the day is fast approaching when I will have to explain particle-wave duality and Heisenberg uncertainty to a 13-year-old
You need to read Deep Down Things: the Breathtaking Beauty of Particle Physics by Bruce Schumm! It has the best demonstration of particle wave duality I have ever seen in my life! Also Bruce is the best physics professor I ever had and deserves all the love forever. (His book self bills as "the first comprehensive book on particle physics for a lay audience." And it's purple). But it's not like "here's a cute metaphor" it actually shows you how it works. I actually got it for a hot second.
The cute metaphor version is that "billiard balls" and "the movement of the ocean" are both inadequate metaphors for describing what light is. And the worst version of this is that "wave" and "particle" are mathematically equivalent notational variants of each other, and you use whichever one that makes the math easier. Which lets physicists pull bs like: "okay light can be modeled as waveforms or as particles called photons" okay good with you so far "so given that these are notational variants of each other, we can model sound waves as particles called phonons" *eye twitch* I Guess dot jpg "so for this problem we are going to model the ripples on the surface of a pond as particles called ripplons" *table flip* SCIENCE HAS GONE TOO FAR
The most intuitive understanding of Uncertainty is when Dave Dorfan, the head of our department, was walking by and grabbed one of the students and was like "Uncertainty is this. Imagine Troy [the student] is standing in an ice rink with the lights off and the only way to find out where he is is to throw rocks at him." (Troy: Hey!) The point being that to observe is to interact - not on a philosophical but on a physical level - and to interact is to effect. Every time a rock hits Troy it imparts a bit of energy to him and he moves a little bit on his frictionless surface, so the information you get about his location from this interaction is necessarily going to be slightly wrong. To measure something is to change it.
Mathematically of course it's just linear algebra. Can you teach your 13 year old linear algebra? p and x don't commute. That's it that's the whole Uncertainty Principle. The matrices don't commute. They have different eigenstates. To measure a value you have to be in an eigenstate for that value. You can't be in the eigenstate for position and momentum at the same time, so if you're measuring one you are not measuring the other. Because the matrices don't commute.
(We got to that point in out Quantum class and it was like Oh. Oh that's it isn't it. It was just that the whole time. Well okay then)
Anyway, good luck to you! These are some of my very favorite topics!
I entirely agree that talking about how it actually works is better than cute metaphors, and the way people sensationalize the ~power of observation~ is tiresome when it makes perfect sense as a practical problem.
Overall the approach I've been taking to talking about the history of chemistry is talking about things from the point of view of the scientists who discovered them- what did they already know (or think they knew), what unanswered questions were they trying to understand, what experiments did they do and what conclusions did they draw from the results? There's a bit less of that to talk about with the wave-equation model of the atom, but I talked to the 13-year-old about waves and diffraction and then we watched a video where you can see electrons make a diffraction pattern after going through a barrier.
One kind of nice part, though, is that the people who came up with these ideas re: particle-wave duality also thought they were pretty strange; it was just the only answer that fit the data. Why are the electrons limited to only traveling in certain specific "orbits" even though common sense says they could travel at any speed? I don't know, says Niels Bohr, but the data says that's what they do, so there must be some reason.
I sadly had to get rid of my college notebooks when I moved- I wish I still had them to refer back to, because once upon a time I did actually have to work with wave equations (the "particle in a box" one, that describes just one dimension, a particle moving back and forth along a line). But I told the 13-year-old that we could see what the equations look like, and then I would explain what they tell us, but we wouldn't get into how they actually work mathematically.















