On time and the quantum-to-classical transition in Jordan-Brans-Dicke quantum gravity

TL;DR

This paper explores how decoherence can explain the unobservability of superpositions of different gravitational constant states in Jordan-Brans-Dicke quantum gravity, analyzing time concepts and implications for cosmology.

Contribution

It provides a canonical quantization framework for Jordan-Brans-Dicke theory and demonstrates how decoherence suppresses superpositions of different gravitational constant eigenstates.

Findings

Off-diagonal elements of the density matrix are sufficiently suppressed.

The formalism supports the unobservability of superpositions of different gravitational constants.

Discussion of tunneling into regions with negative gravitational constant.

Abstract

Any quantum theory of gravity which treats the gravitational constant as a dynamical variable has to address the issue of superpositions of states corresponding to different eigenvalues. We show how the unobservability of such superpositions can be explained through the interaction with other gravitational degrees of freedom (decoherence). The formal framework is canonically quantized Jordan-Brans-Dicke theory. We discuss the concepts of intrinsic time and semiclassical time as well as the possibility of tunneling into regions corresponding to a negative gravitational constant. We calculate the reduced density matrix of the Jordan-Brans-Dicke field and show that the off-diagonal elements can be sufficiently suppressed to be consistent with experiments. The possible relevance of this mechanism for structure formation in extended inflation is briefly discussed.