On reference frames and the definition of space in a general spacetime

First, we review local concepts defined previously. A (local) reference frame $\mathrm{F}$ can be defined as an equivalence class of admissible spacetime charts (coordinate systems) having a common domain $\mathrm{U}$ 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 $\,v\,$ 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 $\mathrm{F}$: (i) any of those integral curves $l$ has constant space coordinates $x^j$, and (ii) the mapping $l\mapsto (x^j)$ 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.

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.

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.

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

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./

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