5 ms·

Scroll down to the bottom of the front page to see the Highlighted Explorables. My favorite is the standing waves simulation. I'd love someone to critique my e

Scroll down to the bottom of the front page to see the Highlighted Explorables. My favorite is the standing waves simulation. I'd love someone to critique my explanation of quantum mechanics at the start of the quantum section. I worked hard on it, but QM is hard, and I may have got some details wrong.

rsfern 7y ago
Lots of nice content here. I started with the QM section, and it felt like you jumped right in to the particle theory of light. I realized later that of course you have an in depth discussion of the wave theory of light, but I think a bit more explicit connection to that discussion could be helpful. I particularly like coming back to Young’s double slit experiment, which I saw in your discussion of diffraction. To me, the most surprising illustration of the wave/particle duality of light is that single photons passing sequentially through the double slit still form a diffraction pattern. So these particles sort of ‘self-interfere’. One other thought regarding the standing wave demo — maybe you are already familiar with this, but setting up higher order harmonics is a pretty common technique among guitar players (and other stringer instruments), where you pluck a string while touching one of the standing wave nodes. If you’re not familiar with ‘portrait of Tracy’ by Jaco Pistorius, it’s a really cool and unique example of this technique https://m.youtube.com/watch?v=JXOnhzoC-i8 https://m.youtube.com/watch?v=JXOnhzoC-i8
- lilgreenland 7y ago
  Revisiting the double slit for a single particle makes sense. I don't know why I forgot to do it. thanks!
madhadron 7y ago
I started reading last night to try to give you some feedback, then bedtime for my kids arrived, etc. I haven't found a way to start people into quantum mechanics that I like. All the material on states and superposition really doesn't help unless you've got a lot more math than a highschooler does. It also is a complete departure from the previous material because suddenly it's this mass of abstraction without reference to a physical system. The best that I've found so far goes something like this: When we talked about a ball flying through the air, we talked about its path. But our eyes can only distinguish changes that take at least a thousandth of a second. A camera takes a series of snapshots. We idealize that we can do 2000 measurements, or 4000, or any number and so in the usual passage from discrete to continuous we get the idea of a bath. Implicit in this is that shining a light on the ball and measuring where it is has negligible effect on the ball. But when we assume quantization, when we assume that there are photons and leptons, smallest particles and smallest units of interaction, we reach a point where we can't neglect the effect of the measurement. Any interaction that lets us measure it will disturb the system. So if we double the frame rate of our measurement, we disturb the system twice as often, so measuring it at 1000fps is not the same as measuring it as 2000fps and ignoring half of the frames. The more often we measure, the more disturbance we have, and it doesn't converge to a path anymore. It's probably worth pausing and pointing out that a measurement here is linking what occurs from the interaction with the system we're measuring with a macroscopic, irreversible process. For example, a photomultiplier tube where a single incoming electron kicks off a cascade of more electrons, which kicks off even more in the next layer. But if a measurement consists of this giant thing, and more measurements don't converge to a path, there's this big gap. Is there actually an underlying position of the particle outside of that measurement? It's not accessible to us, even if there is. And at this point you go straight into Bell's inequalities to rule out hidden variables. There's a lot of pedagogical problems with this, but I feel like it's the most promising route I know of.
- lilgreenland 7y ago
  Good improvement, I've added "include something about the nature of measurement and irreversibility to QM notes"
Chris2048 7y ago
Maybe I'm wrong, but whenever I look up the topic there seems to be contradictory information. Maybe the latest in QM is too new to be stable? For ppl in the know, here is a simple (maybe) question: I can model "spin" of a photon such that two photons added with opposite spin direction will result in a polarised profile: but I can also add two polarised photons that produce a rotating pattern. polarisation always seemed unnatural to me - do "real" photons spin (one way, or another) and only combinations result in polarisation? Because photons are often depicted as elementary (not the result of combining multiple photons), but also polarisable..

rsfern 7y ago

Lots of nice content here. I started with the QM section, and it felt like you jumped right in to the particle theory of light. I realized later that of course you have an in depth discussion of the wave theory of light, but I think a bit more explicit connection to that discussion could be helpful. I particularly like coming back to Young’s double slit experiment, which I saw in your discussion of diffraction. To me, the most surprising illustration of the wave/particle duality of light is that single photons passing sequentially through the double slit still form a diffraction pattern. So these particles sort of ‘self-interfere’. One other thought regarding the standing wave demo — maybe you are already familiar with this, but setting up higher order harmonics is a pretty common technique among guitar players (and other stringer instruments), where you pluck a string while touching one of the standing wave nodes. If you’re not familiar with ‘portrait of Tracy’ by Jaco Pistorius, it’s a really cool and unique example of this technique https://m.youtube.com/watch?v=JXOnhzoC-i8 https://m.youtube.com/watch?v=JXOnhzoC-i8

lilgreenland 7y ago
Revisiting the double slit for a single particle makes sense. I don't know why I forgot to do it. thanks!

madhadron 7y ago

I started reading last night to try to give you some feedback, then bedtime for my kids arrived, etc. I haven't found a way to start people into quantum mechanics that I like. All the material on states and superposition really doesn't help unless you've got a lot more math than a highschooler does. It also is a complete departure from the previous material because suddenly it's this mass of abstraction without reference to a physical system. The best that I've found so far goes something like this: When we talked about a ball flying through the air, we talked about its path. But our eyes can only distinguish changes that take at least a thousandth of a second. A camera takes a series of snapshots. We idealize that we can do 2000 measurements, or 4000, or any number and so in the usual passage from discrete to continuous we get the idea of a bath. Implicit in this is that shining a light on the ball and measuring where it is has negligible effect on the ball. But when we assume quantization, when we assume that there are photons and leptons, smallest particles and smallest units of interaction, we reach a point where we can't neglect the effect of the measurement. Any interaction that lets us measure it will disturb the system. So if we double the frame rate of our measurement, we disturb the system twice as often, so measuring it at 1000fps is not the same as measuring it as 2000fps and ignoring half of the frames. The more often we measure, the more disturbance we have, and it doesn't converge to a path anymore. It's probably worth pausing and pointing out that a measurement here is linking what occurs from the interaction with the system we're measuring with a macroscopic, irreversible process. For example, a photomultiplier tube where a single incoming electron kicks off a cascade of more electrons, which kicks off even more in the next layer. But if a measurement consists of this giant thing, and more measurements don't converge to a path, there's this big gap. Is there actually an underlying position of the particle outside of that measurement? It's not accessible to us, even if there is. And at this point you go straight into Bell's inequalities to rule out hidden variables. There's a lot of pedagogical problems with this, but I feel like it's the most promising route I know of.

lilgreenland 7y ago
Good improvement, I've added "include something about the nature of measurement and irreversibility to QM notes"

Chris2048 7y ago

Maybe I'm wrong, but whenever I look up the topic there seems to be contradictory information. Maybe the latest in QM is too new to be stable? For ppl in the know, here is a simple (maybe) question: I can model "spin" of a photon such that two photons added with opposite spin direction will result in a polarised profile: but I can also add two polarised photons that produce a rotating pattern. polarisation always seemed unnatural to me - do "real" photons spin (one way, or another) and only combinations result in polarisation? Because photons are often depicted as elementary (not the result of combining multiple photons), but also polarisable..