Today's post, Decoherence was originally published on 22 April 2008. A summary (taken from the LW wiki):

A quantum system that factorizes can evolve into a system that doesn't factorize, destroying the illusion of independence. But entangling a quantum system with its environment, canappearto destroy entanglements that are already present. Entanglement with the environment can separate out the pieces of an amplitude distribution, preventing them from interacting with each other. Decoherence is fundamentally symmetric in time, but appears asymmetric because of the second law of thermodynamics.

Discuss the post here (rather than in the comments to the original post).*This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was Three Dialogues on Identity, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.Sequence reruns are a community-driven effort. You can participate by re-reading the sequence post, discussing it here, posting the next day's sequence reruns post, or summarizing forthcoming articles on the wiki. Go here for more details, or to have meta discussions about the Rerunning the Sequences series.*

Corroborated by this peer-reviewed article, published two days ago in Physical Review Letters:

Link:

Physical Review Letters 108, 11. April 2012.Actually, that's still factorizable. You just need to change basis to the diagonal. Effectively, you're treating them as one particle. The other dimension is their relative motion, and 'being a particle' corresponds to one value in that dimension.

The ability to make this transformation is why we can speak of protons and neutrons and atoms and quasiparticles. And bricks.

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 ifthe 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.In the model we suppose that the particles are attracted to each other. So what exactly does this sentence mean -- that if both particles have wide amplitude spread, they somehow stop attracting each other?

I would expect that even if we start with a system "a positive article can be anywhere, a negative particle may be anywhere", it would develop towards "positive and negative particles anywhere, but probably close to each other". Wouldn't that make a dark-gray line?

Please help.

EDIT: Found this.