Second Paper: "Unifying Microscopic and Continuum Treatments of van der Waals and Casimir Interactions"

My second paper has been published! It is in volume 118, issue 26 of Physical Review Letters, and an older preprint of it is available too for those who don't have access to academic journals (it has all of the same figures and ideas, though it is missing a few sentences of further explanation as well as a couple of new citations that were inserted for the final publication). As with my first paper, in the interest of explaining these ideas in a way that is easy to understand, I am using the ten hundred most used words in English (except for the two lines that came before this one), as put together from the XKCD Simple Writer. I will use numbers sometimes without completely writing them out, use words for certain names of things without explaining further, and explain less used words when they come up. Keep reading to see what comes next.

In the paper that came before this one, I looked at the force that lets geckos, which are small animals with hard skin over which your finger can slip easily, stick to any hard surface, no matter what the surface is made of. That force is called the van der Waals (called "vdW" for short) force. In that case, I was looking at hard surfaces with special shapes that are close to wet water-like surfaces, making the wet surfaces change shape because of the vdW force; I was able to consider both surfaces as if I didn't care so much about the smaller things that make up the larger things, and I only cared about the shapes of the surfaces. It turns out that while there are easy and hard ways to figure out what the vdW forces are, special hard surface shapes make the easy way give the wrong answer, where the hard way is made to give the right answer.

For this paper, the idea is sort of the same, but the stuff is a little different. I consider the vdW force on or between molecules, which are the little things that make up most of the stuff we see, and are in turn made of smaller things called atoms. The molecules I consider are pretty large, but the forces on or between them are changed when they are close to things that are so much bigger that we don't care as much about the smaller things that make them up. It turns out that for certain distances that are smaller than the sizes of the smallest living things but bigger than the sizes of atoms, it makes sense to consider the molecules, but not the larger things, as if they're made of small things, rather than doing both or none for both cases. So far, people have only considered either the vdW forces of large things on each other at pretty large distances, or the vdW forces of molecules alone on each other at very small distances. The other problem is that finding out what the vdW forces are in this case is still hard, so a lot of people have tried to use easier ways (like in the paper before) to figure out what the vdW forces are. In this paper, I show that a lot of cool new stuff comes out when figuring out what vdW forces are the hard way, and at small-but-not-too-small distances when molecules but not larger things can be considered to be made of smaller stuff like atoms; how fast light goes actually matters a lot, and a lot of these forces need more than two atoms to be considered at a time to get the right answer.