Classical and Quantum Physical Geometry

Jeeva S. Anandan

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arXiv · gr-qc/9712015

Classical and Quantum Physical Geometry

Jeeva S. Anandan

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Abstract

The task of quantizing gravity is compared with Einstein's relativization of gravity. The philosophical and physical foundations of general relativity are briefly reviewed. The Ehlers-Pirani-Schild scheme of operationally determining the geometry of space-time, using freely falling classical particle trajectories, is done using operations in an infinitesimal neighborhood around each point. The study of the free fall of a quantum wave suggests a quantum principle of equivalence. The principle of general covariance is clarified. The sign change of a Fermion field when rotated by $2π$ radians is used to argue for a quantum mechanical modification of space-time, which leads naturally to supersymmetry. A novel effect in quantum gravity due to the author is used to extend Einstein's hole argument to quantum gravity. This suggests a quantum principle of general covariance, according to which the fundamental laws of physics should be covariant under `quantum diffeomorphisms'. This heuristic principle implies that space-time points have no invariant meaning in quantum gravity.

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Jeeva S. Anandan. 1997-12-02. Classical and Quantum Physical Geometry. https://arxiv.org/abs/gr-qc/9712015

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