Collapse of the wavefunction, the information paradox and backreaction

Modak, Sujoy K.; Sudarsky, Daniel

doi:10.1140/epjc/s10052-018-6032-5

“…In any case, in one or other of these variants, semiclassical gravity continues to be of great interest, and has been applied to problems or inspired studies in black hole physics [49,50,58,78,80,102], cosmology [13,16,20,23,45,61,77,[89][90][91], cosmic censorship [11,12,19,24,55,56,59,64], quantum inequalities and singularity theorems [27-30, 30, 35, 37, 39], the ruling-out of faster-than-light communication and time travel [14,15,34,38,51,68,69], etc. Conceptual questions have been addressed, for instance, in [73,80,86,99], while the mathematical structure of the theory has been studied e.g. in [20, 35, 36, 45, 62, 63, 65, 77, 79, 86, 90-92, 95, 97].…”

Section: Jcap01(2023)040mentioning

confidence: 99%

On the initial value problem for semiclassical gravity without and with quantum state collapses

Juárez-Aubry

¹

,

Kay

²

,

Miramontes

³

et al. 2023

J. Cosmol. Astropart. Phys.

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Semiclassical gravity is the theory in which the classical Einstein tensor of a spacetime is coupled to quantum matter fields propagating on the spacetime via the expectation value of their renormalized stress-energy tensor in a quantum state. We explore two issues, taking the Klein Gordon equation as our model quantum field theory. The first is the provision of a suitable initial value formulation for the theory. Towards this, we address the question, for given initial data consisting of the classical metric and its first three 'time' derivatives off the surface together with a choice of initial quantum state, of what is an appropriate 'surface Hadamard' condition such that, for initial data for which it is satisfied it is reasonable to conjecture that there will be a Cauchy development whose quantum state is Hadamard. This requires dealing with the fact that, given two points on an initial surface, the spacetime geodesic between them does not, in general, lie on that surface. So the (squared) geodesic distance that occurs in the Hadamard subtraction differs from that intrinsic to the initial surface. We handle this complication by expanding the former as a suitable 3-dimensional covariant Taylor expansion in the latter. Moreover the renormalized expectation value of the stress-energy tensor in the initial surface depends explicitly on the fourth, 'time', derivative of the metric, which is not part of the initial data, but which we argue is given, implicitly, by the semiclassical Einstein equations on the initial surface. (The rôle played by those equations also entails that the surface Hadamard condition subsumes the constraints.) We also introduce the notion of physical solutions, which, inspired by a 1993 proposal of Parker and Simon, we define to be solutions which are smooth in ħ at ħ = 0. We conjecture that for these solutions the second and third time derivatives of the metric will be determined once the first and second time derivatives are specified. We point out that a simpler treatment of the initial value problem can be had if we adopt yet more of the spirit of Parker and Simon and content ourselves with solutions to order ħ which are Hadamard to order ħ. A further simplification occurs if we consider semiclassical gravity to order ħ 0. This resembles classical general relativity in that it is free from the complications of higher derivative terms and does not require any Hadamard condition. But it can still incorporate nontrivial quantum features such as superpositions of classical-like quantum states of the matter fields. Our second issue concerns the prospects for combining semiclassical gravity with theories of spontaneous quantum state collapse. We will focus our attention on proposals involving abrupt changes in the quantum field state which occur on certain (random, non-intersecting) Cauchy surfaces according to some — yet to be developed — generally covariant objective collapse model but that, in between such collapse surfaces, we have a physical semiclassical solution (or a solution of order O(ħ) or a solution of order O(ħ 0)). On each collapse surface, the semiclassical gravity equations will necessarily be violated and, as Page and Geilker pointed out in 1981, there will therefore necessarily be a discontinuity in the expectation value of the renormalized stress-energy tensor. Nevertheless, we argue, based on our conjecture about the well-posedness of the initial value problem for physical solutions, that, with a suitable rule for the jump in the metric and/or the extrinsic curvature, the time evolution will still be uniquely determined. We tentatively argue that a natural jump rule would be one in which the metric itself and the transverse traceless part of the extrinsic curvature will be continuous and the jump will be confined to the remaining parts of the extrinsic curvature. We aid and complement our discussion by studying our two issues also in the simpler cases of a semiclassical scalars model and semiclassical electrodynamics.

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“…In any case, in one or other of these variants, semiclassical gravity continues to be of great interest, and has been applied to problems or inspired studies in black hole physics [47,48,75,96,73], cosmology [12,15,19,22,43,57,72,84,85,86], cosmic censorship [10,11,18,23,53,54,55,60], quantum inequalities and singularity theorems [33,26,27,28,29,29,35,37], the ruling-out of faster-than-light communication and time travel [13,14,32,36,49,65,64], etc. Conceptual questions have been addressed in [75,68,81,93], while the mathematical structure of the theory has been studied e.g. in [19,43,72,85,86,…”

Section: Introductionmentioning

confidence: 99%

On the initial value problem for semiclassical gravity without and with quantum state collapses

Juárez-Aubry¹,

Kay²,

Miramontes³

et al. 2022

Preprint

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0

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Semiclassical gravity is the theory in which the classical Einstein tensor of a spacetime is coupled to quantum matter fields propagating on the spacetime via the expectation value of their renormalized stress-energy tensor in a quantum state. We explore two issues, taking the Klein Gordon equation as our model quantum field theory. The first is the provision of a suitable initial value formulation for the theory. Towards this, we address the question, for given initial data consisting of the classical metric and its first three 'time' derivatives off the surface together with a choice of initial quantum state, of what is an appropriate 'surface Hadamard' condition such that, when the relevant constraint equations hold too, it is reasonable to conjecture that there will be a Cauchy development whose quantum state is Hadamard. This requires dealing with the fact, that given two points on an initial surface, the spacetime geodesic between them does not, in general, lie in that surface. So the geodesic distance that occurs in the Hadamard subtraction differs from the geodesic distance intrinsic to the initial surface. We handle this complication with a suitable 3dimensional covariant Taylor expansion. Moreover the renormalized expectation value of the stress-energy tensor in the initial surface depends explicitly on the fourth 'time' derivative of the metric, which is not part of the initial data, but which we argue is given, implicitly, by the semiclassical Einstein equations on the initial surface. We also introduce the notion of physical solutions, which, inspired by a 1993 proposal of Parker and Simon, we define to be solutions which are smooth in at = 0 -and conjecture that, for these, the second and third time derivatives of the metric will be determined by the remaining initial data. Finally we point out that a simpler treatment of the initial value problem can be had if we adopt yet more of the spirit of Parker and Simon and content ourselves with solutions to order which are Hadamard to order . A further simplification occurs if we consider semiclassical gravity to order 0 . This resembles classical general relativity in that it is free from the complications of higher derivative terms and does not require any Hadamard condition. But it can still incorporate nontrivial quantum features such as superpositions of classical-like quantum states of the matter fields. Our second issue concerns the prospects

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“…Having a model calculation for the formation of a black hole and its evaporation including quantum effects induced by horizon fluctuations would be very useful to gain greater understanding of this process. Alternative ansatze have been proposed to solve this difficult problem, proposing that the information goes to another universe [9], subtly changing the rules of quantum mechanics [10,11], proposing quantum information theory and tools such as relativistic quantum information as key to avoid unnecessary contradictions in the process of information retrieval process [12][13][14]. Departures from thermality have also been associated to partial recovery of the information of the black hole forming structures [15,16].…”

Section: Introductionmentioning

confidence: 99%

“…Two-dimensional models of black holes were introduced some twenty five years ago [18][19][20][21][22]. Even though they are simpler than the four-dimensional case, most of the previously mentioned problems are still present [10,11,16,[23][24][25][26], and a complete quantum analysis of a collapsing system is still lacking. In this paper we start the study of a collapsing quantum shell of matter in two dimensions.…”

Section: Introductionmentioning

confidence: 99%

Quantum fluctuating CGHS geometries and the information paradox

Eyheralde¹,

Campiglia²,

Gambini³

et al. 2019

Class. Quantum Grav.

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We study Hawking radiation on the quantum spacetime generated by a quantum ingoing null shell in the 2d theory proposed by Callan-Giddings-Harvey-Strominger (CGHS). The quantum spacetime is a superposition of classical geometries with uncertainty in position and momentum of the collapsing shell. The Hawking radiation spectrum is computed, revealing a non-thermal behaviour for finite time as well as a dependence on the shell's physical degrees of freedom. Hawking radiation's dependence on the collapsing shell becomes irrelevant in the late time approximation as we reach i + since the radiation's temperature depends exclusively on the cosmological constant. However, we argue that the information of the quantum state of a collapsing shell can be read from the Hawking radiation if we perform measurements at I + R taking into account backreaction effects. *

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Collapse of the wavefunction, the information paradox and backreaction

Cited by 5 publications

References 55 publications

On the initial value problem for semiclassical gravity without and with quantum state collapses

On the initial value problem for semiclassical gravity without and with quantum state collapses

On the initial value problem for semiclassical gravity without and with quantum state collapses

Quantum fluctuating CGHS geometries and the information paradox

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