Gravitation and Irreversibility

Details Gravitation and Irreversibility Gravitation and Irreversibility

Oct 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984ijtp...23.1009n&link_type=abstract

International Journal of Theoretical Physics, Volume 23, Issue 10, pp.1009-1024

Physics

1

Scientific paper

The internal time operator M is an alternative to the usual dynamic time, an independent parameter of motion. Even when the dynamical entity is the three-geometry(3) G and we are concerned with its evolution in superspace (the problem of cosmological evolution), dynamical time remains an independent parameter associated with a choice of lapse and shift functions. The quantity M is, on the contrary, an ensemble-dependent parameter related to the “age” of a process: the entirety of the ensemble's evolution. With this different view of time as age, we seek a geometrical counterpart to M for the(3) G as an “ensemble.” For a closed negatively curved universe, a Lyapounov function can be established which allows an M to be defined for the Robertson-Walker universe. The time component of superspace momentum π uv is introduced, and we identify its conjugate energy ∂S/∂π uv with dissipation due to the evolving universe. A geometrical counterpart of M is introduced by a conformal invariant Γ. This quantity simultaneously expresses (i) the topological feature of orientation-preserving transformations, and (ii) the Hamiltonian treatment of dissipative systems. This dual character of Γ, which links topological change to dissipative systems, suggests a geometrical basis for M. In this sense irreversibility is incorporated into the geometric structure of space-time, along with gravitation.

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