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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 t
by lisper 6y 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 6y agowhat is configuration space
- jfengel 6y 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 6y 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 6y ago> means that the state of the world is described by some list of numbers How is that different from hidden variables?
- Cookingboy 6y agoYeah 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.
- jfengel 6y agoThe difference is that they're not localized. It's only local hidden variables that are forbidden by theory. One way to look at it is that every one of those pieces of configuration space apply to all of space and all of time. That's not forbidden. But it also means that these values aren't directly accessible. They can only be partially inferred.
- Smithalicious 6y agoSo the universe is governed by inaccessible magic numbers, like a kind of divine DRM?
- Smithalicious 6y agoThis is being downvoted, perhaps because I put a humorous analogy in there, but I really am curious, isn't this what is claimed? The "real" ground truth of the universe is "configuration space", which is some kind of mathematical construct, and which can't be perceived directly but only partially inferred? I'd like to know more about this since I have never heard of this concept before and I feel like it has far-reaching implications
- baldeagle 6y agoI’m not sure I’m following… are you saying that the wave functions are just a yaml for the behavior in physical space?
- lisper 6y agoHm, that's an interesting analogy, and not entirely off the mark. It misses a few essential things though, which is that the mathematical relationship between the wave function and what we call "physical reality" has a very different structure from the relationship between yaml and server configs, and this structure actually matters. But with those caveats in mind, yeah, you can kinda sorta think of it that way.
- boublepop 6y agoThe wave function is “the sum of faces on two rolled d6” reality is “it they landed with a sum of 8”.
- senko 6y agoWow. Is there a resource (book, videos, ...) that takes this approach to teaching it (and accessible to/understandable by a motivated layman?)
- lisper 6y agoI don't know of any resource that explicitly takes this approach. The closest thing I know of is David Z. Albert's "Quantum Mechanics and Experience". AFAICT I am the primary proponent of the pedagogical significance of this idea, so maybe I should write something up. Watch my blog.
- deleted 6y ago[deleted]
- Cookingboy 6y ago>How physical space emerges from configuration space is a deep mystery. Exactly, how quantum collapse happens, or what quantum collapse even is, is one of the biggest mysteries of physics. And I'll argue that as long as we don't have an explanation for that bridge between the "configuration space" and the "physical space" like you call them, the former may as well be magic. Yes it would make learning and explaining the rules of magic a bit easier if you get into that mindset, but it still doesn't make it intuitive, but just easier to accept. If anything, it does feel we could very well be living in a simulation governed by arbitrarily defined rules that exist on a different plane than other physical laws. Hmmm maybe we should give non-local hidden variable theories another look...
- canjobear 6y agoYou are right that realizing that the wavefunction lives in configuration space is a big leap that is hard for people, but there is another leap which is more difficult IMO. It is that quantum probability amplitudes are not like classical probabilities: they have phases and can interfere with each other in ways that classical probabilities do not. This explains the weird interference patterns in the cool animation in the article. In my experience, understanding the idea of a distribution over configuration space isn't so hard. But getting an intuitive grasp of the behavior of probability amplitudes that can interfere with each other is hard.