I'll be reading about a prominent AI researcher getting murdered, ostensibly by his own AI, but really by anti-Skynet wackadoos. It's okay. Sherlock Holmes will be on the case.
(Sorry... spoiler alert?)
One particle doesn't interfere with itself, and can't because the interference pattern is seen in the density of collisions over an area.
As many of these single dots build up, they tend to cluster around an interference pattern - as if some particles went through one slit, and some particles went through the other slit.
Not quite--and that's really the key element of this whole thing: the particle somehow DOES interfere with itself, because the interference pattern that builds up, just one particle / one dot at a time is DIFFERENT than what you'd get if each particle only went through one hole. Imagine you're up on a ladder, dropping beanbags through a plank with two slits in it (you can cover those slits if you want), and they form a pile on the ground below. If the beanbags can only go through one slit, the pile you get on the ground is a nice mound. If you open up BOTH slits, then what you expect is TWO mounds. If the slits are close enough together, you expect those mounds to overlap, with the height at each spot being AT LEAST AS HIGH as the height you'd see dropping the beanbags through just one hole.
But instead, what you see in the double-slit experiment is that, in between the two mounts, you get spots where there are FEWER beanbags than you'd get dropping them through just one hole. Somehow, instead of getting that 1+1=2, you're finding that 1+1=0. The beanbags are all still there--it's not like they're cancelling each other out.. they're just not all where you'd expect them.
The ONLY WAY to explain this (that we've found so far) is if each beanbag, which, again, you're dropping one at a time, somehow goes through BOTH slits and INTERFERES WITH ITSELF. This is where the idea of wave-particle duality comes in, because the patterns that you see (with valleys where there should be ridges) are similar to what you'd see with water waves or sound waves (sound waves can cancel each other out--that's the whole premise behind noise-cancelling headphones).
So then why don't we just say that photons (and beanbags) are waves and not particles at all? Well, because classical waves aren't "quantal," meaning you can't divide sound waves into discrete, indivisible components. You can have one "particle" of light (a photon). There's no corresponding discrete element of sound. So we say that they're particles after all, and simply adjust our thinking regarding just what a particle is and how one behaves.
Ok, let me give this a crack.
You build a box. That box contains a Geiger counter, which clicks if it detects the decay of a particle. Because you're a sick, sadistic fuck, you hook up that Geiger counter to a hammer such that if the Geiger counter detects the decay, it engages the hammer to smash a vial of poison, thus releasing it into the box. You then--because, as I said, have issues with sociopathy--put a cat in the box and close the lid. The box is very thick, completely opaque and completely soundproof. You have no way of knowing what's going on inside the box.
You wait an hour. In that hour, you do some maths that shows that there was a 50% chance that the particle decayed, triggering the Geiger counter, which triggered the hammer to break the vial of poison, releasing the gas and killing the cat.
The question becomes: before you open the box, is the cat alive or dead? Or is it somehow...both?
Your gut instinct is to say, "That's stupid. Of course it's either alive or dead. How the fuck could it be both?"
But the thing is, there are certain, non-cat-related experiments that we've done that REQUIRE the answer to be BOTH. Perhaps the simplest (and certainly the one we physicists learn about first) is the double-slit experiment. The basic idea is, you shoot a beam of something (light, gold atoms, DNA, doesn't really matter) at a slit, and it forms a pattern on a wall. It'll form this pattern even if you shoot your particles one at a time. Then, you close that slit and open another one, and fire your beam again. It forms a different pattern.
Now you open BOTH slits and fire your beam. What happens? Well, what you'd expect is to get a pattern that's the SUM of the pattern you get through each slit. That corresponds to the idea that the particles each go through either Slit 1 or Slit 2. But instead what you get is an INTERFERENCE pattern, which can ONLY happen if the particles are going through BOTH HOLES. And recall I said earlier--you get the same pattern even if you shoot your particles one at a time, which means THE PARTICLE MUST BE INTERFERING WITH ITSELF.
So back to the cat: is it alive or dead, or is it alive AND dead? According to the Copenhagen Interpretation, it's both. But that's why the cat thought experiment was devised in the first place: to highlight how RIDICULOUS that was. The crazy thing is that, seventy years later, we don't really have a better interpretation (at least not one that's widely accepted). So until someone builds this possibly-cat-killing box, we won't really know if the Copenhagen Interpretation is right, or whether something even stranger goes on when quantum events get amplified to the macro level.
One final note: practically speaking, there's no way to build this experiment, because of the whole "you have no way of knowing if the cat is alive or dead without opening the box" part. Isolating a system as big as a cat-box from the rest of the universe is not really feasible. You would also have to construct a particle decay detector that did not, itself, "collapse" the waveform of the decaying particle (otherwise the paradox is resolved before you ever make it to the cat).
Hope that was helpful!
Here we show that [wave-particle duality relations] correspond precisely to a modern formulation of the uncertainty principle in terms of entropies, namely the min- and max-entropies. This observation unifies two fundamental concepts in quantum mechanics. Furthermore, it leads to a robust framework for deriving novel WPDRs by applying entropic uncertainty relations to interferometric models.
So they're looking at it in terms of entropies, and when they do, it resolves a debate about whether WPDRs are equivalent to the Uncertainty Principle AND generates new WPDRs.