Eliezer, thank you for your posts. I'm new to this site—not to mention to QM—and I've been reading this series with much interest, albeit with fluctuating success.
I've been concentrating on the Intuitive Explanation index, re-reading the posts and comments several times over, but I'm pretty sure I'm still missing some important aspect. This is what I'm getting so far. I would love it if somebody more knowledgeable could point out where exactly my understanding went astray.
I get that any particle, such as an electron, is actually a (part of a) wave moving over some field. This wave, or wavefunction, has values all over the place: it is a complex-valued, continuous and differentiable distribution over 3 dimensions (plus time.)
Because of the constraints implicit in the wave mechanics, these 3 dimensions can be taken to be the position space or equivalently the momentum space. You stated in some other post that you prefer the position space, as it makes the "locality principle" of the universe more readily apparent. Ok.
This is already suggesting that a "particle" does not have a definite position, nor a definite momentum, only a definite, complex-valued distribution over both, that's constantly changing over time.
So for example, at position (x, y, z) and time (t), there is a complex amplitude (r, φ) on the quantum field for electrons. It's a distribution because it is zero at any single point and only the integral has non-zero values. (By the way, how many quantum fields are there?)
The distribution, which comprises all existing electrons in the universe, is moving through space with some kind of wave dynamics, so that the way it evolves over time is determined by its very shape and motion (its derivatives.) Just like an ocean or sound wave, except with complex values—and I bet complex math :-) All right so far.
So it can happen that two particles of the same kind (two wavelets on the same field) manage to evolve into exactly opposite distributions and thus cancel each other out. No big deal, this happens all the time with fluid or sound waves too.
As far as I can see, this should explain "entangled" particles, as they would be wavelets originating from the same wave, so that their sub-distributions are closely related to each other. If you measure some quantity on one of them, then you know the quantity of the other, because it's closely related, such as the opposite.
As far as the half-silvered mirrors go, if you can detect one path an electron or photon takes, you cannot detect any other path it took (being a wave it took all possible paths) because on the other paths the wave has a different complex phase. Except that if you direct them back on the same path, they can cancel each other out. This does not usually happen with two generic particles (wavelets) created from different sources, because they would have different distributions (would not be coherent.)
This is also true of complex waveforms, such as humans or cats or tables, except that, out of all their Feynman paths, only the tiniest slice does not cancel out, and that's why we don't see tables moving around.
What I don't get is the need to call the collective distribution (or wave, or wavefunction) of all the electrons in the universe a "configuration" and posit that it has itself an amplitude (or amplitude distribution) over the infinitely larger space of all possible configurations, something the mind has a hard time grasping. I'm not even sure this is exactly what is being suggested, but I'm afraid it is so, because of the many-world interpretation that comes out of it.
I'm sure I'm missing something very important in all this, or I got different concepts mixed together. Exactly which one of the half-silvered mirror experiments or other posts explains the need for such a complication? Which parts of my understanding above are wrong?
Eliezer, thank you for your posts. I'm new to this site—not to mention to QM—and I've been reading this series with much interest, albeit with fluctuating success.
I've been concentrating on the Intuitive Explanation index, re-reading the posts and comments several times over, but I'm pretty sure I'm still missing some important aspect. This is what I'm getting so far. I would love it if somebody more knowledgeable could point out where exactly my understanding went astray.
I get that any particle, such as an electron, is actually a (part of a) wave moving over some field. This wave, or wavefunction, has values all over the place: it is a complex-valued, continuous and differentiable distribution over 3 dimensions (plus time.)
Because of the constraints implicit in the wave mechanics, these 3 dimensions can be taken to be the position space or equivalently the momentum space. You stated in some other post that you prefer the position space, as it makes the "locality principle" of the universe more readily apparent. Ok.
This is already suggesting that a "particle" does not have a definite position, nor a definite momentum, only a definite, complex-valued distribution over both, that's constantly changing over time.
So for example, at position (x, y, z) and time (t), there is a complex amplitude (r, φ) on the quantum field for electrons. It's a distribution because it is zero at any single point and only the integral has non-zero values. (By the way, how many quantum fields are there?)
The distribution, which comprises all existing electrons in the universe, is moving through space with some kind of wave dynamics, so that the way it evolves over time is determined by its very shape and motion (its derivatives.) Just like an ocean or sound wave, except with complex values—and I bet complex math :-) All right so far.
So it can happen that two particles of the same kind (two wavelets on the same field) manage to evolve into exactly opposite distributions and thus cancel each other out. No big deal, this happens all the time with fluid or sound waves too.
As far as I can see, this should explain "entangled" particles, as they would be wavelets originating from the same wave, so that their sub-distributions are closely related to each other. If you measure some quantity on one of them, then you know the quantity of the other, because it's closely related, such as the opposite.
As far as the half-silvered mirrors go, if you can detect one path an electron or photon takes, you cannot detect any other path it took (being a wave it took all possible paths) because on the other paths the wave has a different complex phase. Except that if you direct them back on the same path, they can cancel each other out. This does not usually happen with two generic particles (wavelets) created from different sources, because they would have different distributions (would not be coherent.)
This is also true of complex waveforms, such as humans or cats or tables, except that, out of all their Feynman paths, only the tiniest slice does not cancel out, and that's why we don't see tables moving around.
What I don't get is the need to call the collective distribution (or wave, or wavefunction) of all the electrons in the universe a "configuration" and posit that it has itself an amplitude (or amplitude distribution) over the infinitely larger space of all possible configurations, something the mind has a hard time grasping. I'm not even sure this is exactly what is being suggested, but I'm afraid it is so, because of the many-world interpretation that comes out of it.
I'm sure I'm missing something very important in all this, or I got different concepts mixed together. Exactly which one of the half-silvered mirror experiments or other posts explains the need for such a complication? Which parts of my understanding above are wrong?