Unitarity and information in quantum gravity: a simple example
Résumé
In approaches to quantum gravity, where smooth spacetime is an emergent approximation of a discrete Planckian fundamental structure, any effective smooth field theoretical description would miss part of the fundamental degrees of freedom and thus break unitarity. This is applicable also to trivial gravitational field (low energy) idealizations realized by the use of the Minkowski background geometry which, as any other spacetime geometry, corresponds, in the fundamental description, to infinitely many different and closely degenerate discrete microstates. The existence of such microstates provides a large reservoir q-bits for information to be coded at the end of black hole evaporation and thus opens the way to a natural resolution of the black hole evaporation information puzzle. In this paper we show that these expectations can be made precise in a simple quantum gravity model for cosmology motivated by loop quantum gravity. Concretely, even when the model is fundamentally unitary, when microscopic degrees of freedom irrelevant to low-energy cosmological observers are suitably ignored, pure states in the effective description evolve into mixed states due to decoherence with the Planckian microscopic structure. Moreover, in the relevant physical regime these hidden degrees of freedom do not carry any `energy' and thus realize in a fully quantum gravitational context the idea (emphasized before by Unruh and Wald) that decoherence can take place without dissipation, now in a concrete gravitational model strongly motivated by quantum gravity. All this strengthens the perspective of a quite conservative and natural resolution of the black hole evaporation puzzle where information is not destroyed but simply degraded (made unavailable to low energy observers) into correlations with the microscopic structure of the quantum geometry at the Planck scale.
Mots clés
Quantum Gravity
quantum cosmology
planckian discreteness
unitarity
Black hole evaporation
black hole: evaporation
energy: low
quantum gravity: model
quantum gravity: loop space
space-time: geometry
gravitation: model
approximation: discrete
background: geometry
scale: Planck
decoherence
microstate
cosmological model
information theory
quantum geometry
conservation law
dissipation
space-time: Minkowski
quantization
matter: coupling
Hamiltonian
big bang
field theory: scalar
entanglement
Hilbert space