## Cosmology: The Professor’s Old Clothes

After spending  a big chunk of yesterday afternoon chatting the cosmic microwave background, yesterday evening I remembered a time when I was trying to explain some of the related concepts to an audience of undergraduate students. As a lecturer you find from time to time that various analogies come to mind that you think will help students understand the physical concepts underpinning what’s going on, and that you hope will complement the way they are developed in a more mathematical language. Sometimes these seem to work well during the lecture, but only afterwards do you find out they didn’t really serve their intended purpose. Sadly it also  sometimes turns out that they can also confuse rather than enlighten…

For instance, the two key ideas behind the production of the cosmic microwave background are recombination and the consequent decoupling of matter and radiation. In the early stages of the Big Bang there was a hot plasma consisting mainly of protons and electrons in an intense radiation field. Since it  was extremely hot back then  the plasma was more-or-less  fully ionized, which is to say that the equilibrium for the formation of neutral hydrogen atoms via

$p+e^{-} \rightarrow H+ \gamma$

lay firmly to the left hand side. The free electrons scatter radiation very efficiently via Compton  scattering

$\gamma +e^{-} \rightarrow \gamma + e^{-}$

thus establishing thermal equilibrium between the matter and the radiation field. In effect, the plasma is opaque so that the radiation field acquires an accurate black-body spectrum (as observed). As long as the rate of collisions between electrons and photons remains large the radiation temperature adjusts to that of the matter and equilibrium is preserved because matter and radiation are in good thermal contact.

Image credit: James N. Imamura of University of Oregon.

Eventually, however, the temperature falls to a point at which electrons begin to bind with protons to form hydrogen atoms. When this happens the efficiency of scattering falls dramatically and as a consequence the matter and radiation temperatures are no longer coupled together, i.e. decoupling occurs; collisions can longer keep everything in thermal equilibrium. The matter in the Universe then becomes transparent, and the radiation field propagates freely as a kind of relic of the time that it was last in thermal equilibrium. We see that radiation now, heavily redshifted, as the cosmic microwave background.

So far, so good, but I’ve always thought that everyday analogies are useful to explain physics like this so I thought of the following.

When people are young and energetic, they interact very extensively with everyone around them and that process allows them to keep in touch with all the latest trends in clothing, music, books, and so on. As you get older you don’t get about so much , and may even get married (which is just like recombination, not only that it involves the joining together of previously independent entities, but also in the sense that it dramatically  reduces their cross-section for interaction with the outside world).  As time goes on changing trends begin to pass you buy and eventually you become a relic, surrounded by records and books you acquired in the past when you were less introverted, and wearing clothes that went out of fashion years ago.

I’ve used this analogy in the past and students generally find it quite amusing even if it has modest explanatory value. I wasn’t best pleased, however, when a few years ago I set an examination question which asked the students to explain the processes of recombination and decoupling. One answer said

Decoupling explains the state of Prof. Coles’s clothes.

Anyhow, I’m sure there’s more than one reader out there who has had a similar experience with an analogy that wasn’t perhaps as instructive as hoped or which came back to bite you. Feel free to share through the comments box…

### 5 Responses to “Cosmology: The Professor’s Old Clothes”

1. Colin Rosenthal Says:

“and wearing clothes that went out of fashion years ago” and where their increasing shabbiness is analogous to the redshift?

2. I find that the expression ‘decoupling’ is quite confusing for students: they confuse the decoupling of matter and radiation with the coupling (really recombination) of matter, i.e. formation of atoms. It doesn’t help that we say recombination when we mean combination!

• telescoper Says:

Yes. Decoupling, however, is something that happens in a number of contexts in cosmology (e.g. neutrinos when weak interactions go out of equilibrium). Neither is a good word, however, and I wish we had better ones.

3. Some people criticize the balloon analogy for the expanding universe, pointing out that an expanding balloon has an outside surface. I think such people fail to grasp that an analogy is never perfect. When I say I spent the morning running around like a blue-arsed fly, I don’t mean that I resembled a fly in every respect

4. andyinkuwait Says:

Oh Yes. While teaching low ability Yr 11 I had to teach geostationary orbits to them. The nearest thing to hand was a metre rule which I put on my forehead and turned my entire body in an attempt to show them that the end of the rule always appeared in front of me, even though I was rotating.

Exam question ‘Explain the principles of geostationary orbits’. Answer ‘It is a big stick attached to the surface of the Earth’. Facepalm.
Won’t use that analogy in a hurry.