What I have heard about Bose-Einstein condensation makes it sound really weird. What is it really, and how did someone think of it?

In the early 1920s Satyendra Nath Bose was trying to understand why objects glowed different colors as they were heated, using the new idea at that time that the light came in little discrete packets (we now call these "quanta" or "photons"). Bose showed that he could explain the observed color changes if he assumed certain rules for deciding when two photons should be counted up as either identical or different.

You mean like deciding when you have one photon or two?

No, it is more like deciding when you can tell identical twins apart when you meet them. If they live together and wear exactly the same clothes and hair style, when you meet one, you can't really tell. But if they move farther apart, or start changing how they wear their hair, you can start to tell them apart. Essentially, Bose worked out rules for just how far apart and/or how different the colors of photons had to be before you could be pretty sure which one you were looking at. We now call these rules "Bose statistics" (or sometimes "Bose-Einstein statistics"), and objects that obey them we call "Bosons".

So where does Einstein come in?

Bose had trouble getting people to believe him and to publish his ideas in the scientific magazines of the day, so he sent them to Einstein. Einstein liked them, and he was a very important scientist at that time, so he used his influence to get them published.

So all he did was use his influence, and for that he got his name on it?

No, he actually did something very important on his own. Einstein guessed that these same rules Bose invented for photons might apply to atoms in a gas, instead of the rules people had been using. He worked out the theory for how atoms would behave in a gas if these new rules applied. What he found was that the equations said that generally there would not be much difference, except at very low temperatures, where something very unusual was supposed to happen. It was so strange he was not sure it was correct.

I thought Einstein was always right.

Not in this case. He was only sort of half correct, or maybe a little less. First, not all types of atoms actually follow the rules for Bose statistics. We now know that many types of atoms, as well as most other particles you have heard of, like electrons and protons, follow a different set of rules that we call Fermi statistics, after another famous physicist, Enrico Fermi. Particles that follow Fermi's rules, like electrons, can never be identical, so two can never be in exactly the same place with the same energy. However Einstein was partly right because some atoms are Bosons, and for those Einstein's predictions were right. But even for those kinds of atoms, he did not realize the most important effects that his equations were predicting.

If Einstein missed them, they must have been pretty hard to see. What were they and how did anyone figure them out?

The effects come from the fact that, at very low temperatures, most of the atoms are in the same quantum mechanical state. It took a lot of years for people to appreciate what that meant. The most important of the people who figured this out was Fritz London.

Uh, the same quantum mechanical state? What does that mean?

Remember how we talked about how electrons in an atom can only have certain energies which we called the quantum mechanical energy levels?

Vaguely I guess.

If you put an atom in any kind of container, even a mixing bowl, it also can only have certain particular energies. It can not roll around in there with just any speed it wants. It has to choose from a particular set of allowed energies. When the atoms are in the same energy level, we call that being in the same quantum mechanical state.

That does not make sense. I can put a ball bearing in a bowl and give it any speed I want. So where are your particular energies?

They are so close together in energy that you cannot see them. The bigger the bowl, the closer together are the energy levels. When an electron is in an atom it is like being in a very small bowl. In an atom the levels are very close together by everyday standards, but can be easily detected with scientific instruments. However, if the electron is held in a much bigger bowl, say the size of a thimble, the levels are so close together that even the most sensitive instruments cannot tell them apart.

So how do you know they are really there at all?

Actually, we couldn't be certain. It just seemed very likely because we had looked at all different sizes of small bowls such as different sized atoms and molecules, and they always showed quantized energy levels in just the ways predicted. It was only when Bose-Einstein condensation was made in a gas that we had direct evidence that there were only certain levels allowed even in fairly large containers.

How is that?

Well, what Einstein's equations predicted was that at any temperature attainable at the time the atoms would be distributed over many of the enormous number of closely spaced allowed energy levels, with two atoms almost never being in the same level. However, at very low temperatures, a large fraction of the atoms would suddenly go crashing down into the very lowest energy level, so it could have thousands, or even millions of atoms in the same level. The example below shows a model of atoms in a bowl with greatly magnified energy levels.

When I make the temperature low, they are all in the bottom. What does that mean?

The atoms piling up in the bottom is what we call Bose-Einstein condensation, and it happens because this demonstration is built to match Einstein's equations. "What it really means" is probably a question Einstein should have asked, but did not. He did not realize how weird a material would be with all the atoms in one level like this. It means that all the atoms are absolutely identical. There is no possible measurement that can tell them apart.

But I can just look and see the different black spots that represent different atoms. How can they be identical?

Good point. You have just picked out a mistake in this demonstration. Really, an atom in the lowest energy level is spread out a little, so it looks like a very small fuzzy ball. When you have lots of atoms in the same state, all these fuzzy balls lie exactly on top of each other.

Now I can't tell one atom from another; they are all in the same place. But I know that atoms don't really do that. I have tables, chairs, and all these other objects that have their shapes because their atoms are arranged in different places.

Now you can see why it was so long before people understood what BEC really meant. Atoms really can all be in the same place like this, but it goes against everything we see around us. You are of course right that at normal temperature atoms all occupy their own individual space. It is only at the special incredibly low temperatures needed for BEC that they lose their individual identities and coalesce into a single entity. Some people have called this a "super atom" for just that reason.

Wow, sort of an atomic identity crises when they get too cold. Are there any other weird things about BEC?

Actually there are a lot of them. When you have many atoms in a single quantum energy level they act very differently than the way objects in the world around us behave. Normally, quantum effects only occur in tiny hard-to-see things like individual atoms. However, BEC gives us a way to put a lot of atoms, enough to see by eye, in a single level, and then the quantum weirdness really jumps out at us. That is how a superconductor can suddenly lose all resistance to electricity flowing -- some of the electrons have all gone into a single level. In superfluid helium, some of the helium atoms are in the same level, and that is why it can flow through impossibly tiny holes, and uphill, and do all sorts of other strange things. There are similar strange behaviors for a BEC. For example, when it is released from a container it does not spread out the same in all directions like a normal gas. Instead it spreads out faster in certain directions and when two condensates overlap, they interfere, just like waves.