45 research outputs found
Explaining Leibniz-equivalence as difference of non-inertial appearances: dis-solution of the Hole Argument and physical individuation of point-events
"The last remnant of physical objectivity of space-time" is disclosed in the
case of a continuous family of spatially non-compact models of general
relativity (GR). The {\it physical individuation} of point-events is furnished
by the intrinsic degrees of freedom of the gravitational field, (viz, the {\it
Dirac observables}) that represent - as it were - the {\it ontic} part of the
metric field. The physical role of the {\it epistemic} part (viz. the {\it
gauge} variables) is likewise clarified as emboding the unavoidable
non-inertial aspects of GR. At the end the philosophical import of the {\it
Hole Argument} is substantially weakened and in fact the Argument itself
dis-solved, while a specific four-dimensional {\it holistic and structuralist}
view of space-time, (called {\it point-structuralism}), emerges, including
elements common to the tradition of both {\it substantivalism} and {\it
relationism}. The observables of our models undergo real {\it temporal change}:
this gives new evidence to the fact that statements like the {\it frozen-time}
character of evolution, as other ontological claims about GR, are {\it model
dependent}. \medskip Forthcoming in Studies in History and Philosophy of Modern
PhysicsComment: 37 pages, talk at Oxford Conference on Spacetime (2004), to appear in
Studies in History and Philosophy of Modern Physics. Affiliations Correcte
Ephemeral point-events: is there a last remnant of physical objectivity?
For the past two decades, Einstein's Hole Argument (which deals with the
apparent indeterminateness of general relativity due to the general covariance
of the field equations) and its resolution in terms of Leibniz equivalence (the
statement that Riemannian geometries related by active diffeomorphisms
represent the same physical solution) have been the starting point for a lively
philosophical debate on the objectivity of the point-events of space-time. It
seems that Leibniz equivalence makes it impossible to consider the points of
the space-time manifold as physically individuated without recourse to
dynamical individuating fields. Various authors have posited that the metric
field itself can be used in this way, but nobody so far has considered the
problem of explicitly distilling the metrical fingerprint of point-events from
the gauge-dependent components of the metric field. Working in the Hamiltonian
formulation of general relativity, and building on the results of Lusanna and
Pauri (2002), we show how Bergmann and Komar's intrinsic pseudo-coordinates
(based on the value of curvature invariants) can be used to provide a physical
individuation of point-events in terms of the true degrees of freedom (the
Dirac observables) of the gravitational field, and we suggest how this
conceptual individuation could in principle be implemented with a well-defined
empirical procedure. We argue from these results that point-events retain a
significant kind of physical objectivity.Comment: LaTeX, natbib, 34 pages. Final journal versio
Marzke-Wheeler coordinates for accelerated observers in special relativity
In special relativity, the definition of coordinate systems adapted to
generic accelerated observers is a long-standing problem, which has found
unequivocal solutions only for the simplest motions. We show that the
Marzke-Wheeler construction, an extension of the Einstein synchronization
convention, produces accelerated systems of coordinates with desirable
properties: (a) they reduce to Lorentz coordinates in a neighborhood of the
observers' world-lines; (b) they index continuously and completely the causal
envelope of the world-line (that is, the intersection of its causal past and
its causal future: for well-behaved world-lines, the entire space-time). In
particular, Marzke-Wheeler coordinates provide a smooth and consistent
foliation of the causal envelope of any accelerated observer into space-like
surfaces.
We compare the Marzke-Wheeler procedure with other definitions of accelerated
coordinates; we examine it in the special case of stationary motions, and we
provide explicit coordinate transformations for uniformly accelerated and
uniformly rotating observers. Finally, we employ the notion of Marzke-Wheeler
simultaneity to clarify the relativistic paradox of the twins, by pinpointing
the local origin of differential aging.Comment: AmsLaTeX, 22 pages, 8 eps figures; revised, references added. To
appear in Foundations of Physics Letters, October 200
General Covariance and the Objectivity of Space-Time Point-Events
"The last remnant of physical objectivity of space-time" is disclosed, beyond the Leibniz equivalence, in the case of a continuous family of spatially non-compact models of general relativity. The "physical individuation" of point-events is furnished by the intrinsic degrees of freedom of the gravitational field, (viz, the "Dirac observables") that represent - as it were - the "ontic" part of the metric field. The physical role of the "epistemic" part (viz. the "gauge" variables) is likewise clarified. At the end, a peculiar four-dimensional "holistic and structuralist" view of space-time emerges which includes elements common to the tradition of both "substantivalism" and "relationism". The observables of our models undergo real "temporal change" and thereby provide a counter-example to the thesis of the "frozen-time" picture of evolution
General Covariance and the Objectivity of Space-time Point-events
"The last remnant of physical objectivity of space-time" is disclosed, beyond the Leibniz equivalence, in the case of a continuous family of spatially non-compact models of general relativity. The physical individuation of point-events is furnished by the intrinsic degrees of freedom of the gravitational field, (viz, the "Dirac observables") that represent - as it were - the "ontic" part of the metric field. The physical role of the "epistemic" part (viz. the "gauge" variables) is likewise clarified. At the end, a peculiar four-dimensional "holistic and structuralist" view of space-time emerges which includes elements common to the tradition of both substantivalism and relationism. The observables of our models undergo real "temporal change" and thereby provide a counter-example to the thesis of the "frozen-time" picture of evolution
The Physical Role of Gravitational and Gauge Degrees of Freedom in General Relativity - II: Dirac versus Bergmann observables and the Objectivity of Space-Time
(abridged)The achievements of the present work include: a) A clarification of
the multiple definition given by Bergmann of the concept of {\it (Bergmann)
observable. This clarification leads to the proposal of a {\it 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 Newman-Penrose
formalism). b) The analysis of the so-called {\it Hole} phenomenology in strict
connection with the Hamiltonian treatment of the initial value problem in
metric gravity for the class of Christoudoulou -Klainermann space-times, in
which the temporal evolution is ruled by the {\it weak} ADM energy. It is
crucial the re-interpretation of {\it active} diffeomorphisms as {\it passive
and metric-dependent} dynamical symmetries of Einstein's equations, a
re-interpretation which enables to disclose their (nearly unknown) connection
to gauge transformations on-shell; this is expounded in the first paper
(gr-qc/0403081). The use of the Bergmann-Komar {\it intrinsic
pseudo-coordinates} allows to construct a {\it physical atlas} of 4-coordinate
systems for the 4-dimensional {\it mathematical} manifold, in terms of the
highly non-local degrees of freedom of the gravitational field (its four
independent {\it Dirac observables}), and to realize the {\it physical
individuation} of the points of space-time as {\it point-events} as a
gauge-fixing problem, also associating a non-commutative structure to each
4-coordinate system.Comment: 41 pages, Revtex