## Wednesday, August 26, 2009

### Gravitational potential wells (final)

In the last post, I compared the early universe to a mattress with a number of bowling balls on it, creating divots for matter to fall in and out of. I have to admit that it isn't the best analogy; the behavior I'm trying to describe is relatively universal, however. Imagine a really great vacation spot - initially, people will be attracted to this spot. As more and more people visit it, the pressure of all those people mean that it's no longer an attractive location and they stop coming. Also not a good analogy.

In the end, the point is that local density fluctuations created sources of oscillation. Matter was attracted to regions of high density and fell into the well, before photon pressure became too great and pushed it back out. The final piece of information we need before we can finish this particular section is that regions of high density are hotter than regions of low density. And as we already know, the temperature or energy of a photon is related to its wavelength. Therefore, a photon coming from a region of high density is "hotter" or has a higher frequency than a photon coming from a region of low density. This is how the CMB tells us about the early universe. By looking at the temperature fluctuations of the CMB, we can understand the density fluctuations in the early universe.

To once again plagiarize Wayne Hu's website, he has an expanded version of the movie in the previous post. Here, there are two potential wells with a hill in the middle. When the balls are at the bottom of the well, the temperature is hotter and photons departing at that time are correspondingly hotter. When the balls are not in the well, things are colder and the photons reflect it accordingly (I believe in this movie, hotter is represented by blue and colder by red, since blue light has more energy than red light). By detecting these photons we now know about how uniform the early universe was and we can make conclusions about the distribution of matter and energy. In the next post, I'll start talking about how we decode these photons using Fourier analysis.

## Saturday, August 8, 2009

### Gravitational potential wells (part 2)

In the last post I described gravity as the curvature of space, creating little wells for other masses to fall into. This is the image we want to think about as we imagine the early universe. At that time, the structure we see in the universe today hadn't formed yet - there were no planets, galaxies or clusters of galaxies. Instead, there were small perturbations, small potential wells that contained the seeds of future galaxies. Returning to the image of a bowling ball on a mattress, we can imagine a giant mattress with many small little bowling balls on it. These bowling balls were placed at random, simply because nothing is perfectly smooth. In addition to the bowling balls, there are countless smaller marbles moving at random across the surface of the mattress. None of the bowling balls was very large, but they did create small little divots for the little marbles to fall into or orbit around or bounce in and out.

This isn't the whole picture though. Over a month ago, I described the thermal equilibrium of the early universe, where everything was reacting with everything else, atoms were ionized and electrons were constantly interacting with photons. There was a lot of energy involved in those reactions. In particular, this energy was enough to keep the marbles from settling down in the divots. If too many marbles gathered in a particular place, the pressure caused by all the photons bouncing around tended to push the marbles apart. In this way, a situation very much like the pendulum on the spring was created. The marbles were attracted to the wells created by the bowling balls, but when they tried to reach the center, there was enough energy to push them back out. Once out, they were again attracted to the bottom of the well, and therefore we have an oscillation.

I've taken a nice illustration from University of Chicago Professor Wayne Hu's website. In this movie, the well is caused by the random gravitational fluctuations, or the bowling balls. The marbles are represented by the yellow balls, and the pressure caused by all the photons is represented by the springs, pushing the marbles apart when they get too close to the bottom of the well.

### Gravitational potential wells

I've changed my mind on how I want to proceed with the CMB. I had a post starting to talk about general relativity, but I've decided that it is too much for this particular sequence. I'd want to really talk about special relativity and general relativity to really do it justice, therefore I've decided to skip it for now. However, that still leaves us needing to understand just what is the information encoded in the Cosmic Microwave Background, so I'll try to do a slightly different description.

Imagine a pendulum - like this one!

The pendulum oscillates back and forth, and as it does so, it traces out a well. The pendulum wants to rest at the bottom of the well, but it has too much energy, and so it continuously overshoots the bottom. The well looks like the line drawn in the still picture to the right. In physics, something like this is known as a potential well - the force of gravity is pulling the weight downward, towards the bottom of the well, but because of the string, the pendulum just bobs up and down in the well.

There are a surprising number of situations like this, and most gravitational interactions can be described in terms of potential wells. For example, the motion of the Earth around the Sun is an orbit that follows the same path as a pendulum in two dimensions. The Earth wants to go straight to the center of the Sun, just like the ball wants to rest at the bottom of the well; instead, the Earth goes around the Sun forever, unable to reach the middle (thankfully).

General relativity is a theory of gravity. Why does gravity create these potential wells? The answer can be thought of in terms of curvature. Large masses tend to curve the space around them, so that other masses will fall in towards the large one. In this framework, one can imagine the Sun as a giant bowling ball on a very smooth mattress. The mattress dips because of the mass of the Sun, and so the space around the Sun curves. Now, one can imagine rolling a bunch of marbles around the divot left by the Sun; if there were no friction, those marbles could roll around the Sun forever in an orbit, just like the planets.

In this sense, then, mass will curve the space around it to attract other masses. But those masses won't necessarily just fall straight in (although that can happen), but can oscillate, much as the Earth oscillates around the Sun, or as the pendulum above keeps going back and forth.