I'm reading this article (the link is to the PDF file), and I got stuck on a detail right away. There's a clock at A and a mirror at B. We want to measure the distance L between A and B by measuring the time it takes a light signal to travel from A to B and back. The mass of the clock is m. Its position is represented by a wave function spread out over an interval of length dL. (Pretend that space is one-dimensional). The article claims that in the time that it takes a photon to travel from A to B and back, the clock's wave function will have spread out further, so that the width is now dL+(hbar*L)/(mc*dL). Appareantly this is something that Wigner proved in 1957. I don't see how to obtain this result. Am I missing something simple? I assume that we can take the wave function to have a gaussian shape (exp(-ax^2)), but how do we find how much the width has increased in a certain time? I suppose we should have a time evolution operator exp(-iHt) act on this wave function, but I don't see a way to simplify the result. I'm hoping it's just because I haven't been doing this sort of thing in a while.