Spectral Geometry and Causality

Details Spectral Geometry and Causality Spectral Geometry and Causality

1996-09-21

arxiv.org/abs/gr-qc/9609050v1

Int.J.Mod.Phys. A13 (1998) 2693-2708

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

AMS-Latex, 14 pages, 3 figures, using epsf macro

Scientific paper

10.1142/S0217751X98001360

For a physical interpretation of a theory of quantum gravity, it is necessary to recover classical spacetime, at least approximately. However, quantum gravity may eventually provide classical spacetimes by giving spectral data similar to those appearing in noncommutative geometry, rather than by giving directly a spacetime manifold. It is shown that a globally hyperbolic Lorentzian manifold can be given by spectral data. A new phenomenon in the context of spectral geometry is observed: causal relationships. The employment of the causal relationships of spectral data is shown to lead to a highly efficient description of Lorentzian manifolds, indicating the possible usefulness of this approach. Connections to free quantum field theory are discussed for both motivation and physical interpretation. It is conjectured that the necessary spectral data can be generically obtained from an effective field theory having the fundamental structures of generalized quantum mechanics: a decoherence functional and a choice of histories.

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