Open thread, August 5-11, 2013

David_Gerard

If it's worth saying, but not worth its own post (even in Discussion), then it goes here.

Can somebody explain a particular aspect of Quantum Mechanics to me?

In my readings of the Many Worlds Interpretation, which Eliezer fondly endorses in the QM sequence, I must have missed an important piece of information about when it is that amplitude distributions become separable in timed configuration space. That is, when do wave-functions stop interacting enough for the near-term simulation of two blobs (two "particles") to treat them independently?

One cause is spatial distance. But in Many Worlds, I don't know where I'm to understand these other worlds are taking place. Yes, it doesn't matter, supposedly; the worlds are not present in this world's causal structure, so an abstract "where" is meaningless. But the evolution of wavefunctions seems to care a lot about where amplitudes are in N-dimensional space. Configurations don't sum unless they are the same spatial location and are representing the same quark type, right?

So if there's another CoffeeStain that splits off based on my observation of a quantum event, why don't the two CoffeeStains still interact, since they so obviously don't? Before my two selves became decoherent with their respective quantum outcomes (say, of a photon's path), the two amplitude blobs of the photon could still interact by the book, right? On what other axis has I, as a member of a new world, split off that I'm a sufficient distance from my self that is occupying the same physical location?

Relatedly, MWI answers "not-so-spooky" to questions regarding the entanglement experiment, but a similar confusion remains for me. Why, after I observe a particular polarization on my side of the galaxy and fly back in my spaceship to compare notes with my buddy on the other side of the galaxy, do I run into one version of him and not the other? They are both equally real, and occupying the same physical space. What other axis have the self-versions separated on?

First: check this out.

Second: Suppose I want to demonstrate decoherence. I start out with an entangled state - two electrons that will always be magnetically aligned, but don't have a chosen collective alignment. This state is written like |up, up> + |down, down> (the electrons are both "both up" and "both down" at the same time; the |> notation here just indicates that it's a quantum state).

Now, before introducing decoherence, I just want to check that I can entangle my two electrons. How do I do that? I repeat what's cal... (read more)

2Emile13y

(Warning: I am not a physicist; I learnt a bit of about QM from my physics classes, the Sequences, Feynmann Lectures on Physics, and Good and Real, but I don't claim to even understand all that's in there) I'm not sure I totally understand your question, but I'll take a stab at answering: The important thing is configuration space, and spatial distance is just one part of that; there is just one configuration space over which the quantum wave-function is defined, and points in configuration space correspond to "universe states" (the position, spin, etc. of all particles). So two points in configuration space A and B "interfere" if they are similar enough that both can "evolve" into state C, i.e. state C's amplitude will be function of A and B's amplitudes. The more different A and B are, the less likely they are to have shared "descendant states" (or more precisely, descendant states of non-infinitesimal amplitude), so the more they can be treated like "parallel branches of the universe". Differences between A and B can be in psychical distance of particles, but also of polarity/spin, etc. - as long as the distance is significant on one axis (say spin of a single particle), physical distance shouldn't matter. I think spin could be an example of "another axis" you're looking for (though even thinking in terms of Axis may be a bit misleading, since all the attributes aren't nice and orthogonal like positions in cartesian space).

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Open thread, August 5-11, 2013

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Open thread, August 5-11, 2013

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