NYTimes.com: Physicists Create ‘the Smallest, Crummiest Wormhole You Can Imagine’
John Clark
Physicists Create ‘the Smallest, Crummiest Wormhole You Can Imagine’
Scientists used a quantum computer to explore the ultimate escape route from a black hole.
https://www.nytimes.com/2022/11/30/science/physics-wormhole-quantum-computer.html?unlocked_article_code=XVtb5GbqAJCKuIbVZnZI4V473ClGQirfRORw-8pNMyKoSnL4EZWuXj1j4wi5159aIGiJyTZSPEvRDCM62LhRl5A9WbjjkWgF-oET7FCQ2raR4m1epOMmJNFg8YbPX81Jq7we2tXl9CwQXMdVhKkc4Z8fR0aVuxSdpTQ7xJW5S_bBrB__Mh7FZ6EB4bHE0BpYfPtozmhybaRrwL8fYWeI2aHqPcF58OopNfMmJjstAyD2AWeAyfe8T4CVCw8cT03lMfSu6mRqHViaNHLTguF21k9cDj0uOk73P-LW0-ig1qNiChI4b5MSx-L6z4ruwNp_nkG5U6QyucfWhWeim2ViVipeoPFu3p1TToB5&smid=em-share
Lawrence Crowell
spudb...@aol.com
Lawrence Crowell
There has been a lot of buzz over the supposed creation of a wormhole in a quantum computer. I am going to comment on this from a middle ground perspective. There are those who have condemned this as absolute nonsense, Peter Woit for instance, and a lot of science media attention filled with hype. I want to give some idea on what this is about and how on the one hand this is an important result, but on the other hand we do not have a real wormhole that we can travel across the universe with. In the end this is just a demonstration of how quantum mechanics and general relativity have a correspondence. Here the entanglement of many states has properties corresponding to spacetime physics. This fairly remarkable.
This experiment published in https://www.nature.com/articles/s41586-022-05424-3 involves an extension of the ER = EPR result of Maldacena and Susskind from nontraversable to traversable wormholes. Below a discussion on the role of ER = EPR with respect to the conservation of quantum information is given. The truncated Penrose diagram illustrates a green region with fields interior to the black hole entangled with fields in the interior. However, after the Page time this region splits into the interior island, states entangled with the observer and the exterior states.
On arXiv:2006.06872 the paper "The entropy of Hawking radiation" by A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, A. Tajdini examins this problem by looking at a new approach to the entropy of a black hole. A method for computing the fine-grained entropy of a black hole is employed to compute entropy of Hawking radiation. This technique extends the Bekenstein entropy S = k A/4ℓ_p^2 into S = k A/4L_p^2 + 〈 quantum corrections 〉 so for small black hole these are corrections that maintain unitary evolution of black hole dynamics and quantum evaporation.
This is a way to use Cardy's 4-dimensional conformal geometry. The Penrose diagram, taken from the paper by Almeheiri et al is show in figure 2. After the page time the geometry is like what occurs to an observer in the pure Penrose diagram. Nothing is labelled, but the island of interior entangled states is identified with the left-hand blue region. The QES is the left vertex between the blue and green where the additional particle is localized, and the right vertex is the later Hawking particle.
This is to be compared to Susskind’s ER = EPR hypothesis for a nontraversable wormhole, or a pure conformal black hole. This is a theory to two entangled blackholes that share the same interior. The unlabeled diagram shows the black hole interior as the upper triangle, while the lower triangle is the white hole. The two squares on the left and right are two exterior regions or “universes” which contain a black hole. The two interior regions, black hole and white hole, have analogues to the absorption and emission of particles and their operators b and b^†. The white hole produces radiation, and the black hole absorbs it. Susskind’s hypothesis is that this is a form of quantum entanglement, and that particles emitted by the black hole on the right are entangled with this alternative region.
The two diagrams are not mapped into each other. The one below is for a pure spacetime region without matter sources for the black hole, while the above is not conformally equivalent on the left. This truncated Penrose diagram removes the white hole, which we do not expect to exist on a large scale, and changes the topology of the spacetime. There is a timelike boundary on the left and a I^+, I^- null boundary on the right. The two have inequivalent information or are not conformally equivalent. What is needed is gravitational radiation associated with the backreaction of the metric.
We may interpret the gravitational information propagated to I^+ is carries the topology of the pure vacuum solution. The truncated diagram has gravitational waves propagating to the I^+ boundary, and this carries the topological quantum numbers that defines the pure vacuum solution. In work that I did this role for gravitational information is shown to play a role https://www.frontiersin.org/articles/10.3389/fphy.2022.734199/full In the end the Susskind “octopus” of wormhole based entanglements are carried in a spacetime manner by gravitons. A bipartite entanglement of a qubit with a black hole is a 4-entanglement, where the other two quantum units are in the polarization directions of a weak graviton. This theory is approximately workable for weak gravitons that are linear and obey a Schrödinger equation. In the UV limit this theory will break down.
The most important feature of wormholes in the ER = EPR paradigm is that quantum information is conserved. The simplest way to think of this is that an EPR pair, where one enters a black hole, never fundamentally loses entanglement. The exterior qubit become entangled with the black hole. The exterior observer, say Bob, loses contact with Alice and her state, but this is not what happens from the standpoint of Alice. The two descriptions are a matter of reference frame and are not fundamentally important. If Alice attempts to teleport a state to Bob, Bob can never receive a signal pertaining to the setting of an apparatus in order to properly read the teleported state. Bob, however, can teleport a state to Alice. This issue pertains to causal domains in spacetime, where a black hole is a trapped region bounded by a congruence of null rays, called the event horizon. Quantum entanglement is independent of causality.
To consider this experiment in particular this does involve a quantum computer entanglement experiment that has an ER = EPR correspondence with a wormhole. Further, a phase shift on qubits simulates the negative energy condition. This involves 2^7 = 512 qubits, which is far from the N → ∞ of the SYK theory. This is the nontraversable wormhole. What follows is the SYK theory for a traversable wormhole. A traversable wormhole requires a negative vacuum energy, or a violation of the averaged weak energy condition T^{00} ≥ 0. This might be arranged with a Casimir cavity with a confined vacuum that has a lower energy than the vacuum of free space. This is emulated by a magnetic field induce shift of qubits. Kip Thorne has even suggested using this as a way to pull a wormhole out of the vacuum. A sparse matrix-like method in 2 spatial dimensions resulted in a signature of the occurrence of a transported quantum bit, like what is expected from a wormhole.
This result is interesting from an academic perspective, for it indicates a correspondence between quantum states and spacetime physics. This is very far from generating a real wormhole in spacetime. This does illustrate how quantum states have a dualism with spacetime physics, which is interesting since the nonlinearity of spacetime makes quantum mechanics problematic. From that perspective this is an interesting result. This is though very far from any spacetime engineering of a wormhole.
LC
Brent Meeker
Google’s Sycamore chip: no wormholes, no superfast classical simulation either
December 2nd, 2022
https://scottaaronson.blog/
Brent
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