Three denials of time in the interpretation of canonical gravity

The analysis of the temporal structure of canonical general relativity and the connected interpretational questions with regard to the role of time within the theory both rest upon the need to respect the fundamentally dual role of the Hamiltonian constraints found within the formalism. Any consistent philosophical approach towards the theory must pay dues to the role of these constraints in both generating dynamics, in the context of phase space, and generating unphysical symmetry transformations, in the context of a hypersurface embedded within a solution. A first denial of time in the terms of a position of reductive temporal relationalism can be shown to be troubled by failure on the first count, and a second denial in the terms of Machian temporal relationalism can be found to be hampered by failure on the second. A third denial of time, consistent with both of the Hamiltonian constraints roles, is constituted by the implementation of a scheme for constructing observables in terms of correlations and leads to a radical Parmenidean timelessness. The motivation for and implications of each of these three denials are investigated. (C) 2012 Elsevier Ltd. All rights reserved.