Teaching Quantum is fun

[steuard]

I'm really enjoying teaching Quantum Mechanics this year. I've got some fun and interested students, and it's an absolute thrill to watch them figure this stuff out (and to completely blow their minds with quantum weirdness from time to time).

Today's class was a great example: I spent half an hour carefully explaining what a "hidden variables" theory is and why that approach is so much more sensible than the usual interpretation of quantum mechanics. I showed them how they could use very general statements about all possible hidden variable theories to make predictions about the results of various experiments. And then at the end of the class period, I got to see them exclaim in frustration when I did a calculation and showed them that those predictions are inconsistent with the predictions of quantum mechanics, and told them that the quantum prediction is confirmed every time someone tries that sort of experiment.

One of my favorite things about the way Townsend approaches this subject in his book is that students are confronted with the crazy aspects of quantum mechanics right from the start and then repeatedly along the way, so that they have just as much time to improve their mistaken intuition as they do to master the technical details of the calculations. It's a real joy to see them go from disbelief to furious concentration to dawning understanding. I like my job.

Comments

[invisibor.livejournal.com]

My (high-school) students were having a discussion the other day about true randomness and hidden variables. I could only remember that hidden variables theories were not compatible with observations, but I couldn't remember what exactly the predictions or observations were. Luckily they are inclined to take my word for things, but I couldn't really remember. Any quick answer? (I also remember that there is a proof of the uncountability of the reals, but I couldn't remember that either.)

[steuard.livejournal.com]

Unfortunately, I can't think of an answer that's even remotely quick for the "no hidden variables" evidence, let alone convincing.

I probably ought to just leave it at that, but... The gist of it is that if you measure pairs of observables that ought to be only partially correlated (like, say, spin along the z-axis and spin of an entangled particle along an axis 120 degrees from it), any hidden variables theory will predict a weaker correlation than quantum mechanics does. (In my example, they'd both agree that measuring with axes 180 degrees apart would give perfect correlation and measuring with axes 90 degrees apart would give no correlation: just a 1/2 chance of matching answers. But interpolating between the two, by the time you reach 120 degrees, quantum mechanics still gives a 3/4 chance of correlation while any hidden variables theory will give at most a 2/3 chance.) Careful observations confirm the quantum prediction every time.

Uncountability of the reals is cuter. If you can count the reals, then you can write them as (infinite) decimals and put them all in a list, one to a row: row 1, row 2, row 3, etc. But no matter what order you put them in, it's easy to come up with a real number that isn't anywhere on the list! Just make sure that the first decimal place of the new number is different from the first decimal place of row 1, the second decimal place is different from that of row 2, the third is different from row 3, and so on. (One safe rule for this: make every decimal digit "7" unless the corresponding row/place is already "7", in which case, make it "6". The subtle pitfall to avoid is not to ever assign to "9", so you don't run into that sneaky "0.99999... = 1.00000..." equivalence.)

[pearmeson.livejournal.com]

Are you talking about his newer Modern book (Phys 52 at Mudd) or his older Quantum book (Phys 116(?) at Mudd)? I haven't looked at his new one yet. I've come to appreciate the older one more than I did back then, though I still wish it had more history in it.

[steuard.livejournal.com]

The older one, for Big Quantum. (I haven't seen much of his Modern book yet, though he and I had a good conversation about it while he was finishing it up. A colleague of mine at Joint Science used it the year after I left, and his impression seemed mixed. I suspect that my take on it would be more uniformly positive, but perhaps not entirely so. John does sometimes come a little too close to assuming that the students will have Mudd-caliber backgrounds.) It turns out that Modern is one of the only classes in the undergraduate curriculum that I haven't yet taught; I'll certainly be looking at John's new book when that time comes.

John's original Quantum Mechanics book more or less defined the way that I think about quantum physics, to the extent that I can hardly bear the thought of teaching the course at that level in any other way. I think it does a better job of making it clear what quantum mechanics "is" than a traditional wave function approach does: it's all too easy to mistake the mathematical mechanics of integrals and densities for the essence of the subject. John's approach also gets at the core of "quantum weirdness" much more directly and with fewer distractions, at least to my eye.

And personally, I've got to admit, I don't miss the history at all. I mean, I hope the students learn it at some point, maybe in a Modern Physics course among other places: it's valuable culture, and it's good to know how our modern understanding of the world developed. But to a substantial degree, I think the topic is challenging and subtle enough even when explained based on our best-developed understanding of how to do it. The historical development of the field took a long time to really figure out how to make sense of all this stuff!

On top of that, I simply don't think that most students are remotely prepared to understand the impact of the history as it's usually taught. I mean, black body radiation? My statmech students rarely leave the class with a 100% solid understanding of what it's all about and why the classical prediction didn't make sense. To expect students who haven't ever heard of the concept before to grasp the impossibility of the classical result and the importance of Planck's quantum hypothesis as a resolution is just madness. The same goes for most of the historical examples we usually use: they're subtle, and only a fully-trained classical physicist is likely to understand why they're so intractable. The only historical example that I've typically used in my lower-level classes to motivate the quantum idea is the photoelectric effect, because there I feel like the students have developed at least a moderate feel for how the classical physics involved is supposed to work (so that when the experimental results turn out inconsistent with that, they know to be surprised).

Whew. Apparently I really go on about this subject. :) What were your complaints at the time? (I know that a revision is on John's radar...)

[pearmeson.livejournal.com]

Yeah, it's definitely subtle. I think part of my issue is that I want more history/philosophy in all the classes. For the non-majors because I want them to take a scientific mindset away from the class, and I think the twists and turns and blind alleys are an important component of that. For the majors because I really believe in the Mudd mission, even though I don't think they were accomplishing it in the late 90's (or, to qualify even more, I didn't accomplish it -- I got the history/philosophy on my own, and didn't actually learn the physics until grad. school) I don't think you can really educate scientists who understand the impact of their work on society unless you talk about how that work impacted society *while you are learning it*. Some of them might pick it up on their own or through separate humanities requirements, but not most.

But I know that too much history/philosophy, or history/philosophy done badly, prevents learning, transfer, etc. of the skills we want them to take away. So if juniors aren't ready to handle it in Quantum, when will they? Graduate courses have no interest in history, it's all just "shut up and calculate" in my experience, and by your premise, they aren't ready in Modern either. So when?

As for Townsend's book, I don't think I could make useful commentary that wouldn't turn it into a different book. For the purposes he set out to accomplish, I think it's excellent. I think the generator approach is really elegant, and I'm glad to have a book that doesn't focus on the wave formulation (starting from wave mechanics is ahistorical anyway).