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I have added the following commentary. What do you think:
This idea may usefully be compared – and maybe is in parts a way of turning into prose – the Ryu-Takayanagi formula (which has a more well-defined content is a theorem in a class of toy examples), which equates
with
For more on this see at holographic entanglement entropy.
I have further expanded (here) on the relation to the Ryu-Takayanagi formula, pointing out how the Majorana dimer code model of JGPE 19 gives a yet more concrete theorem resembling the “ER = EPR” slogan: They show that the entanglement entropy in a holographic tensor network model is encoded entirely by the underlying chord diagram, where each chord reflects two things at once:
(ER) an entangled pair of qbits at their endpoints on the boundary
(EPR) a geodesic through the hyperbolic bulk.
In the discussion of understanding “ER=EPR” as being about the RT-formula, I have added this remark:
A precursor to this picture is the “bit-thread”-interpretation of entanglement entropy due to Freedman & Headrick 16 (notice the use of “EPR pair” in their Figure 4.)
added pointer to yesterday’s preprint:
(which effectively claims priority on the issue)
made some adjustments to the wording around the referencing of Ryu & Takayanagi, and added the actual reference:
I have expanded the Idea-section a fair bit (here)
Incidentally, I am still fond of the suggestion to think of the slogan “ER = EPR” as like a Zen koan for the hard facts around the Ryu-Takayanagi formula (which I have taken the liberty of linking into the entry). When Peter Shor thinks (here) that this means not taking it seriously this seems to be a misunderstanding of the purpose of Zen koans.
I think Peter Shor’s point is that your point of view of “ER = EPR” as a mere slogan is significantly different from Leonard Susskind’s point of view of “ER = EPR” as some physical phenomena and that this difference in points of view has caused a lot of confusion amongst journalists, who has largely taken to Susskind’s view rather than yours.
I had another look at the “cool horizons” paper (arXiv:1306.0533) to remind myself of how exactly (or rather: how vaguely ;-) the claim is phrased.
This makes me think that a key problem in their presentation may be that it does not seem to become clear (if it is even intended) that the spacetime geometry reflecting any quantum entanglement is that of a holographic bulk, with the entangled quantum physics confined to the boundary wall.
Of course, if one conflates bulk and boundary in the Ryu-Takayanagi story, then it becomes confusing.
(Generally, i am wondering at times how many people really appreciate that all evidence points to us sitting on the “wall of the cave” with much of the holographic quantum gravity discussed these days happening in an unobserved bulk.)
added pointer to:
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