[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.