6,298 research outputs found
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
Why the Quantum Must Yield to Gravity
After providing an extensive overview of the conceptual elements -- such as
Einstein's `hole argument' -- that underpin Penrose's proposal for
gravitationally induced quantum state reduction, the proposal is constructively
criticised. Penrose has suggested a mechanism for objective reduction of
quantum states with postulated collapse time T = h/E, where E is an
ill-definedness in the gravitational self-energy stemming from the profound
conflict between the principles of superposition and general covariance. Here
it is argued that, even if Penrose's overall conceptual scheme for the
breakdown of quantum mechanics is unreservedly accepted, his formula for the
collapse time of superpositions reduces to T --> oo (E --> 0) in the strictly
Newtonian regime, which is the domain of his proposed experiment to corroborate
the effect. A suggestion is made to rectify this situation. In particular,
recognising the cogency of Penrose's reasoning in the domain of full `quantum
gravity', it is demonstrated that an appropriate experiment which could in
principle corroborate his argued `macroscopic' breakdown of superpositions is
not the one involving non-rotating mass distributions as he has suggested, but
a Leggett-type SQUID or BEC experiment involving superposed mass distributions
in relative rotation. The demonstration thereby brings out one of the
distinctive characteristics of Penrose's scheme, rendering it empirically
distinguishable from other state reduction theories involving gravity. As an
aside, a new geometrical measure of gravity-induced deviation from quantum
mechanics in the manner of Penrose is proposed, but now for the canonical
commutation relations [Q, P] = ih.Comment: 33 pages (TeX, uses mtexsis) plus 3 figures (epsf). To appear in
``Physics Meets Philosophy at the Planck Scale'' (Cambridge University
Press). Two footnotes adde
P-spline anova-type interaction models for spatio-temporal smoothing
In recent years, spatial and spatio-temporal modelling have become an important area of research in many fields (epidemiology, environmental studies, disease mapping, ...). However, most of the models developed are constrained by the large amounts of data available. We propose the use of Penalized splines (P-splines) in a mixed model framework for smoothing spatio-temporal data. Our approach allows the consideration of interaction terms which can be decomposed as a sum of smooth functions similarly as an ANOVA decomposition. The properties of the bases used for regression allow the use of algorithms that can handle large amount of data. We show that imposing the same constraints as in a factorial design it is possible to avoid identifiability problems. We illustrate the methodology for Europe ozone levels in the period 1999-2005
Nanoscale diffractive probing of strain dynamics in ultrafast transmission electron microscopy
The control of optically driven high-frequency strain waves in nanostructured
systems is an essential ingredient for the further development of
nanophononics. However, broadly applicable experimental means to quantitatively
map such structural distortion on their intrinsic ultrafast time and nanometer
length scales are still lacking. Here, we introduce ultrafast convergent beam
electron diffraction (U-CBED) with a nanoscale probe beam for the quantitative
retrieval of the time-dependent local distortion tensor. We demonstrate its
capabilities by investigating the ultrafast acoustic deformations close to the
edge of a single-crystalline graphite membrane. Tracking the structural
distortion with a 28-nm/700-fs spatio-temporal resolution, we observe an
acoustic membrane breathing mode with spatially modulated amplitude, governed
by the optical near field structure at the membrane edge. Furthermore, an
in-plane polarized acoustic shock wave is launched at the membrane edge, which
triggers secondary acoustic shear waves with a pronounced spatio-temporal
dependency. The experimental findings are compared to numerical acoustic wave
simulations in the continuous medium limit, highlighting the importance of
microscopic dissipation mechanisms and ballistic transport channels
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
Coordinates with Non-Singular Curvature for a Time Dependent Black Hole Horizon
A naive introduction of a dependency of the mass of a black hole on the
Schwarzschild time coordinate results in singular behavior of curvature
invariants at the horizon, violating expectations from complementarity. If
instead a temporal dependence is introduced in terms of a coordinate akin to
the river time representation, the Ricci scalar is nowhere singular away from
the origin. It is found that for a shrinking mass scale due to evaporation, the
null radial geodesics that generate the horizon are slightly displaced from the
coordinate singularity. In addition, a changing horizon scale significantly
alters the form of the coordinate singularity in diagonal (orthogonal) metric
coordinates representing the space-time. A Penrose diagram describing the
growth and evaporation of an example black hole is constructed to examine the
evolution of the coordinate singularity.Comment: 15 pages, 1 figure, additional citation
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