Infinity Coincidence

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 function, things would be very different… the interaction would get stronger with longer distances… so things would interact more strongly for wider separations, and so become weakly interacting at tiny distances. Odd indeed. They all dutifully ventured that this is what happens with quarks, and so I was happy they’d learned a bit of history (“asymptotic freedom”… a Nobel Prize not so long ago). I urged them to chase that story down and read up on it, and study the beta function computation for Quantum Chromodynamics (QCD), since it is a wonderful and interesting chapter in modern physics… illustrating a wonderful dialogue between puzzling experimental results (scattering that probed the structure of the nucleus), constructing of interesting theories just because it’s interesting (what we now call non-Abelian gauge theory), and painstaking computational searches for theories with the right sort of properties (a negative beta function) that would help explain the fact that at higher and higher energy it seemed that the nucleus was made of point particles that become more and more distinct (later identified as quarks and gluons…)

So I got back to my office and there was a large envelope in my mailbox. I opened it up and it was a book from a publisher. They’d sent me a copy of the new book by Frank Close entitled “The Infinity Puzzle”. Guess what it is about? The precise area of history and physics that I was talking about in class. Frank Close has gone and written a lovely book on the subject of the development of various modern ideas and theories and experiments in contemporary particle physics, with great chapters on subjects like renormalization, asymptotic freedom (and the famous stories involving t’Hooft, Gross, Coleman, Wilczek, Polizter, etc), symmetry breaking (with all of the authorship and naming issues surrounding the Higgs mechanism and the Higgs particle), and so on and so forth. What an excellent coincidence. I went for lunch, and then began to browse the book… by dinner time I’d finished it (it is an easy read if you know the physics and much of the history already since you’re then just lingering at the new stuff coming from interviews, new sources, and of course, Close’s very balanced and fair (I thought) treatments of some of the more disputed matters… and his set-the-record-straight quest to give more credit to several forgotten (or not mentioned enough) characters – also, I got long stretches of reading done on the bus and on the walk to and from it), and was very pleased with it overall.

Why do publishers send me these books? Well, no doubt because they hope I will mention it on this blog of course (some of them address the mail to this blog by name at times) and I don’t mind. I’ve no obligation to do so, and end up looking at only a fraction of those that are sent, so it is a lottery. It has little to do with how good a book is – I just don’t have an awful lot of time, and in any case am right now more interested in focusing my scarce available spare time concerning general science books to creating rather than consuming. But this book is a happy exception. There’s not enough good writing about that particular set of ideas (at the level that can be done by someone who has worked on the material and knows many of the people involved) and it also happened to be a topic I was recommending my students to look at… and so this caught my attention. So anyway, I recommend it to you if you’re looking for a book in the area for either yourself or to recommend to others.


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7 Responses to Infinity Coincidence

  1. Paul Clapham says:

    I dropped out of physics as an undergraduate when I found I was terrible at lab work; but I did go on to get a PhD in mathematics. So would you recommend that book as something I might read?

  2. Plato says:

    Have come across Prof. Matt Strassler’s explanations working from QFT perspective has been most helpful as well.


  3. Clifford says:

    Paul: Yes, of course.
    Plato: Matt’s a great person to learn from.


  4. Paul Clapham says:

    Thank you Clifford… my public library has it “On Order” and I’m now the first one on the hold list. Along with Brian Cox’s “Quantum Universe” and several other things which aren’t likely to show up until next year.

  5. Clifford says:




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