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Self-gravitating interferometry and intrinsic decoherence Gooding, David William Francisco

Abstract

To investigate the possibility that an intrinsic form of gravitational decoherence can be theoretically demonstrated within canonical quantum gravity, we develop a model of a self-gravitating interferometer, and analyze the WKB regime of its reduced phase space quantization. We search for evidence in the resulting interference pattern that general relativity necessarily places limits on coherence, due to the inherent ambiguity associated with forming superpositions of geometries. We construct the "beam" of the interferometer out of WKB states for an infinitesimally thin shell of matter, and work in spherical symmetry to eliminate the occurrence of gravitational waves. For internal consistency, we encode information about the beam optics within the dynamics of the shell itself, by arranging an ideal fluid on the surface of the shell with an equation of state that enforces beam-splitting and reflections. The interferometric analysis is performed for single-mode inputs, and coherence is shown to be fully present regardless of gravitational self-interaction. Next we explore the role coordinate choices play in our description of the interferometer, by considering a family of generalized coordinate systems and their corresponding quantizations. Included in this family are the Painleve-Gullstrand coordinates, which are related to a network of infalling observers that are asymptotically at rest, and the Eddington-Finkelstein coordinates, which are related to a network of infalling observers that travel at the speed of light. We then introduce another model, obtained by adding to the shell a harmonic oscillator as an internal degree of freedom. The internal oscillator evolves with respect to the local proper time of the shell, and therefore serves as a clock that ticks differently depending on the shell's position and momentum. If we focus only on the external dynamics, we must trace out the clock degree of freedom, and this results in a form of intrinsic decoherence that shares some features with a recently-proposed "universal" decoherence mechanism attributed to gravitational time dilation. We discuss some variations of this proposal, and point out a way to bootstrap the gravitational contribution to the time dilation decoherence with self-gravitation. We interpret this as a fundamentally gravitational intrinsic decoherence effect.

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Attribution-NonCommercial-NoDerivs 2.5 Canada

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