I found some unanswered questions, and despite they are 1 and 4 years old, I’ll try to answer them, because someone might have the same question now (just as I did, in another comment).
(Psy-Kosh) I’m still confused as to why the individual blobs would tend to be more factorable. Why would they factorize easily post decoherence?
Intuitively, factorizing is translating a description to a set of shorter, independent descriptions. I will give a mathematical, non-physical, analogy. Imagine that you have a knowledge “X=3 and Y=5”. You can translate it into two shorter pieces of knowledge: “X=3″, “Y=5”. Together they mean the same thing as the original knowledge. But it allows you speak about X while ignoring Y. (Quantum analogy: It allows to to speak about one particle, while ignoring the rest of the universe.)
More complex example: “either (X=2 and Y=5) or (X=2 and Y=6) or (X=3 and Y=5) or (X=3 and Y=6)”. Fortunately, this can be factorized into “either X=2 or X=3″, “either Y=5 or Y=6”. Two independent knowledges. Now assume that you only care about X and ignore Y, and your colleague only cares about Y and ignores X. Later, your colleague discovers that in fact Y=5. Is this information useful for you? Absolutely not.
Another example: “either (X=2 and Y=5) or (X=3 and Y=6)”. This knowledge cannot be factorized. If your colleague later discovers that in fact Y=5, it helps you know that X=2.
Now imagine parallel universes, in an old-fashioned sci-fi meaning, not quantum mechanical meaning. You have information “either (X=2 and Y=5 and we live in universe U1) or (X=3 and Y=6 and we live in universe U2)”. This information, as it is, is not factorable. But if you know which universe you live in, the rest of it becomes factorable.
Quantum analogy: replace “we live in universe U1” with “my brain (which also consists of elementary particles) is in state B1″. If your brain can execute the algorithm “state B1 believes that X=2 and Y=5; state B2 believes that X=3 and Y=6”, then you are thinking about the particles as if the situation is easy to factorize. And it’s not only about state of your brain, but also about the state of the whole universe.
(DavidAgain) I’m not clear on why the amplitude involving more particles means that they’re further apart in configuration space.
Imagine a line of length 1; the distance between its ends is 1. Imagine a square of size 1; the distance between its opposite corners is 1.4. Imagine a cube of size 1; the distance between its opposite edges is 1.7. Add more dimensions, and the distance of the opposite edges increases.
Or more precisely, imagine an N-dimensional cube for very large N (something like number of elementary particles in the situation). The distance between two edges becomes greater if they differ in more coordinates. Point (0, 0, 0) is closer to point (0, 0, 1) than to point (1, 1, 1). If you can’t imagine it, just calculate the distance by formula distance((x0, y0, z0), (x1, y1, z1)) = sqrt((x1 - x0)^2 + (y1 - y0)^2 + (z1 - z0)^2). The more coordinates differ, the greater the resulting distance.
I found some unanswered questions, and despite they are 1 and 4 years old, I’ll try to answer them, because someone might have the same question now (just as I did, in another comment).
Intuitively, factorizing is translating a description to a set of shorter, independent descriptions. I will give a mathematical, non-physical, analogy. Imagine that you have a knowledge “X=3 and Y=5”. You can translate it into two shorter pieces of knowledge: “X=3″, “Y=5”. Together they mean the same thing as the original knowledge. But it allows you speak about X while ignoring Y. (Quantum analogy: It allows to to speak about one particle, while ignoring the rest of the universe.)
More complex example: “either (X=2 and Y=5) or (X=2 and Y=6) or (X=3 and Y=5) or (X=3 and Y=6)”. Fortunately, this can be factorized into “either X=2 or X=3″, “either Y=5 or Y=6”. Two independent knowledges. Now assume that you only care about X and ignore Y, and your colleague only cares about Y and ignores X. Later, your colleague discovers that in fact Y=5. Is this information useful for you? Absolutely not.
Another example: “either (X=2 and Y=5) or (X=3 and Y=6)”. This knowledge cannot be factorized. If your colleague later discovers that in fact Y=5, it helps you know that X=2.
Now imagine parallel universes, in an old-fashioned sci-fi meaning, not quantum mechanical meaning. You have information “either (X=2 and Y=5 and we live in universe U1) or (X=3 and Y=6 and we live in universe U2)”. This information, as it is, is not factorable. But if you know which universe you live in, the rest of it becomes factorable.
Quantum analogy: replace “we live in universe U1” with “my brain (which also consists of elementary particles) is in state B1″. If your brain can execute the algorithm “state B1 believes that X=2 and Y=5; state B2 believes that X=3 and Y=6”, then you are thinking about the particles as if the situation is easy to factorize. And it’s not only about state of your brain, but also about the state of the whole universe.
Imagine a line of length 1; the distance between its ends is 1. Imagine a square of size 1; the distance between its opposite corners is 1.4. Imagine a cube of size 1; the distance between its opposite edges is 1.7. Add more dimensions, and the distance of the opposite edges increases.
Or more precisely, imagine an N-dimensional cube for very large N (something like number of elementary particles in the situation). The distance between two edges becomes greater if they differ in more coordinates. Point (0, 0, 0) is closer to point (0, 0, 1) than to point (1, 1, 1). If you can’t imagine it, just calculate the distance by formula distance((x0, y0, z0), (x1, y1, z1)) = sqrt((x1 - x0)^2 + (y1 - y0)^2 + (z1 - z0)^2). The more coordinates differ, the greater the resulting distance.