Holographic Regulation From Threads As Well As Bottlenecks

Matt Headrick in addition to Michael Freedman convey released an interesting newspaper on holography in addition to entanglement:

Bit threads in addition to holographic entanglement

First, I must tell that Matt is at faculty of Brandeis (we've known each other inwards Greater Boston). Michael Freedman is the most senior someone at Station Q (stands for "quantum computing", I guess) of Microsoft Research inwards Santa Barbara. He's the same adult man who received a Fields medal for his contributions to the Poincaré conjecture (now theorem) inwards the 1980s in addition to who co-discovered things similar exotic 4-spheres.

We could tell that they convey proposed a novel mode to visualize the Ryu-Takayanagi (RT) formula every bit an emergent number of a pic with threads connecting points at the boundary (or perchance a holographic surface).




To remind you, the RT formula is a quantitative resultant inside the Van Raamsdonk et al. (who doesn't larn cited) "entanglement is glue" minirevolution. This RT formula formally looks similar the Bekenstein-Hawking law\[

southward = \frac{A}{4G}

\] except that the precise pregnant of the variables is special in addition to optimized for the "geometrical connector of infinite is entanglement" paradigm. Here, nosotros convey a spatial percentage on the boundary \(R\) in addition to desire to determine the entanglement entropy \(S\) betwixt this percentage in addition to the remainder of the boundary. The resultant is given yesteryear the expanse \(A\) of the minimum surface inwards the volume that terminates at the percentage \(R\).




If you lot formulate it inwards this way, it looks similar that you lot outset ask to listing all possible surfaces, detect the minimum one, in addition to only when you lot stair out its area, the key shape of the RT formula may live on formulated. And you lot don't actually know where it came from.

Freedman in addition to Headrick create out to decompose this RT resultant to smaller ones – to "derive it" from simply about to a greater extent than simple axioms. You may run across that Freedman has worked on the "Riemannian flows" inwards the context of the Poincaré conjecture because these flows are everywhere inwards this paper, too.

They endeavor to attach a collection of threads to the percentage \(R\) inwards all possible ways. Each thread is an "information flux tube" that carries i bit. I suppose that they should convey called them wires, in addition to non threads, because such strings should meliorate live on conductors to transfer information. ;-)

According to their story, the "minimum surface" \(A\) appears inwards the entanglement entropy because the minimum is the "bottleneck" where the lowest possible number of wires may live on squeezed in addition to "a chain is only every bit rigid every bit its weakest link", but i must consider the "bottleneck" of the "best" mode to connect \(A\) with other surfaces inwards the same homology class. So the relevant expanse enumerating the entanglement entropy results from simply about "minimum of maxima" or vice versa procedures in addition to I don't desire to larn confused also much.

But the betoken is that assuming the legitimacy of their wires, i may derive why this particular construction of "minimum of maxima" emerges in addition to why it's related to the minimal surfaces of the RT formula. The RT formula is basically derived from 1) the supposition of the wires, in addition to 2) to a greater extent than frequently than non valid considerations close the period of time of data in addition to entanglement.

The appearance of the "bottlenecks" makes it irresistible to cry Raphael Bousso's covariant [holographic] entropy bounds. In the belatedly 1990s, Bousso generalized the Bekenstein bounds to to a greater extent than general, time-dependent spacetimes, using simply about (null) lite sheets in addition to the minimum areas inside them.

First, I can't larn rid of the feeling that because Headrick in addition to Freedman verbalize close the bottlenecks inwards a "proof of holography", they are using a flim-flam that outset appeared inwards Bousso's caput because he had to consider the expanse of the "bottlenecks" of this lite sheets, too. Second, Freedman in addition to Headrick don't verbalize close whatever (null) lite sheets in addition to then this particular is unlike from Bousso's methodology. But maybe they should orient the wires along simply about zilch surfaces at the halt because it's the superior affair to do.

The novel Headrick-Freedman mode to empathize the RT formula is "newer" than things similar Bousso's bounds because the RT formula itself is newer. But I convey non soundless decided whether the overall pic of Headrick in addition to Freedman is conceptually newer or to a greater extent than accurate than the older "pictures of holography". Is it clear that positive progress is existence made?

At the end, I exercise believe that results such every bit the RT formula, the ER-EPR correspondence, in addition to the PR formulae for the dark hole interior fields etc. (and maybe things similar the fuzzball representation of dark hole microstates or additional ideas that are currently known or unknown), with other things, volition live on pretty much "derived" from simply about to a greater extent than simple starting betoken (in this respect, it volition live on similar to Headrick-Freedman) in addition to this derivation volition become far much clearer why all these things are truthful (or why simply about of them are imitation if they are false).

On the other hand, I am non certain whether these wires are actually the novel "elementary edifice blocks", peculiarly because nosotros haven't been shown how they may live on reconciled with the detailed mathematics of string theory yet. If all of string theory could live on reformulated using a dual formalism based on the "wires connecting points at the boundary" in addition to if the prove (or proof) of this duality were given, that would live on an exclusively unlike story.

Incidentally, it seems also plausible to me (but this is fifty-fifty to a greater extent than speculative than all the things above) that if dark holes are added to the configuration, the Headrick-Freedman "threads" (which I called "wires") are basically the same sort of one-dimensional objects (solution-generating strings) that are also used yesteryear Mathur in addition to pals to build fuzzballs. The Mathur fuzz could live on made out of the Freedman-Headrick threads, although i has to alternative a shut topology of them to plough them into a "fuzz". ;-)