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**Kay2018_Article_TheMatter-GravityEntanglementH**735 KB, PDF document

Journal | Foundations of Physics |
---|---|

Date | Submitted - 13 Feb 2018 |

Date | Accepted/In press - 1 Mar 2018 |

Date | E-pub ahead of print - 27 Mar 2018 |

Date | Published (current) - 1 May 2018 |

Issue number | 5 |

Volume | 48 |

Number of pages | 16 |

Pages (from-to) | 542-557 |

Early online date | 27/03/18 |

Original language | English |

I outline some of my work and results (some dating back to 1998, some more recent) on my matter-gravity entanglement hypothesis, according to which the entropy of a closed quantum gravitational system is equal to the system's matter-gravity entanglement entropy. The main arguments presented are: (1) that this hypothesis is capable of resolving what I call the second-law puzzle, i.e.\ the puzzle as to how the entropy increase of a closed system can be reconciled with the asssumption of unitary time-evolution; (2) that the black hole information loss puzzle may be regarded as a special case of this second law puzzle and that therefore the same resolution applies to it; (3) that the black hole thermal atmosphere puzzle (which I recall) can be resolved by adopting a radically different-from-usual description of quantum black hole equilibrium states, according to which they are total pure states, entangled between matter and gravity in such a way that the partial states of matter and gravity are each approximately thermal equilibrium states (at the Hawking temperature); (4) that the Susskind-Horowitz-Polchinski string-theoretic understanding of black hole entropy as the logarithm of the degeneracy of a long string (which is the weak string coupling limit of a black hole) cannot be quite correct but should be replaced by a modified understanding according to which it is the entanglement entropy between a long string and its stringy atmosphere, when in a total pure equilibrium state in a suitable box, which (in line with (3)) goes over, at strong-coupling, to a black hole in equilibrium with its thermal atmosphere. The modified understanding in (4) is based on a general result, which I also describe, which concerns the likely state of a quantum system when it is weakly coupled to an energy-bath and the total state is a random pure state with a given energy. This result generalizes Goldstein et al.'s 'canonical typicality' result to systems which are not necessarily small.

© The Author(s) 2018. Written version of talk given at 18th UK and European Conference on Foundations of Physics (16-18 July 2016, LSE, London, UK). To appear in 'Foundations of Physics' Special Issue entitled "Philosophical Aspects in the Foundations of Physics" (Guest editors: Harvey Brown, Klaas Landsman, Miklos Redei.)

- Matter-gravity entanglement, Information loss , String theory approach to black hole entropy, Gravitational decoherence, Second law of thermodynamics, Canonical typicality

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