This is the final report on my modern physics class from last term, covering the last week of classes, which generally deal with nuclear and particle physics. This was actually three-and-a-bit classes, because I lost one class to a nasty cold a few weeks earlier, and used part of the lab period to make up for it.
Class 28 was actually taught by a colleague of mine (thanks, Rebecca!), because Kate and I were in Boston for her father's wake. She taught off my notes, though, so I'll still report it as if I did the class.
This class opens with a brief return of the historical treatment of the early weeks of the course, talking about Rutherford's discovery of the nucleus-- Marsden and Geiger, and "It was as amazing as if you fired a fifteen-inch shella t a piece of tissue paper and it came back and hit you." The book goes through the derivation of Rutherford scattering in great detail, but there's not much done with it after all that math, so I just state the results.
Rutherford scattering is used to introduce the idea of learning about subatomic structure by slamming things into other things, and then I talk about what we know of the structure of the nucleus. I talk about how there must be some very short-range force that acts between nuclei, in order to keep the nucleus from just flying apart into a billion pieces, and sketch the form of the potential.
I run through what can be inferred about the strong nuclear force from this, and then state that this comes about because the strong force really acts between quarks. I discuss color charge briefly, and make an analogy to the dipolar force between atoms that we talked about with molecules.
Class 29 picks up from there, and introduces all the Standard Model particles-- six quarks, six leptons, and the four fundamental interactions. I talk very briefly about all the botany that goes on with naming different particle types.
Then we move back up to nuclei, and talk about the stability of nuclei. I show a chart of the nuclides, and point out the two main features, namely that the number of protons and neutrons is roughly equal in light elements, but there are always more neutrons in heavy elements. This can be explained (following the Six Ideas model) by thinking of two sets of bound states in each nucleus, one for protons and another for neutrons, and filling those states according to Pauli exclusion.
For light elements, the proton and neutron states are at roughly the same energy, so the lowest energy configuration will have roughly equal numbers of the two. A large excess of one or the other produces a system whose energy can be lowered by converting protons to neutrons (or vice versa) through the weak force, so the nucleus will undergo beta decay until roughly equal numbers are obtained.
In heavy nuclei, with lots of protons, the repulsion between protons shifts their energy states up relative to the neutron states, meaning that equal numbers of protons and neutrons leads to many protons being above the energy of the last neutron state. This system can lower its energy by beta decay, leading to more neutrons than protons.
It's a nice, qualitative explanation of how nuclear stability works, that captures both of the main features in a very natural way. It's also one of the few things from this section that leads to homework and exam questions, as I'm free to make up absurd unstable isotopes, and ask students to explain why and how they decay.
Class 29a, part of the lab period, rounds out nuclear physics by explaining the statistical treatment of radioactive decay. I describe alpha, beta, and gamma emission, and then show how you get exponential decay from the assumption of a constant decay probability. This leads into half-lives and radioactive dating, and all that fun stuff.
Class 30 is basically Chapter 9 of the book-in-production, the Bunnies Made of Cheese chapter, framed as an explanation of the absurdly good precision of the g-factor of the electron. I talk about the exchange model of interactions, how energy-time uncertainty helps explain the range of forces, and draw a few Feynman diagrams. Then I talk about virtual particles, and the extra diagrams added by those. I explain that the theoretical calculation of the g-factor involves the summing of nearly 1000 Feynamn disgrams, up to something like eight virtual particles, and that it agree perfectly with experiment (to the point where the most recent experiments have stopped comparing to theoretical predictions, but use the experimental number and the theoretical coefficients to obtain a measurement of the fine-structure constant alpha.
It's entirely qualitative-- I don't tell them how to calculate anything from a Feynman diagram-- but it's great fun. This is consistently the class with the most questions, mostly of the form "Wait-- what? Are you kidding?" And I think it ties the whole thing together very nicely-- the agreement between QED and experiment is one of the real triumphs of modern physics, and a fitting end to the course.
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Neutron stars! Nuclear matter is amazingly stiff. Whether a dozen fermis or sixteen miles in diameter, the internal density sits around 10^15 g/cm^3. For all that, muonic heavy atoms have their muon's equilibrium orbit inside the nucleus. Fermions ignore the Strong Force.
Naked nucleus electron-capture decay is cute for being rendered stable, there being no electrons to capture. Nominal half-life is small percentage dependent upon oxidation state modulating s- and d-electron density at the nucleus. MeV processes are diddled by eV external interactions.
Sounds like a fun course. One day, I WILL finish my damn physics degree!
Sigh...
It's really interesting to read these. I'm always on the lookout for some more quantitative things I can do with my only-barely-algebra-literate "QM for Poets" course... and I think the uncertainty/force range thing might be something to add to the list.
It is amazing to me how much I would have learned had I taken your course instead of the course I actually took (followed up by two terrible QM courses).
I discuss color charge briefly, and make an analogy to the dipolar force between atoms that we talked about with molecules. Sweet. Although the analogy is not strictly valid, the nuclear force is just a shadow of the extremely strong force between quarks. The "hard core" repulsion in the nucleon-nucleon potential is due to fermi exclusion, just as with atoms (and it is this repulsion that is responsible for both the uniform density of heavy nuclei and neutron stars the Uncle Al described as well as the "bounce" part of a supernova explosion). The long-range part comes from quark exchange getting stretched to the point where the oppositely moving quarks look like a quark-antiquark pair - a pion.
But, no strong force between fermions? Sorry, Uncle Al, but nucleons and quarks are both fermions. I think he meant to say Leptons (electrons and muons and tau).
PS - I think Brad's experience is typical, and is an examply of why I think QM is the part of physics that is most in need of "reform".
One of the best uses of Feynman diagrams is to keep straight the fact that an electron in beta decay must have an anti-lepton (an anti-neutrino) come out at the same time ... and that you can detect an incoming neutrino by the same reaction with the lepton line flipped down.
I'm going to have to read this post over a few times to wrap my head around all the stuff I should've learned the first time through.
I love the Rutherford quote about the shell and the tissue paper. Back in the day, a few of my physics pals would console ourselves as not being as wrong as Rutherford re: backscatter probability. I'm back doing radiological analysis so I'm looking at radioactive decay again along with atmospheric dispersion and biological dose models, groundshine, cloudshine and all that pragmatic 'look it up in a table' modeling that separates engineering from physics. And while the totality of the problems I'm trying to solve is interesting, I still feel like I left physics too early. I went from modern physics to nucleonics, binding energy, neutronics, and reactor theory, detection and measurement, shielding, biological effects. After that, it was all learning to boil water and bashing equations with computers the way an otter opens clams.
I vaguely remember some interesting math behind the quantization of angular momentum, and the reasoning behind the differences in shell-filling patterns between bosons & fermions, but I was down the path of engineering before I hit quantum mechanics. And even modern physics felt vague and baffling much of the time. It could be that the class was taught early enough in the program that the bulk of the class didn't have the mathematical sophistication that might have made explanations clearer. And granted, the whole notion of time dilation and the Lorentz transformation are brain-hurty even with the mathematical background to understand how the theory came about.
In some ways, I see modern physics more as an exercise in history - trying to understand the current state of the theory is much more difficult without understanding how the old theory fell apart and how the new experimental results were interpreted, both physically and mathematically. I'm currently reading Lillian Lieber's 1936 'layman's guide to relativity which (so far) has been the most gentle and lucid explanation of the curvature tensor I've ever seen. And while this is probably not a high bar, the fact that the book was written over 70 years ago is a testament to Lieber's dedication to making such an inaccessible subject more accessible.
So you have my respect and appreciation for explaining the subatomic; hopefully one day I'll go back to my copy of Krane and find my 'aha!' moment. Better late than never.
"In some ways, I see modern physics more as an exercise in history - trying to understand the current state of the theory is much more difficult without understanding how the old theory fell apart and how the new experimental results were interpreted, both physically and mathematically"
I am coming to disagree with this. It seems like people who have some exposure to QM are stuck around 1925 because of the way a lot of popularization's have been done. I kind of like what has happened with Quantum Computers - a bunch of people came in to use the "mechanics" of QM as a tool and they can thus dispense with a lot of the cruft. Bracket notation from the start and different ways to approach the subject. I wonder how the subject will be taught in 25 years.
I'm currently reading Lillian Lieber's 1936 'layman's guide to relativity which (so far) has been the most gentle and lucid explanation of the curvature tensor I've ever seen. And while this is probably not a high bar, the fact that the book was written over 70 years ago is a testament to Lieber's dedication to making such an inaccessible subject more accessible.
I'm not surprised. A lot of the time, an older popular or semi-popular treatment of a topic will be more accessible, since the mathematical apparatus used to describe it is newer to the physicists themselves than it is in later treatments. In the first few decades of a field, the books and articles for the general public are being written by people who remember what it's like to encounter the subject for the first time, and have to feel things out. Later on, you're dealing with people for whom the subject has always been the way it is now, and they're less likely to have gone through the fumbling and blind-alley chasing that you get even among professionals when a new subject first opens up.
A big part of writing for a general audience is remembering what it feels like to be completely bewildered by the subject.