Decoherence in the density matrix describing quantum three-geometries and the emergence of classical spacetime

Journal Article · Mon May 15 00:00:00 EDT 1989 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.39.2924· OSTI ID:6387212

Padmanabhan, T

We construct the quantum gravitational density matrix /rho/(/ital g//sub ..cap alpha beta../,/ital g//sub ..cap alpha beta..//sup '/) for compact three-geometries by integrating out a set of unobserved matter degrees of freedom from a solution to the Wheeler-DeWitt equation /Psi/(/ital g//sub ..cap alpha beta../,/ital q//sub /ital k/(matter)/). In the adiabatic approximation, /rho/ can be expressed as exp(/minus//ital l//sup 2/) where /ital l//sup 2/(g/sub ..cap alpha beta../,/ital g//sub ..cap alpha beta..//sup '/) is a specific ''distance'' measure in the space of three-geometries. This measure depends on the volumes of the three-geometries and the eigenvalues of the Laplacian constructed from the three-metrics. The three-geometries which are ''close together'' (/ital l//sup 2//much lt/1) interfere quantum mechanically; those which are ''far apart'' (/ital l//sup 2//much gt/1) are suppressed exponentially and hence contribute decoherently to /rho/. Such a suppression of ''off-diagonal'' elements in the density matrix signals classical behavior of the system. In particular, three-geometries which have the same intrinsic metric but differ in size contribute decoherently to the density matrix. This analysis provides a possible interpretation for the semiclassical limit of the wave function of the Universe.

• Research Organization: Astrophysics Group, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India(IN)
• OSTI ID: 6387212
• Journal Information: Phys. Rev. D; (United States), Vol. 39:10
• Country of Publication: United States
• Language: English

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657003* - Theoretical & Mathematical Physics- Relativity & Gravitation