rainer Plaga, Stacy McGaugh, and me. It’s a bit of old news, but I thought there would still be some interest in our discussion, so (with permission) I’m posting our emails here. Seeing how the sausage is made, as it were. It’s a bit of a long read, sorry about that.

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