Picturing Quantum Mechanics

They say a picture is worth a thousand words. But what if those words are wrong?

Very cool recent experiments demonstrated a chemical reaction between molecules below a millionth of a degree (in Science, subscription required). My latest story for Physical Review Focus describes theoretical modeling of this reaction. We accompanied the story with this picture from the news release issued by the Joint Quantum Institute (a partnership between the National Institute of Standards and Technology and the University of Maryland), where the work was done.

It's a pretty picture, with its superhero color scheme and all, and it satisfies our need to avoid a solid block of text. But although it might not be a bad illustration of a room-temperature chemical reaction, it distorts much of what makes these ultra-low-temperature reactions special.

It's clear in the picture that two diatomic molecules are approaching each other, with dramatic consequences in store. The details of how the artist represents the bonds connecting a potassium and a rubidium atom in each molecule don't bother me too much. It doesn't match either of the customary representations, which are ball-and-stick models and the more accurate space-filling models, but there's no perfect way to represent something that can never be seen with visible light. Of course everyone knows that potassium atoms are green, but we'll let that slide, too.

The really problematic part of this picture is very difficult to avoid: the molecules really aren't anywhere, in the sense the picture conveys.

As first shown by experiments at Bell Labs in 1927, matter acts as waves as well as particles. At temperatures below a millionth of a degree, the relevant wavelength for these molecules is hundreds of nanometers, which is much, much larger than the separation of molecules shown in the experiment. There is no meaning to saying that these molecules are separated by such a short distance. They are simultaneously close and far away.

One way to think about this is to invoke Heisenberg's uncertainty principle. According to this principle, if you know an object's momentum with very high precision, you can't, even in principle, know its position very accurately. For these ultracold molecules, the momentum is almost zero, with very high precision, so you can only know where it is to the nearest hundreds of nanometers.

There's a second problem, too. The picture shows the molecules with particular orientations in space. That may not seem strange, but the molecules in the experiment were prepared in the rotational "ground state," with the lowest possible energy. Like the s-orbitals of electrons in a hydrogen atom, this state is spherically symmetrical. This means that the molecule is equally likely to be pointing in any direction. This isn't the same thing as saying we don't know what direction it's pointing (even though it does). Quantum mechanics says that it has no direction, at least until an experiment requires it to.

So the reacting molecules really aren't at any particular distance from one another, and they don't have any particular orientation relative to each other. That's one of the things that makes this chemical reaction--and the theoretical description of it--so interesting.

But good luck drawing that.