108 research outputs found
Gravity as Archimedes' thrust and a bifurcation in that theory
Euler's interpretation of Newton's gravity (NG) as Archimedes' thrust in a
fluid ether is presented in some detail. Then a semi-heuristic mechanism for
gravity, close to Euler's, is recalled and compared with the latter. None of
these two "gravitational ethers" can obey classical mechanics. This is logical
since the ether defines the very reference frame, in which mechanics is
defined. This concept is used to build a scalar theory of gravity: NG
corresponds to an incompressible ether, a compressible ether leads to
gravitational waves. In the Lorentz-Poincar\'e version, special relativity is
compatible with the ether, but, with the heterogeneous ether of gravity, it
applies only locally. A correspondence between metrical effects of uniform
motion and gravitation is assumed, yet in two possible versions (one is new).
Dynamics is based on a (non-trivial) extension of Newton's second law. The
observational status for the theory with the older version of the
correspondence is summarized.Comment: 24 pages, invited contribution to the Franco Selleri Festschrift, to
appear in Found. Physics. v3: Endnote 45 on absolute simultaneity improved
(formerly footnote 6: class file changed to revtex4), a few references
updated (and now with titles). v2: minor correction in subsect. 3.2, some
wording improvements, and a few references adde
Non-uniqueness of the Dirac theory in a curved spacetime
We summarize a recent work on the subject title. The Dirac equation in a
curved spacetime depends on a field of coefficients (essentially the Dirac
matrices), for which a continuum of different choices are possible. We study
the conditions under which a change of the coefficient fields leads to an
equivalent Hamiltonian operator H, or to an equivalent energy operator E. In
this paper, we focus on the standard version of the gravitational Dirac
equation, but the non-uniqueness applies also to our alternative versions. We
find that the changes which lead to an equivalent operator H, or respectively
to an equivalent operator E, are determined by initial data, or respectively
have to make some point-dependent antihermitian matrix vanish. Thus, the vast
majority of the possible coefficient changes lead neither to an equivalent
operator H, nor to an equivalent operator E, whence a lack of uniqueness. We
show that even the Dirac energy spectrum is not unique.Comment: 13 pages (standard 12pt article format). Text of a talk given at the
1st Mediterranean Conference on Classical and Quantum Gravity, Kolymbari
(Greece), Sept. 14-18, 200
Equations of motion according to the asymptotic post-Newtonian scheme for general relativity in the harmonic gauge
The asymptotic scheme of post-Newtonian approximation defined for general
relativity (GR) in the harmonic gauge by Futamase & Schutz (1983) is based on a
family of initial data for the matter fields of a perfect fluid and for the
initial metric, defining a family of weakly self-gravitating systems. We show
that Weinberg's (1972) expansion of the metric and his general expansion of the
energy-momentum tensor , as well as his expanded equations for the
gravitational field and his general form of the expanded dynamical equations,
apply naturally to this family. Then, following the asymptotic scheme, we
derive the explicit form of the expansion of for a perfect fluid, and
the expanded fluid-dynamical equations. (These differ from those written by
Weinberg.) By integrating these equations in the domain occupied by a body, we
obtain a general form of the translational equations of motion for a 1PN
perfect-fluid system in GR. To put them into a tractable form, we use an
asymptotic framework for the separation parameter , by defining a family
of well-separated 1PN systems. We calculate all terms in the equations of
motion up to the order included. To calculate the 1PN correction
part, we assume that the Newtonian motion of each body is a rigid one, and that
the family is quasi-spherical, in the sense that in all bodies the inertia
tensor comes close to being spherical as . Apart from corrections
that cancel for exact spherical symmetry, there is in the final equations of
motion one additional term, as compared with the Lorentz-Droste
(Einstein-Infeld-Hoffmann) acceleration. This term depends on the spin of the
body and on its internal structure.Comment: 42 pages, no figure. Version accepted for publication in Physical
Review
Gravitational Energy Loss and Binary Pulsars in the Scalar Ether-Theory of Gravitation
Motivation is given for trying a theory of gravity with a preferred reference
frame (``ether'' for short). One such theory is summarized, that is a scalar
bimetric theory. Dynamics is governed by an extension of Newton's second law.
In the static case, geodesic motion is recovered together with Newton's
attraction field. In the static spherical case, Schwarzschild's metric is got.
An asymptotic scheme of post-Minkowskian (PM) approximation is built by
associating a conceptual family of systems with the given weakly-gravitating
system. It is more general than the post-Newtonian scheme in that the velocity
may be comparable with . This allows to justify why the 0PM approximation of
the energy rate may be equated to the rate of the Newtonian energy, as is
usually done. At the 0PM approximation of this theory, an isolated system loses
energy by quadrupole radiation, without any monopole or dipole term. It seems
plausible that the observations on binary pulsars (the pulse data) could be
nicely fitted with a timing model based on this theory.Comment: Text of a talk given at the 4th Conf. on Physics Beyond the Standard
Model, Tegernsee, June 2003, submitted to the Proceedings (H. V.
Klapdor-Kleingrothaus, ed.
General reference frames and their associated space manifolds
We propose a formal definition of a general reference frame in a general
spacetime, as an equivalence class of charts. This formal definition
corresponds with the notion of a reference frame as being a (fictitious)
deformable body, but we assume, moreover, that the time coordinate is fixed.
This is necessary for quantum mechanics, because the Hamiltonian operator
depends on the choice of the time coordinate. Our definition allows us to
associate rigorously with each reference frame F, a unique "space" (a
three-dimensional differentiable manifold), which is the set of the world lines
bound to F. This also is very useful for quantum mechanics. We briefly discuss
the application of these concepts to G\"odel's universe.Comment: 14 pages in standard 12pt format. v2: Discussion Section 4
reinforced, now includes an application to G\"odel's universe
Equivalent forms of Dirac equations in curved spacetimes and generalized de Broglie relations
One may ask whether the relations between energy and frequency and between
momentum and wave vector, introduced for matter waves by de Broglie, are
rigorously valid in the presence of gravity. In this paper, we show this to be
true for Dirac equations in a background of gravitational and electromagnetic
fields. We first transform any Dirac equation into an equivalent canonical
form, sometimes used in particular cases to solve Dirac equations in a curved
spacetime. This canonical form is needed to apply the Whitham Lagrangian
method. The latter method, unlike the WKB method, places no restriction on the
magnitude of Planck's constant to obtain wave packets, and furthermore
preserves the symmetries of the Dirac Lagrangian. We show using canonical Dirac
fields in a curved spacetime, that the probability current has a Gordon
decomposition into a convection current and a spin current, and that the spin
current vanishes in the Whitham approximation, which explains the negligible
effect of spin on wave packet solutions, independent of the size of Planck's
constant. We further discuss the classical-quantum correspondence in a curved
spacetime based on both Lagrangian and Hamiltonian formulations of the Whitham
equations. We show that the generalized de Broglie relations in a curved
spacetime are a direct consequence of Whitham's Lagrangian method, and not just
a physical hypothesis as introduced by Einstein and de Broglie, and by many
quantum mechanics textbooks.Comment: PDF, 32 pages in referee format. Added significant material on
canonical forms of Dirac equations. Simplified Theorem 1 for normal Dirac
equations. Added section on Gordon decomposition of the probability current.
Encapsulated main results in the statement of Theorem
Post-Newtonian equation for the energy levels of a Dirac particle in a static metric
We study first the Hamiltonian operator H corresponding to the Fock-Weyl
extension of the Dirac equation to gravitation. When searching for stationary
solutions to this equation, in a static metric, we show that just one invariant
Hermitian product appears natural. In the case of a space-isotropic metric, H
is Hermitian for that product. Then we investigate the asymptotic
post-Newtonian approximation of the stationary Schroedinger equation associated
with H, for a slow particle in a weak-field static metric. We rewrite the
expanded equations as one equation for a two-component spinor field. This
equation contains just the non-relativistic Schroedinger equation in the
gravity potential, plus correction terms. Those "correction" terms are of the
same order in the small parameter as the "main" terms, but are numerically
negligible in the case of ultra-cold neutrons in the Earth's gravity.Comment: 12pt LaTeX, 17 pages. v2: version accepted for publication in
Phys.Rev.D: comments on scalar product changed, using a recent paper;
discussion of PN expansions simplified (no change of units any more);
numerical estimates for ultra-cold neutrons in the Earth's gravit
Coronavirus biopolitics: the paradox of France's Foucauldian heritage.
In this short paper we analyse some paradoxical aspects of France's Foucauldian heritage: (1) while several French scholars claim the COVID-19 pandemic is a perfect example of what Foucault called biopolitics, popular reaction instead suggests a biopolitical failure on the part of the government; (2) One of these failures concerns the government's inability to produce reliable biostatistical data, especially regarding health inequalities in relation to COVID-19. We interrogate whether Foucaldianism contributed, in the past as well today, towards a certain myopia in France regarding biostatistics and its relation to social inequalities in health. One might ask whether this very data could provide an appropriate response to the Foucauldian question: What kind of governance of life is the pandemic revealing to us
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