arXiv:gr-qc/9712015v1 2 Dec 1997 Published in Potentiality, Entanglement and Passion-at-a-distance - Quantum Mechanical Studies for Abner Shimony, volume 2, edited by R. S. Cohen, M. Horne and J. Stachel, (Kluwer, Dordrecht, Holland 1997), p. 31-52. CLASSICAL AND QUANTUM PHYSICAL GEOMETRY JEEVA S. ANANDAN Departments of Physics and Philosophy University of South Carolina Columbia, SC 29208, USA. and Sub-Faculty of Philosophy, University of Oxford 10 Merton St., Oxford OX2 4JJ, UK. 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. gr-qc/9712015 1