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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.

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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