Sunday, June 7, 2009

Thermal equilibrium

Last week was graduation at Yale, and a few of my closest friends here were getting their degrees. As such, some celebrating ensued. One of my friends is now doing post-doctoral work at UCLA, while another is working for a financial firm outside of New York. One night we spent some time in the early morning hours discussing the economy and the stock market. In that discussion, I came up with a somewhat stilted metaphor that I'm now going to invert to describe the concept of thermal equilibrium, which is where I want to begin the series on the CMB. In physics, temperature plays a similar role to that of money (or liquidity) in the markets.

First, I'm going to define "ionization" by referring briefly to the Bohr model I described here. Ionization is the process by which an atom loses (or gains) an electron and becomes charged. In the old post, I compared an atom to a building with an elevator which could transfer people (or electrons) between discrete levels. Using that image, ionization would occur if the elevator dropped you off on the roof, at which point you could leave the building entirely. As long as you were within the building, you remained trapped, just as an electron remains trapped by the electric field of the protons at the center of the atom (or as the Earth is trapped by the gravitational field of the Sun). On the roof, however, you have gained enough energy that you can leave the building; if an electron gains enough energy, it can escape from the electric field and be free, leaving the atom positively charged. This positively (or negatively, if it picks up an electron) charged nucleus is referred to as an ion.

One more thing that we should keep in mind about charged particles is that they interact rather strongly with light (or photons, as faithful readers will remember that light is a particle called a photon). A photon traveling through a cloud of charged particles will scatter many times, so that the photon that appears on the other side of the cloud will have very little to do with the one that entered it.

I'll now switch gears completely to describe the relationship between temperature and money. Suppose my mother in her younger days was living in a rather small apartment in London. My mom is a rather accomplished amateur interior decorator, and we'll assume she had those skills in her flat in London. I'm going to go one step further and ascribe a fickle nature to my mother which I would like to emphasize for posterity that she does not in actuality possess; in my hypothetical situation, this invented nature of hers combined with her penchant for interior design led her to continually change her mind on how she wanted to decorate her small house.

Ok, now we'll add money. If my mom had a lot of money, she could indulge her ever-changing whims. One week she could go for ultra modern and the next for antiques. Basically, the furniture would be coming and going, styles would be in and out, her little flat would be in a constant state of flux. Suppose, however, that she suddenly lost all her money; my mother would be forced to pick the cheapest option with which to decorate her house and stick with it. While she may still desire a change, she would have to settle for the most practical option.

In the physics of chemical reactions, temperature is like money. If my mom has money, she can change her flat at will - she can bring in new stuff, get rid of the old stuff easily whenever she wants. If the temperature is very high, a chemical reaction can occur easily and can go in both directions. Specifically for the purposes of the CMB, at high temperatures atoms can easily lose electrons and become ionized, before quickly finding other electrons freed from other atoms to become neutral again. In the early universe, the temperature was very hot and this was happening all the time; the universe was a soup of charged particles and photons bouncing off each other constantly. In particular, the photons never went very far before hitting another charged particle.

However, when my mom no longer had any money, she was forced to pick the cheapest option and stick with it. Similarly, after the big bang the universe began expanding and cooling. As the temperature dropped, it was no longer so easy to ionize atoms. Eventually, the universe cooled enough that it dropped out of thermal equilibrium. That meant that all the atoms had to neutralize, because a neutral atom requires less energy than an ionized atom and free electron, and nature prefers to minimize the amount of energy in any system (just as my mom had to settle for the cheapest decor). Once the atoms were all neutral, any photons that were bouncing around no longer had to travel through a soup of charged particles. In effect, the photons that were produced just as the universe become neutral did not scatter again. These photons are still traveling through the universe and we can detect them now; they are the CMB. They still contain information from the last time they interacted with matter, which was 13 billion years ago, right when the universe became neutral.


  1. I like your analogies, because of course they are much easier to understand than the real thing, which may be dangerous. I see that physics has its own language that non-physicists have to learn like French, say. A new word each post - eg Ions. One question: why did the universe cool?

  2. Mom, I like your questions. The Universe cools because space is expanding. This is not the same way that a pie cools on the window sill because the universe does not transfer heat to a cool breeze. Instead, scientists associate a temperature to light by the blackbody equivalence. A blackbody, usually depicted as a light-tight box with a small hole to receive light, radiates light in proportion to its temperature. The hotter it is the more and higher frequency light that is emitted. Like a blackbody the frequency and abundance of the CMB is associated with a temperature. However, space expansion has the effect of elongating lightwaves through the doppler effect. This effectively 'cools' the universe.

  3. So is dark matter required to conserve energy in the "cooling"? It seems like everything would have lower energy as space expands. Also, how is entropy increasing if the particles have "fewer options"?

    Great blog

  4. Dear Logan,
    You raise a good point about energy conservation as the universe expands. Before the discovery of "dark energy," which I've more or less glossed over in these posts, you would have been right. The energy density of the universe would decrease as the universe expands (although that's not the same thing as not conserving energy, as the total amount of energy would be constant). Dark energy, however, is even more mysterious, because it appears that vacuum or empty space actually has some energy density associated with it. Of course, I think we have even less knowledge about dark energy.

    Regarding entropy, to be honest, I haven't thought about it. My instinct is that as the universe expands, the particles actually have more options regarding spatial distributions, but of course the temperature is lower. Therefore, the entropy remains roughly constant with the evolution of the universe. If I find out differently, I'll post about it.

  5. I think that heating are not working because each day we get so cold more than some years ago in a few years probably we will be living in an Iceberg.