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That animation at the top of the article of the possible locations of the photon is very cool. Quantum behavior seems so counterintuitive to us because we're ju

That animation at the top of the article of the possible locations of the photon is very cool. Quantum behavior seems so counterintuitive to us because we're just apes who evolved minds to survive in the macroscopic world of the African savanna. But I wonder if we perhaps taught quantum behavior to kids from an early age, whether they could get an intuitive understanding for it, in the the same way that I can, like, know what "feels" like the best move in Chess or something, without really being able to articulate why. That kind of intuitive feel for how something works usually leads to concrete logical understanding later on.

lisper 5y ago
It's actually not that hard to get an intuitive understanding of QM even as an adult. The key is having the right pedagogy, which is very rare. IMHO the key to the right pedagogy is just one crucial insight: the wave function lives in configuration space, not in physical space. How physical space emerges from configuration space is a deep mystery. No one knows. But it is CRUCIAL not to conflate these two things. Most "quantum weirdness" is simply a result of confusing them. It is also important to understand that the reason these things are often conflated is that much of what is (or at least used to be before quantum computation became a thing) taught as quantum mechanics focuses on the special case of a single particle considered in isolation. In that one special case -- and ONLY in that one special case -- configuration space is the same as (or at least isomorphic to) physical space. But as soon as you add a second particle, that stops being true. So the key to understanding QM is to START with the multi-particle case. This is actually easier than the single particle case because it forces you to set aside a lot of the things that make quantum mechanics difficult in general and focus on the thing that makes it hard to wrap your brain around: entanglement. But the reason that entanglement is hard to wrap your brain around is that it's weird when considered from the point of view of physical space. If you start with multi-particle systems, that forces you to start with configuration space, and that gets you past the hard part right from the start. After that it's just math.
- Moodles 5y ago
  what is configuration space
  - jfengel 5y ago
    "Configuration space" means that the state of the world is described by some list of numbers that don't actually correspond directly to locations in space or time. Or even mass or energy. It means that those things aren't really fundamental. What's fundamental is some other set of things that aren't too difficult to work with mathematically, but which don't correspond exactly to anything you're familiar with. The best you can do is to add in "probability functions", such that "state of the world X" means that you'd have some chance of detecting a particle here, and some chance of detecting a particle there, and so on. It's that jump from one to the other that's awkward, and to be honest not 100% understood. But it's actually better understood than a lot of the woo-woo descriptions of quantum mechanics make it out to be. Now, when I said that the math isn't too difficult to work with, that's a bit of a lie. It's all about Simple Harmonic Oscillation, except using complex numbers. That's really not too bad, but it's definitely new.
    - lisper 5y ago
      > It's all about Simple Harmonic Oscillation, except using complex numbers And both of those are among the details which can be safely ignored. The only math you really need in order to understand QM conceptually is linear algebra. (And actually, even the harmonic oscillators are not that difficult to understand. If you understand Euler's identity, you're 90% of the way there.)
    - ars 5y ago
      > means that the state of the world is described by some list of numbers How is that different from hidden variables?
      - Cookingboy 5y ago
        Yeah I'm honestly not too sure here either, the more I think the more I believe simulation + hidden variables may be the true explanation behind our reality.
magicalhippo 5y ago
> Quantum behavior seems so counterintuitive While I still feel just that, this post[1] and its reference to Scott Aaronson's lecture[2] on how QM can be seen as a "inevitable" generalization of probability theory did make quantum mechanics more... comforting? acceptable? Something like that. [1]: https://www.physicsforums.com/threads/probability-theory-and-quantum-mechanics.749565/post-4723789 https://www.physicsforums.com/threads/probability-theory-and... [2]: https://www.scottaaronson.com/democritus/lec9.html https://www.scottaaronson.com/democritus/lec9.html

lisper 5y ago

It's actually not that hard to get an intuitive understanding of QM even as an adult. The key is having the right pedagogy, which is very rare. IMHO the key to the right pedagogy is just one crucial insight: the wave function lives in configuration space, not in physical space. How physical space emerges from configuration space is a deep mystery. No one knows. But it is CRUCIAL not to conflate these two things. Most "quantum weirdness" is simply a result of confusing them. It is also important to understand that the reason these things are often conflated is that much of what is (or at least used to be before quantum computation became a thing) taught as quantum mechanics focuses on the special case of a single particle considered in isolation. In that one special case -- and ONLY in that one special case -- configuration space is the same as (or at least isomorphic to) physical space. But as soon as you add a second particle, that stops being true. So the key to understanding QM is to START with the multi-particle case. This is actually easier than the single particle case because it forces you to set aside a lot of the things that make quantum mechanics difficult in general and focus on the thing that makes it hard to wrap your brain around: entanglement. But the reason that entanglement is hard to wrap your brain around is that it's weird when considered from the point of view of physical space. If you start with multi-particle systems, that forces you to start with configuration space, and that gets you past the hard part right from the start. After that it's just math.

Moodles 5y ago
what is configuration space
- jfengel 5y ago
  "Configuration space" means that the state of the world is described by some list of numbers that don't actually correspond directly to locations in space or time. Or even mass or energy. It means that those things aren't really fundamental. What's fundamental is some other set of things that aren't too difficult to work with mathematically, but which don't correspond exactly to anything you're familiar with. The best you can do is to add in "probability functions", such that "state of the world X" means that you'd have some chance of detecting a particle here, and some chance of detecting a particle there, and so on. It's that jump from one to the other that's awkward, and to be honest not 100% understood. But it's actually better understood than a lot of the woo-woo descriptions of quantum mechanics make it out to be. Now, when I said that the math isn't too difficult to work with, that's a bit of a lie. It's all about Simple Harmonic Oscillation, except using complex numbers. That's really not too bad, but it's definitely new.
  - lisper 5y ago
    > It's all about Simple Harmonic Oscillation, except using complex numbers And both of those are among the details which can be safely ignored. The only math you really need in order to understand QM conceptually is linear algebra. (And actually, even the harmonic oscillators are not that difficult to understand. If you understand Euler's identity, you're 90% of the way there.)
  - ars 5y ago
    > means that the state of the world is described by some list of numbers How is that different from hidden variables?
    - Cookingboy 5y ago
      Yeah I'm honestly not too sure here either, the more I think the more I believe simulation + hidden variables may be the true explanation behind our reality.

magicalhippo 5y ago

> Quantum behavior seems so counterintuitive While I still feel just that, this post[1] and its reference to Scott Aaronson's lecture[2] on how QM can be seen as a "inevitable" generalization of probability theory did make quantum mechanics more... comforting? acceptable? Something like that. [1]: https://www.physicsforums.com/threads/probability-theory-and-quantum-mechanics.749565/post-4723789 https://www.physicsforums.com/threads/probability-theory-and... [2]: https://www.scottaaronson.com/democritus/lec9.html https://www.scottaaronson.com/democritus/lec9.html