Dynamical Emergence of Instantaneous 3-Spaces in a Class of Models of General Relativity

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 M 4 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.To appear in the book Relativity and the Dimensionality of the World, A. van der Merwe ed., Springer Series Fundamental Theories of Physics.

Epistemic Primacy vs. Ontological Elusiveness of Spatial Extension: Is There an Evolutionary Role for the Quantum?

“…We have shown ([30, 31,35] and bibliography therein, also [9]). that 'the last remnant of physical objectivity of space-time' that Einstein thought (in 1916) [14] was 'taken away by the requirement of general covariance' (essentially on the basis of the famous 'Hole Argument' or Lochbetrachtung) can indeed be recovered, at least in a continuous family of models of GTR, by exploiting the intrinsic degrees of freedom of the gravitational field in vacuum (viz.…”

“…In spite of the formal operational unification of time and space within the special theory of relativity (STR), time and space maintain a deep ontological difference. Also, in General Theory of Relativity (GTR), once examined from the dynamical (Hamiltonian) point of view, time plays a special role (see [30,31]). Even more, time has a substantially different status from space in quantum theory.…”

“…30 Penrose has repeatedly suggested that a fundamental link should exist between the possible violation of the linear Schroedinger evolution and perception processes (see [37,38]). 31 More specifically, Shimony [46] writes: 'The scientific community is contemplating seriously the idea that one should give up the unrestricted validity of the linear nature of the dynamical evolution. If this is the case, the physical processes which present themselves as the most natural candidates .…”

“…Yet, I must object that space-as conceived by Newton-was uniform, or homogeneous, and strictly speaking it has no structure at all! I suggest a comparison with the rich physical (gravitational) structure of certain general-relativistic spacetimes (see[30,31,35] and Sect. 2.2).…”