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.
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.
You 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.
"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.
> 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.)
The 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.
This 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
It's not quite as dramatic as it sounds. It's a somewhat more mathematically sound way of saying all of the usual stuff about quantum mechanics. It just takes the QM side more seriously, rather than trying to describe it as a bag on the side of classical physics.
The unobservable parts are not really any different from indirectly inferred concepts like potential energy. It's just that even seemingly concrete notions like location turn out to be macro scale approximations of this phase space. They're not accessible only because you are a macro scale object. You can very much demonstrate that it's real by simple experiments. You just need to be able to take them seriously, which is unexpectedly difficult because classical physics seems so intuitively obvious.
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.
where & how is the 'configuration' encoded? [we don't know, right] Is this why string theory requires higher dimensions? Also when I see the term 'harmonic oscillations', I think of plucking a string -- it seems so elegant for the physical particles to be manifestations of higher dimensional ~~vibrating~~ oscillating strings :) (thinking of flat-lander analogy)
gp's premise about learning with the multi-particle landscape first sort of blew my mind.
> Is this why string theory requires higher dimensions?
No. The higher dimensions of string theory are actual physical dimensions. Configuration space dimensions are pure mathematical abstractions, and there are potentially an infinite number of them, one for every degree of freedom in the system. Look up "Hilbert space" if you want the gory details.
>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...
Hm, 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.
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.
They should name this proposal "quantum sneakernet". It's pretty weird to imagine aliens light years away could have a constellation of quantum networked telescopes and be taking Google Maps-resolution photos of Earth.
You can't. This is just covered by classical electrodynamics. Of course in a sense you can say anything is quantum, but then the stability of a table is quantum (which it is). If you were to have a single photon source and avalanche detector, ok now you are talking quantum.
The first 2 minutes of that video make it clear that they think it is "real" quantum effects (e.g. at 1:34 entanglement > EPR paradox > Bell's Theorem > local realism). Those are pretty quantum-y imo.
Yeah. At 9:34 they're dealing with entangled photons passing through 2 filters at different points in space, simultaneously. They affect each other, which is impossible without faster-than-light communication between them. This is absolutely quantum and cannot be explained at all by classical EM.
If you have entanglement then it is quantum. Yes. But the comment was you 'just' need polarized glasses. So if 'just' polarized glasses for a few $ means: "and of course a biphoton source for a couple of thousand $ and some coincidence counters for another couple of thousand $", then you only 'just' need polarizers.
What I really appreciated about this article was its clear explanation of how (quarks?) acts like a wave until it is observed and then acts like a particle.
I'm certainly interested in this, but for different reasons. Over the years, several people have bent my ears about Duane's theorem that suggests the double-slit experiment is not demonstrating quantum effects at all.
It strikes me that this could help establish or overturn such claims.
Seems like this hypothesis shows it is indeed demonstrating “quantum” effects because the math falls out of the quantization of momentum transfer. Of course “quantum” is now widely understood to mean “the weird phenomena like the double slit experiment”... but I get what you’re saying. I wonder what’s with the downvote, though.
No, the Rayleigh Criterion is still correct, you just have to consider the "aperture size" to be the size of the combined multi-telescope device (which would be the size of the Earth if the telescopes are on the opposite sides of the Earth). In practice to get the best quality image you need a telescope every X meters (I'm not sure the exact distance required) but even a 2x2 telescope array over a large distance would still give you significantly more resolving power than just a single telescope on it's own.
