So here’s an interesting sequence of events. On Tuesday in the QFT class I finished the lecture on Renormalization Group Flow, and the idea of a “beta function”, unpacking the results we’d accumulated from QED and quartic scalar field theory to use as illustration. The key result, for those of you about to scroll away (or the few of you who have not, but are hovering over the scroll bar), is as follows. Never mind what a beta function is right now. The issue at hand concerns whether it is positive or negative for a force of interaction being studied. A positive beta function tells you that the strength of the interaction between constituent things (particles, etc) gets weaker as you work at lower energies… This is an important result in understanding how Nature behaves in a variety of situations… one way of seeing variety is to look at different energy scales, and sometimes what seems familiar takes on different character. The converse is true… that positive beta function tells you that the interaction gets stronger at higher energies… Energy is also rather like the inverse of distance scale too, so high energy is akin to shorter distance scales (higher resolution), and low energy like longer distance scales (grainier resolution). In other words, looking at stuff in really tiny detail means using higher energy… and the nature of that stuff can change when you look at that sort of resolution since the way things interact changes… For electromagnetism, for example, we see that it gets stronger the closer we look, digging more deeply into the structure of the atom, say, probing the charged constituents of the nucleus once we’ve understood electrons. The result is that you see the electromagnetic interaction changes, ultimately turning into something else… (it merges with one of the nuclear forces, in fact…but that’s a story for another day)
So anyway one of the things I ended the class with was the idea that if you had a negative beta […] Click to continue reading this post →
Well, it’s a time-consuming process (continuing the new work on The Project mentioned in a recent post), especially when you put in more detail than really needed on what is supposed to be a rough layout. Sigh… Anyway, I’m several pages along in layouts for a story I wrote a while back, and I’m flipping ahead from time to time and wondering how long this beast is going to end up being! In any case, it’s a fun topic (or topics) being explored in this one. I’m wondering if I should try to find a way of splitting it into two stories or perhaps […] Click to continue reading this post 