[zmgsabst]

Is it that hard to talk about?

A tangle in the interior of a cylinder loses information when viewed on the boundary because you lose a dimension (ie, the shadow cast by string around a light bulb as you see it on the lamp shade). You then have to allocate probabilities to pseudoknot resolutions (ie, guesses about crossings). So you end up with something that looks like continuous geometry on the inside and quantized statistics about interactions on the boundary.

Entanglement looks like taking two filaments in a plasma globe and moving one in a circle around the other. Their ribbons are now tangled. (As a 2+1-D analog.)

[zachf]

Respectfully, your metaphor doesn’t bear any similarity to the way AdS/CFT works. In AdS/CFT there are dual quantum systems with no information loss. A bit more precisely, the correspondence relates the partition functions of quantum gravity in AdS with the partition functions of conformal fields. This implies the existence of a map between the two, which in this case happens to be extremely complex and nonlocal.

Another way of saying it is that the two descriptions are different representations of the same object. There is no projection or information lost in switching between descriptions.

[zmgsabst]

Yes — that non-locality on the surface is because the braiding structure is non-local when projected.

You are correct and I misspoke:

You don’t lose the information, it becomes non-local on the surface — and so if you’re building a model of the interior from a local sampling of the surface, you get a statistical model built on pseudoknots (again, like a shadow from a lamp).

[zachf]

I think it proves my point that AdS/CFT is hard to talk about :) I’ve still got mixed feelings about the lamp/shadow analogy but thanks for the clarification.

[zmgsabst]

Sure — just one last thought:

The thread-lamp model isn’t arbitrary; ultimately, we’re looking for some kind of tangle model that rescues geons. So we’re going to need something that looks like continuous tangles on the inside and Feynman diagrams on the outside.