On decoherence in quantum gravity

It was previously argued that the phenomenon of quantum gravitational decoherence described by the Wheeler-DeWitt equation is responsible for the emergence of the arrow of time. Here we show that the characteristic spatiotemporal scales of quantum gravitational decoherence are typically logarithmically larger than a characteristic curvature radius R-1/2 of the background space-time. This largeness is a direct consequence of the fact that gravity is a non-renormalizable theory, and the corresponding effective field theory is nearly decoupled from matter degrees of freedom in the physical limit MP -> infinity . Therefore, as such, quantum gravitational decoherence is too ineffective to guarantee the emergence of the arrow of time and the "quantum-to-classical" transition to happen at scales of physical interest. We argue that the emergence of the arrow of time is directly related to the nature and properties of physical observer.