Dynamical Emergence of Instantaneous 3-Spaces in a Class of Models of General Relativity
arXiv:gr-qc/0611045 · doi:10.1007/978-1-4020-6318-3_13
Abstract
The Hamiltonian structure of General Relativity (GR), for both metric and tetrad gravity in a definite continuous family of space-times, is fully exploited in order to show that: i) the "Hole Argument" can be bypassed by means of a specific "physical individuation" of point-events of the space-time manifold in terms of the "autonomous degrees of freedom" of the vacuum gravitational field ("Dirac observables"), while the "Leibniz equivalence" is reduced to differences in the "non-inertial appearances" (connected to "gauge" variables) of the same phenomena. ii) the chrono-geometric structure of a solution of Einstein equations for given, gauge-fixed, initial data (a "3-geometry" satisfying the relevant constraints on the Cauchy surface), can be interpreted as an "unfolding" in mathematical global time of a sequence of "achronal 3-spaces" characterized by "dynamically determined conventions" about distant simultaneity. This result stands out as an important "conceptual difference" with respect to the standard chrono-geometrical view of Special Relativity (SR) and allows, in a specific sense, for an "endurantist" interpretations of ordinary "physical objects" in GR.
arXiv commentTo appear in the book "Relativity and the Dimensionality of the World", A. van der Merwe ed., Springer Series "Fundamental Theories of Physics"