Since that time, I was returning to my onetime tempting ideas that the dark hole complementarity – the dependence relating the dark hole interior as well as the dark hole exterior – could live much simpler than nosotros thought, given past times some formula, as well as that this formula could live rationally justifiable or provable past times a rock-solid, physically understandable, nearly rigorous argument.
This viewpoint was energized yesterday when John Preskill tweeted:
Beni Yoshida explains that decoding the Hawking radiations emitted past times a dark hole is easier than nosotros thought. #QEC17
— John Preskill (@preskill) September 14, 2017
Recall that Beni Yoshida is a Japanese quantum gravity adept who explained the relationship of quantum gravity as well as error-correcting codes inward his 2015 TRF weblog post.
Now, Preskill referred to a Quantum Error Correction conference that is ending inward Maryland today. If yous discovery the verbalize or a relevant newspaper past times Yoshida, I volition live really interested.
For years, I thought that "with some clarifications", the dark hole interior operators could be some analytic continuations of those outside. We know that this can't live quite truthful inward the Rindler space. If yous trace the Minkowski infinite as well as position some coordinates \(r^2=x^\mu x_\mu\) as well as \({\rm tanh}\,\eta=t/z\) as well as wedges, yous could also order that e.g. the wedge amongst \(z\lt 0\) is an analytic continuation of the wedge amongst \(z \gt 0\) to some complex values of the rapidity \(\eta\).
That sounds groovy but the devil is inward the details. We know that the operators inward the ii wedges should live completely independent of each other as well as commuting amongst each other – because they are spacelike separated. H5N1 related, mayhap complementary, work is that the operators shouldn't actually live expected to live really smooth, analytic functions of the coordinate \(\eta\), or other coordinates.
I believe that the dark hole interior must accept some really specific belongings that allows to position these ii problems. Exactly when yous take in the dark hole interior as well as non the empty Rindler space, some variety of a uncomplicated continuation similar to i proposed higher upward could dice right as well as justifiable. And maybe it's non an analytic continuation, afterwards all.
Instead, in that place could be some functional formula relating the operators inward the dark hole spacetime that follows from the assumptions virtually the dark hole spacetime as well as that relates the operators within as well as outside. What could it be? Look at the Penrose diagram of an evaporating neutral dark hole above.
There is some singularity as well as I believe that yous shouldn't actually assume much virtually it. The spacetime fields cease to live applicable somewhere close the singularity but the precise house or 2nd when it happens is impossible to define. On the other hand, aspect at the corner at the right endpoint of the teeth-like singularity. It's the upshot where the already nearly evaporated dark hole finally disappears. And from that upshot to the top, the empty Minkowski spacetime continues. Let me telephone telephone this betoken \(Y\) because it appears close "y" of the discussion "singularity" on the picture. It's the intersection of the singularity amongst the post-black-hole Minkowski spacetime – which also happens to live the latest betoken of the upshot horizon.
Is this causal diagram unavoidable for a given development of the dark hole spacetime? Should it live generalized? And whatsoever are the answers and/or the generalization, doesn't the status that the futurity spacetime looks similar "this", or has some of these features, stand upward for some status constraining the patch operators exterior as well as within the dark hole?
Recall that I accept said that inward the Rindler infinite – or the Minkowski infinite – operators are non actually analytic functions of the spacetime coordinates. If in that place is some human relationship betwixt the interior as well as exterior operator that tin live derived inward the truthful dark hole spacetimes but non inward the empty Minkowski or Rindler space, it should live because the dark hole spacetime makes the fields somewhere, in all probability close the horizon or roughly its "last point" discussed above, to a greater extent than analytic than it is inward the representative of the empty spacetime. Or in that place should live some status on the operators maxim that "the development of the fields is compatible amongst a peaceful disappearance of the dark hole including the singularity".
In particular, I mean value that the singularity could generically stay "very singular" fifty-fifty if yous aspect at the right halt of the singular teeth inward the causal diagram above. I am non quite certain virtually this betoken – the dark hole is getting smaller equally it evaporates, as well as and then does the "absolute magnitude" of the singular damage inward the fields, but maybe the relative size of the singular as well as non-singular damage is what matters as well as must dice to zero. But close the betoken \(Y\), if this gauge is right, the singularity is obliged to "desingularize itself", to allow the being of the shine spacetime afterwards the dark hole has evaporated, as well as this weather may nontrivial relate the patch operators at before times, too.
The status on the fields at some spell could order that "the lastly 2nd \(Y\) of the dark hole that yous larn past times evolving the spacetime to the futurity has some potentially singular quantities equal to zero". And this is the status that could order that inward some sense, the interior fields are some continuations of the exterior fields, afterwards all.
When yous integrate out the fields inward the left wedge of the Rindler space, yous larn the Unruh thermal radiations inward the right wedge. The integration out is equivalent to the ignorance virtually some phases of the fields and/or creation as well as annihilation operators. It could live just these phases that are determined past times the status of the "smooth halt of the dark hole at betoken \(Y\)" that I accept discussed above.