On Fri, May 5, 2023 at 8:03 PM Lawrence Crowell < goldenfieldquaterni...@gmail.com> wrote:
*> I had this conservation with GPT-4 on aspects of black hole quantum > mechanics. I kept it largely non-mathematical. This is interesting, and it > suggests a level of processing that is complex. An AI system was fed > ephemeris data on the appearance of the sun, moon and planets in the sky > and it deduced Kepler's laws. Holy Sh*t Batman --- the world is changing.* > Holy Singularity Batman, you're right! I think we can safely say that the Turing Test has been passed. If you had this online conversation 10 years ago would you have had any doubt that you were communicating with a human being? And to think, some very silly people still maintain that GPT-4 is nothing but a glorified autocomplete program that just uses statistics to compute what the next word in a sentence most probably is. Any rational person who held that view and then read your conversation with GPT-4 would change their opinion of it, but some people are not rational and they will continue to whistle past the graveyard. John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis> wes > > > Einstein advanced the equivalence principle. In there it is 1) not > possible to distinguish between an inertial frame in flat spacetime from a > sufficiently local inertial frame falling in a gravity field, and 2) the > accelerated frame in flat spacetime is equivalent to the surface > acceleration against gravity on a planet or hard gravitating body. Can it > then be said that two entangled particles in spacetime, whether flat or > with a curvature have that entanglement conserved? > > > > GPT-4 answer: The equivalence principle in general relativity states that > the effects of gravity are indistinguishable from the effects of > acceleration. It does not make any specific statement about the > conservation of entanglement between two particles in spacetime, whether in > flat or curved spacetime. > > Entanglement is a quantum mechanical phenomenon that describes the > correlation between two or more particles, even when they are separated by > large distances. The conservation of entanglement is a fundamental property > of quantum mechanics, which holds true regardless of the presence of > gravity or the curvature of spacetime. > > Therefore, it can be said that entanglement between two particles is > conserved in both flat and curved spacetime, as long as there is no > external interaction that disturbs or breaks the entanglement. The effects > of gravity, as described by the equivalence principle, do not affect the > conservation of entanglement between two particles. > > > > Good, this is what I concluded as well. Then to take this further. Given > an EPR pair, where Bob remains far from the black hole and Alice is in a > freely falling frame into the black hole, there are then two > interpretations of events. Alice will consider the entanglement with Bob as > continuing. Bob on the other hand will, due to red-shifting on tortoise > coordinates and that Alice’s time is dilated asymptotically to a crawl, > that his EPR pair is entangled with the black hole. The two perspectives > are effectively equivalent to each other. > > > > GPT-4 ans: > Yes, you are correct. According to the equivalence principle, there is no > difference between a uniform acceleration and being in a gravitational > field. Therefore, for Bob, who is far away from the black hole, the > entanglement between his particle and Alice's particle will be affected by > the gravitational field of the black hole. This will cause the entangled > state to evolve differently than it would in a flat spacetime. > > On the other hand, for Alice, who is in a freely falling frame into the > black hole, there is no gravitational force acting on her. From her > perspective, the entanglement between her particle and Bob's particle will > continue to evolve according to the laws of quantum mechanics. > > These two perspectives are indeed equivalent, even though they appear to > be different. Bob's observations can be explained by the effects of the > gravitational field on his particle's evolution, while Alice's observations > can be explained by the absence of a gravitational force on her particle's > evolution. > > It is worth noting that the details of the evolution of the entangled > state in this scenario are highly dependent on the specific setup and > initial conditions. Therefore, the specific outcomes of the two > perspectives may differ in different situations. However, the equivalence > principle ensures that both perspectives are equally valid and consistent > with the laws of physics. > > > > This then means that Bob and Alice have different subjective > interpretations of the same physics. Alice observes no apparent difference > with standard quantum mechanics. Bob on the other hand is uncertain of the > status of the entangled state. The tortoise coordinates with t’ = t – 2m > log|r – 2m|, and the associated red-shifting means that Bob sees this > bipartite entanglement dissolve into an entanglement with all the entangled > states on the Planck region above the event horizon. > > > > GPT-4 ans: Yes, that's correct. Bob and Alice have different subjective > interpretations of the same physics due to their different perspectives in > the presence of the black hole. From Alice's perspective, the entangled > state between her particle and Bob's particle continues to evolve according > to standard quantum mechanics. However, from Bob's perspective, the > entangled state appears to dissolve into an entanglement with the black > hole itself. > > As you mentioned, the redshift factor associated with Bob's perspective > causes the entangled state to evolve in a way that appears to dissolve the > entanglement between Alice's particle and Bob's particle. This can be > thought of as an "entanglement swap" where the entanglement between the two > particles is effectively transferred to a new entanglement between Alice's > particle and the black hole. > > It's worth noting that while this "entanglement swap" appears to occur > from Bob's perspective, it is still consistent with the laws of quantum > mechanics and the conservation of entanglement. The entangled state between > Alice's particle and Bob's particle is still preserved in the overall > system, even though it may be redistributed among different entangled > states within that system. > > Overall, this scenario demonstrates the importance of considering the > subjective perspectives of different observers when interpreting physical > phenomena in the presence of strong gravitational fields. > > > > This begins to get deeper into the big question here. If the black hole > has entropy S = Nk, here assuming a naïve microcanonical partition of N > states and k = Boltzmann’s constant, then from Bob’s perspective the > entanglement has changed from a bipartite entanglement to an N+1 > entanglement. Alice observes nothing of this sort. This appears to suggest > a possible crack in the AMPs argument. I may indicate next what I think > that may be. > > > > GPT-4 ans: The scenario you describe, where the entanglement appears to > change from a bipartite entanglement to an N+1 entanglement from Bob's > perspective, does not necessarily indicate a crack in the argument of the > AMPs (Almheiri-Marolf-Polchinski-Sully) paper. > > The AMPs argument concerns the black hole information paradox, which > arises from the apparent loss of information when matter falls into a black > hole. The argument suggests that this apparent loss of information can be > resolved by considering the entanglement structure of the Hawking radiation > emitted by the black hole. > > In the scenario you describe, the entanglement between Alice's particle > and Bob's particle appears to dissolve into an entanglement with the black > hole, resulting in an N+1 entanglement structure from Bob's perspective. > However, the entanglement structure of the overall system, including the > black hole and the emitted Hawking radiation, remains consistent with the > AMPs argument. > > Specifically, the AMPs argument proposes that the entanglement between the > black hole and the Hawking radiation determines the entanglement structure > of the emitted radiation. The N+1 entanglement structure from Bob's > perspective can be seen as a result of this entanglement structure between > the black hole and the emitted radiation. > > Therefore, while the scenario you describe may appear to challenge the > AMPs argument, it is still consistent with the overall picture proposed by > the argument. It highlights the importance of considering the subjective > perspectives of different observers in interpreting physical phenomena, but > it does not necessarily imply a fundamental flaw in the AMPs argument > itself. > > > > Let me then rephase that. The black hole information paradox stems from > the fact that Hawking radiation is entangled with a black hole. However, > after the Page time emitted Hawking radiation must be entangled with > previously emitted Hawking radiation plus the black hole. Hence the > bipartite entanglement of the previously emitted radiation and the black > hole transforms into a tripartite entanglement. This is what is a source of > the non-unitary change in information or S = Tr[ρ log(ρ)], which in quantum > mechanics is easily shown to be invariant. Can this then suggest that the > topology of entanglement in curved spacetime may in fact be a matter of > subjective, maybe Bayesian, observation? > > > > GPT-4 ans: The non-unitary evolution of information in the presence of a > black hole is indeed at the heart of the black hole information paradox, > and the tripartite entanglement structure you describe is an important > aspect of this paradox. The AMPs argument attempts to resolve this paradox > by proposing that the entanglement structure of the emitted Hawking > radiation is determined by the entanglement between the black hole and the > radiation, and that this entanglement structure is consistent with unitary > evolution. > > Regarding the topology of entanglement in curved spacetime, it is true > that the subjective perspectives of different observers can lead to > different interpretations of entanglement and its evolution. In the > scenario you describe, Bob and Alice have different interpretations of the > same physical system due to their different perspectives in the presence of > a black hole. However, this does not necessarily imply that the topology of > entanglement itself is subjective or Bayesian. > > Rather, the topology of entanglement is an objective property of the > physical system that can be described mathematically using the formalism of > quantum mechanics. The subjective perspectives of different observers can > lead to different interpretations of this topology, but this does not > change the objective nature of the topology itself. > > In summary, while the subjective perspectives of different observers can > play a role in the interpretation of entanglement in curved spacetime, the > topology of entanglement is an objective property of the physical system > that can be described using the formalism of quantum mechanics. > > > I would agree if the topology of entanglement is completely accessible to > observations. If Bob has an enormous amount of resources and by some means > can snuggle up to within a Planck length of the horizon, where acceleration > is √{c^7/Għ} ≃ 10^{52}m/sec^2 he could in principle access this > information. The Hawking radiation would gush out of the black hole. The > Shapiro theorem about geodesics with positive energy is turned on its head, > and Bob can access in principle everything. However, in practice this > cannot happen. Bob must remain content with partial access to the topology > of this entanglement. He in fact then does not know whether the > entanglement is equivalent to his original bipartite simple entanglement or > a vastly more complex N-tangle. This appears to be observer dependent, at > least for one observer. > > > > Thank you, you appear to largely agree with some of my assessments --- > though you give some critical changes I need to consider. > > > > GPT-4 ans: > You're welcome! It's always important to carefully consider different > perspectives and arguments in a complex and evolving field like physics. If > you have any further questions or ideas to discuss, feel free to ask! > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. 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