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Authors = 't hooft
Journal = Universe

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12 pages, 271 KB  
Article
Quantum Clones inside Black Holes
by Gerard ’t Hooft
Universe 2022, 8(10), 537; https://doi.org/10.3390/universe8100537 - 18 Oct 2022
Cited by 30 | Viewed by 26782
Abstract
A systematic procedure is proposed for better understanding the evolution laws of black holes in terms of pure quantum states. We start with the two opposed regions I and II in the Penrose diagram, and study the evolution of matter in these [...] Read more.
A systematic procedure is proposed for better understanding the evolution laws of black holes in terms of pure quantum states. We start with the two opposed regions I and II in the Penrose diagram, and study the evolution of matter in these regions, using the algebra derived earlier from the Shapiro effect in quantum particles. Since this spacetime has two distinct asymptotic regions, one must assume that there is a mechanism that reduces the number of states. In earlier work we proposed that region II describes the angular antipodes of region I, the ‘antipodal identification’, but this eventually leads to contradictions. Our much simpler proposal is now that all states defined in region II are exact quantum clones of those in region I. This indicates more precisely how to restore unitarity by making all quantum states observable, and in addition suggests that generalisations towards other black hole structures will be possible. An apparent complication is that the wave function must evolve with a purely antisymmetric, imaginary-valued Hamiltonian, but this complication can be well-understood in a realistic interpretation of quantum mechanics. Full article
(This article belongs to the Section Foundations of Quantum Mechanics and Quantum Gravity)
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16 pages, 322 KB  
Article
The Black Hole Firewall Transformation and Realism in Quantum Mechanics
by Gerard ’t Hooft
Universe 2021, 7(8), 298; https://doi.org/10.3390/universe7080298 - 13 Aug 2021
Cited by 16 | Viewed by 11257
Abstract
A procedure to derive a unitary evolution law for a quantised black hole has been proposed by the author. The proposal requires that one starts off with the entire Penrose diagram for the eternal black hole as the background metric, after which one [...] Read more.
A procedure to derive a unitary evolution law for a quantised black hole has been proposed by the author. The proposal requires that one starts off with the entire Penrose diagram for the eternal black hole as the background metric, after which one has to invoke the antipodal identification in order to see how the two asymptotic domains of this metric both refer to the same outside world. In this paper, we focus on the need to include time reversal in applying this identification. This forces us to postulate the existence of an ‘anti-vacuum’ state in our world, which is the state where energy density reaches a maximal value. We find that this squares well with the deterministic interpretation of quantum mechanics, according to which quantum Hilbert space is to be regarded as the ‘vector representation’ of a real world. One has to understand how to deal with gravity in such considerations. The non-perturbative component of the gravitational force seems to involve cut-and-paste procedures as dynamical features of space and time, of which the re-arrangement of space-time into two connected domains in the Penrose diagram is a primary example. Thus, we attempt to obtain new insights in the nature of particle interactions at the Planck scale, as well as quantum mechanics itself. Full article
(This article belongs to the Special Issue Quantum Field Theory)
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