Lusanna, Luca and Pauri, Massimo
(2002)
General Covariance and the Objectivity of SpaceTime PointEvents: The Physical Role of Gravitational and Gauge Degrees of Freedom  DRAFT.
[Preprint]
Abstract
This paper deals with a number of technical achievements that are instrumental for a dissolution of the socalled "Hole Argument" in general relativity. Such achievements include: 1) the analysis of the "Hole" phenomenology in strict connection with the Hamiltonian treatment of the initial value problem. The work is carried through in metric gravity for the class of ChristoudoulouKlainermann spacetimes, in which the temporal evolution is ruled by the "weak" ADM energy; 2) a reinterpretation of "active" diffeomorphisms as "passive and metricdependent" dynamical symmetries of Einstein's equations, a reinterpretation which enables to disclose their (up to now unknown) connection to gauge transformations onshell; understanding such connection also enlightens the real content of the Hole Argument or, better, dissolves it together with its alleged "indeterminism"; 3) the utilization of the BergmannKomar "intrinsic pseudocoordinates", defined as suitable functionals of the Weyl curvature scalars, as tools for a peculiar gaugefixing to the superhamiltonian and supermomentum constraints; 4) the consequent construction of a "physical atlas" of 4coordinate systems for the 4dimensional "mathematical" manifold, in terms of the highly nonlocal degrees of freedom of the gravitational field (its four independent "Dirac observables"). Such construction embodies the "physical individuation" of the points of spacetime as "pointevents", independently of the presence of matter, and associates a "noncommutative structure" to each gauge fixing or fourdimensional coordinate system; 5) a clarification of the multiple definition given by Peter Bergmann of the concept of "(Bergmann) observable" in general relativity. This clarification leads to the proposal of a "main conjecture" asserting the existence of i) special Dirac's observables which are also Bergmann's observables, ii) gauge variables that are coordinate independent (namely they behave like the tetradic scalar fields of the NewmanPenrose formalism). A byproduct of this achievements is the falsification of a recently advanced argument asserting the absence of (any kind of) "change" in the observable quantities of general relativity. 6) a clarification of the physical role of Dirac and gauge variables as their being related to "tidallike" and "inertiallike" effects, respectively. This clarification is mainly due to the fact that, unlike the standard formulations of the equivalence principle, the Hamiltonian formalism allows to define notion of "force" in general relativity in a natural way; 7) a proposal showing how the physical individuation of pointevents could in principle be implemented as an experimental setup and protocol leading to a "standard of spacetime" more or less like atomic clocks define standards of time. We conclude that, besides being operationally essential for building measuring apparatuses for the gravitational field, the role of matter in the nonvacuum gravitational case is also that of "participating directly" in the individuation process, being involved in the determination of the Dirac observables. This circumstance leads naturally to a peculiar new kind of "structuralist" view of the generalrelativistic concept of spacetime, a view that embodies some elements of both the traditional "absolutist" and "relational" conceptions. In the end, spacetime pointevents maintain a "peculiar sort of objectivity". Some hints following from our approach for the quantum gravity programme are also given.
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