Introductory Abstract
The task of creating a quantum theory of gravity is compared with Einstein’s creation of a relativistic theory of gravity. The philosophical and physical foundations of this theory 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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Anandan, J.S. (1997). Classical and Quantum Physical Geometry. In: Cohen, R.S., Horne, M., Stachel, J. (eds) Potentiality, Entanglement and Passion-at-a-Distance. Boston Studies in the Philosophy of Science, vol 194. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2732-7_3
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DOI: https://doi.org/10.1007/978-94-017-2732-7_3
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