110 research outputs found
On reference frames and the definition of space in a general spacetime
First, we review local concepts defined previously. A (local) reference frame
can be defined as an equivalence class of admissible spacetime
charts (coordinate systems) having a common domain and exchanging
by a spatial coordinate change. The associated (local) physical space is made
of the world lines having constant space coordinates in any chart of the class.
Second, we introduce new, global concepts. The data of a non-vanishing global
vector field defines a global "reference fluid". The associated global
physical space is made of the maximal integral curves of that vector field.
Assume that, in any of the charts which make some reference frame :
(i) any of those integral curves has constant space coordinates , and
(ii) the mapping is one-to-one. In that case, the local space
can be identified with a part (an open subset) of the global space.Comment: 10 pages. Text of a talk given at the Third International Conference
on Theoretical Physics "Theoretical Physics and its Applications", Moscow,
June 24-28, 201
Testing a theory of gravity in celestial mechanics: a new method and its first results for a scalar theory
A new method of post-Newtonian approximation (PNA) for weak gravitational
fields is presented together with its application to test an alternative,
scalar theory of gravitation. The new method consists in defining a
one-parameter family of systems, by applying a Newtonian similarity
transformation to the initial data that defines the system of interest. This
method is rigorous. Its difference with the standard PNA is emphasized. In
particular, the new method predicts that the internal structure of the bodies
does have an influence on the motion of the mass centers. The translational
equations of motion obtained with this method in the scalar theory are adjusted
in the solar system, and compared with an ephemeris based on the standard PNA
of GR.Comment: v2: links to quoted arXiv papers. LaTeX, 28 pages including 2
figures. This is a revised version of a lecture given at the 8th. Conf.
``Physical Interpretations of Relativity Theory'' (London, September 2002),
organized by the British Society for the Philosophy of Sciences. The initial
version will appear in the proceedings of that conference (M. C. Duffy, ed.
Point-particle limit in a scalar theory of gravitation and the weak equivalence principle
A scalar theory with a preferred reference frame is summarized. To test that
theory in celestial mechanics, an "asymptotic" post-Newtonian (PN) scheme has
been developed. This associates a conceptual family of self-gravitating systems
with the given system, in order to have a true small parameter available. The
resulting equations for a weakly-self-gravitating system of extended bodies
include internal-structure effects. The internal-structure influence subsists
at the point-particle limit--a violation of the weak equivalence principle. If
one could develop an "asymptotic" approximation scheme in general relativity
also, this could plausibly be found there also, in a gauge where the PN space
metric would not be "conformally Euclidean".Comment: LaTeX, 6 pages. Text of a talk given at the Rencontres de Moriond:
Gravitational Waves and Experimental Gravity, Les Arcs, France (March 22-29,
2003). Submitted to the Proceedings (J. Dumarchez, ed.
Scalar ether theory of gravity: a modification that seems needed
The construction of the scalar theory based on the concept of gravity as
Archimedes' thrust is briefly summarized, emphasizing the two (extreme)
possibilities that result from this concept for the gravitational rod
contraction: it can either occur in only one direction, or be isotropic. A
modified equation for the scalar field is stated for the new, isotropic case.
The reasons to consider this case are: i) it is almost as natural as the other
case, and ii) it should avoid the violation of the weak equivalence principle,
found for a small extended body with the directional contraction. The dynamical
equation stays unchanged.Comment: LaTeX, 7 pages. Summary of a talk to be given at the IXth Conference
"Physical Interpretations of Relativity Theory" (London, 3--6 September
2004). This text will be published in the Proceedings (M. C. Duffy, ed.). v2:
Redactional improvements in Sects. 3 (Dynamics) and 5 (Modified Equations), a
new result announced in Sect. 5, a few references updated or adde
On the non-uniqueness problem of the covariant Dirac theory and the spin-rotation coupling
Gorbatenko & Neznamov [arXiv:1301.7599] recently claimed the absence of the
title problem. In this paper, the reason for that problem is reexplained by
using the notions of a unitary transformation and of the mean value of an
operator, invoked by them. Their arguments actually aim at proving the
uniqueness of a particular prescription for solving this problem. But that
prescription is again shown non-unique. Two Hamiltonians in the same reference
frame in a Minkowski spacetime, only one of them including the spin-rotation
coupling term, are proved to be physically non-equivalent. This confirms that
the reality of that coupling should be checked experimentally.Comment: 17 pages. V2: Version to appear in Int. J. Theor. Phys.: Details
about the (gross) inequivalence of the Hamiltonians with either the inertial
tetrad or the rotating one on pp. 11-12. Added Appendix proving that, for the
(standard) covariant Dirac equation, the mean values of the energy can not be
shifted by a constant after a smooth change of the tetrad field. Added
Footnote 2 on p.
Some remarks on quantum mechanics in a curved spacetime, especially for a Dirac particle
Some precisions are given about the definition of the Hamiltonian operator H
and its transformation properties, for a linear wave equation in a general
spacetime. In the presence of time-dependent unitary gauge transformations, H
as an operator depends on the gauge choice. The other observables of QM and
their rates also become gauge-dependent unless a proper account for the gauge
choice is done in their definition. We show the explicit effect of these
non-uniqueness issues in the case of the Dirac equation in a general spacetime
with the Schwinger gauge. We show also in detail why, the meaning of the energy
in QM being inherited from classical Hamiltonian mechanics, the energy operator
and its mean values ought to be well defined in a general spacetime.Comment: 25 pages, conforms exactly with the published version. arXiv admin
note: text overlap with arXiv:1312.670
The Scalar Ether-Theory of Gravitation and its First Test in Celestial Mechanics
The motivations for investigating a theory of gravitation based on a concept
of "ether" are discussed-- a crucial point is the existence of an alternative
interpretation of special relativity, named the Lorentz-Poincar\'e ether
theory. The basic equations of one such theory of gravity, based on just one
scalar field, are presented. To check this theory in celestial mechanics, an
"asymptotic" scheme of post-Newtonian (PN) approximation is summarized and its
difference with the standard PN scheme is emphasized. The derivation of PN
equations of motion for the mass centers, based on the asymptotic scheme, is
outlined. They are implemented for the major bodies of the solar system and the
prediction for Mercury is compared with an ephemeris based on general
relativity.Comment: LaTeX, 6 pages, one figure. Text of a talk at the 5th Friedmann
International Seminar on Gravitation and Cosmology, Joao Pessoa (Brazil),
23-30 April 2002. Will be submitted to a special issue of Int. J. Mod.
Phys./
Accelerated Expansion as Predicted by an Ether Theory of Gravitation
Cosmology is investigated within a new, scalar theory of gravitation, which
is a preferred-frame bimetric theory with flat background metric. Before coming
to cosmology, the motivation for an " ether theory " is exposed at length; the
investigated concept of ether is presented: it is a compressible fluid, and
gravity is seen as Archimedes' thrust due to the pressure gradient in that
fluid. The construction of the theory is explained and the current status of
the experimental confrontation is analysed, both in some detail. An analytical
cosmological solution is obtained for a general form of the energy-momentum
tensor. According to that theory, expansion is necessarily accelerated, both by
vacuum and even by matter. In one case, the theory predicts expansion, the
density increasing without limit as time goes back to infinity. High density is
thus obtained in the past, without a big-bang singularity. In the other case,
the Universe follows a sequence of (non-identical) contraction-expansion
cycles, each with finite maximum energy density; the current expansion phase
will end by infinite dilution in some six billions of years. The density ratio
of the present cycle (ratio of the maximum to current densities) is not
determined by the current density and the current Hubble constant H0, unless a
special assumption is made. Since cosmological redshifts approaching z = 4 are
observed, the density ratio should be at least 100. From this and the estimate
of H0, the time spent since the maximum density is constrained to be larger
than several hundreds of billions of years. Yet if a high density ratio,
compatible with the standard explanation for the light elements and the 2.7 K
radiation, is assumed, then the age of the Universe is much larger still.Comment: 32 pages, Post-Script. v4 : Section 2 (general presentation of the
theory and its motivation) still reinforced, Subsection 5.3 added (Comments
on accelerated expansion and infinite dilution). To appear in "Physics
Essays", Vol. 14, No. 1, 200
Equations of motion for the mass centers in a scalar theory of gravitation
A scalar theory of gravitation with a preferred reference frame (PRF) is
considered, that accounts for special relativity and reduces to it if the
gravitational field cancels. The gravitating system consists of a finite number
of perfect-fluid bodies. An " asymptotic " post-Newtonian (PN) approximation
scheme is used, allowing an explicit weak-field limit with all fields expanded.
Exact mass centers are defined and their exact equations of motion are derived.
The PN expansion of these equations is obtained: the zero-order equations are
those of Newtonian gravity (NG), and the equations for the first-order (PN)
corrections depend linearly on the PN fields. For PN corrections to the motion
of the mass centers, especially in the solar system, one may assume "
very-well-separated " rigidly moving bodies with spherical self-fields of the
zero-order approximation. The PN corrections reduce then to a time integration
and include spin effects, which might be significant. It is shown that the
Newtonian masses are not correct zero-order masses for the PN calculations. An
algorithm is proposed, in order to minimize the residual and to assess the
velocity in the PRF.Comment: Post-Script, 32 page
- …