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Generally covariant dynamical reduction models and the Hadamard condition

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JournalPhysical Review D
DateAccepted/In press - 11 Dec 2017
DateE-pub ahead of print - 17 Jan 2018
DatePublished (current) - 17 Jan 2018
Issue number2
Volume97
Number of pages19
Pages (from-to)1-19
Early online date17/01/18
Original languageEnglish

Abstract

We recall and review earlier work on dynamical reduction models, both non-relativistic and relativistic, and discuss how they may relate to suggestions which have been made (including the matter-gravity entanglement hypothesis of one of us) for how quantum gravity could be connected to the resolution of the quantum-mechanical measurement problem. We then provide general guidelines for generalizing dynamical reduction models to curved spacetimes and propose a class of generally covariant relativistic versions of the GRW model. We anticipate that the collapse operators of our class of models may play a r\^ole in a yet-to-be-formulated theory of semiclassical gravity with collapses. We show explicitly that the collapse operators map a dense domain of states that are initially Hadamard to final Hadamard states -- a property that we expect will be needed for the construction of such a semiclassical theory. Finally, we provide a simple example in which we explicitly compute the violations in energy-momentum due to the state reduction process and conclude that this violation is of the order of a parameter of the model -- supposed to be small. We briefly discuss how this work may, upon further development of a suitable semiclassical gravity theory with collapses, enable further progress to be made on earlier work one of us and collaborators on the explanation of structure-formation in a homogeneous and isotropic quantum universe and on a possible resolution of the black hole information loss puzzle.

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© 2018 American Physical Society

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