Gauge protected entanglement between gravity and matter

Abstract

We show that gravity and matter fields are generically entangled, as a consequence of the local Poincaré symmetry. First, we present a general argument, applicable to any particular theory of quantum gravity with matter, by performing the analysis in the abstract nonperturbative canonical framework, demonstrating the nonseparability of the scalar constraint, thus promoting the entangled states as the physical ones. Also, within the covariant framework, we show explicitly that the Hartle-Hawking state in the Regge model of quantum gravity is necessarily entangled. Our result is potentially relevant for the quantum-to-classical transition, taken within the framework of the decoherence programme: due to the gauge symmetry requirements, the matter does not decohere, it is by default decohered by gravity. Generically, entanglement is a consequence of interaction. This new entanglement could potentially, in form of an "effective interaction", bring about corrections to the weak equivalence principle, further confirming that spacetime as a smooth four-dimensional manifold is an emergent phenomenon. Finally, the existence of the gauge-protected entanglement between gravity and matter could be seen as a criterion for a plausible theory of quantum gravity, and in the case of perturbative quantisation approaches, a confirmation of the persistence of the manifestly broken gauge symmetry.

v4: published version, 30 pages

References in corpus (10)

• Quantum Gravity at a Lifshitz Point
• Nonperturbative Quantum Gravity
• The Gravity Dual of Renyi Entropy
• Gravitational Decoherence
• No Rescue for the No Boundary Proposal
• Quantum Gravity on the Lattice
• Two-slit diffraction with highly charged particles: Niels Bohr's consistency argument that the electromagnetic field must be quantized
• Cosmic Decoherence: Massive Fields
• Solution to the Cosmological Constant Problem in a Regge Quantum Gravity Model
• Gravity-Matter Entanglement in Regge Quantum Gravity

Cited by in corpus (3)

• Equivalence Principle in Classical and Quantum Gravity
• The Equivalence Principle as a Noether Symmetry
• Entanglement-induced deviation from the geodesic motion in quantum gravity