Decoherence is the process that makes it impractically difficult for an experiment to be designed that makes your observations the two interfering possibilities in some kind of double-slit experiment.
Interpreting this in the many-particle case is more difficult, but the basic idea is that due to single-particle uncertainty, you can't have a definite number of particles indexed by momentum and a definite number of particles indexed by position at the same time. If I had 100 particles that were definitely at x=0, in terms of momentum they'd be spread out over the range of possibilities unpredictably.
Not exactly. The Heisenburg uncertainty principle doesn't apply to knowledge (actual observations), it applies to observables (things that could affect interactions in principle). That is, Heisenburg uncertainty is not merely a limit on how fine our measurement instruments could get, or even how much information about an interaction we could conceive of and store. It's a limit on how strongly those properties can affect an interaction at all.
That is, the future direction and momentum of an interaction between two particles can't depend very strongly on both the position where the interaction happened, and on the momentum the particles had before the interaction. If the interaction is a direct collision, so the position is heavily constrained, then the momentum the particles had before the collision will not really matter a lot for what happens after they collide.
If you were to "put yourself in the shoes of" one of the particles, you could say that, because it "knows" where the other particle is at the time of the collision with high precision, it can't "know" the momentum the other particle had with any precision, so it's future movement can't depend strongly on that. But this stretches the definition of "knowledge" far beyond the normal understanding of the word.
> It happens outside QM, and even outside physics. It’s not a physical attribute, it’s statistical.
This is not true at all. In classical mechanics, particles have fully definite properties. In the theory, if two particles collide, the position and momentum they'll have after the collision depend on their exact position and exact momentum before the collision, with no bound on precision.
Of course, classical mechanics admits that we can't measure things to any level of precision, there is some practical bound below which noise in the measurement will drown out the signal. But the interaction itself has no such bound, it happens with infinite precision. If the speed of one of our particles were higher by just 10^-100 m/s, its trajectory might be completely different.
This is not possible in QM. In QM, if the particles collide (they meet at an exact point in space-time), then their trajectories afterwards wouldn't change even if one of their speeds were 10 times higher: if they have definite position, their speed is extremely fuzzy, and it can't significantly affect their trajectories after the event.
And QM turns out to be right abput this, when you measure things precisely enough.
I was making the point that the uncertainty principle is not about QM. And it is not. It occurs in a wide range of even classical systems.
As for your comment about them not having defined proporties; this is also just one interpretation. You argue for violation of realism. That’s fine, but unnecessary.
Violation of locality or realism is only needed in the context of Bell inequalities, and this assumes there is no superdeterminism and you are “free” to choose your experiment, which is of course a rather strange argument to have to begin with.
To spare your struggle with language: commutator of hermitian operators is a physical property of mathematical origin, inherited from linear algebra, because QM is described by linear algebra, so physics inherits all aspects of linear algebra as physical properties.
How frequently a wave would go through just 1 of the slits. If you threw a baseball at a wall with two baseball sized slits it would basically always go through just one of the slits. You would never see an interference pattern.
This is because a baseball is interacting with other matter on the way to the slit. A photon on the other hand might not interact with any matter and it stays as a wave and you can see an interference pattern on the other side.
