arXiv subjects

Mayeul Arminjon

Publications and source records attributed to Mayeul Arminjon.

At least 73 records · Page 4Linked to original sources

arXiv2004

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-Poincaré 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.

physics.gen-ph↗

arXiv2004

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.

physics.gen-ph↗

arXiv2003

Gravitational effects on light rays and binary pulsar energy loss in a scalar theory of gravity

A scalar bimetric theory of gravity with a preferred reference frame is summarized. 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 found. Asymptotic schemes of post-Newtonian (PN) and post-Minkowskian (PM) approximation are built, each based on associating a conceptual family of systems with the given system. At the 1PN approximation, there is no preferred-frame effect for photons, hence the standard predictions of GR for photons are got. At the 0PM approximation, an isolated system loses energy by quadrupole radiation, without any monopole or dipole term. Inserting this loss into the Newtonian 2-body problem gives the Peters-Mathews coefficients of the theory.

gr-qc↗

arXiv2003

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 $c$. 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.

gr-qc↗

arXiv2003

Equations of motion of the mass centers in a scalar theory of gravitation: Expansion in the separation parameter

An asymptotic framework is defined for the small parameter eta which quantifies a good separation between the extended bodies that make a weakly gravitating system. This is introduced within an alternative scalar theory of gravitation, though it may be defined similarly in other theories. This framework allows one to truncate the translational equations of motion at any well-defined order. Here, the post-Newtonian (PN) equations valid in the scalar theory are truncated beyond the order eta^3. The PN approximation scheme used is the asymptotic scheme, that expands all fields. To get the explicit form of the equations of motion for the mass centers, the bodies are assumed spherical, merely for calculating the PN corrections. It is found that, due to the use of the asymptotic PN scheme, the internal structure of the bodies does play a role in the equations of motion.

gr-qc↗

arXiv2003

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.

gr-qc↗

arXiv2003

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".

gr-qc↗

arXiv2002

A numerical solution of the inverse problem in classical celestial mechanics, with application to Mercury's motion

It is attempted to obtain the masses of the celestial bodies, the initial conditions of their motion, and the constant of gravitation, by a global parameter optimization. First, a numerical solution of the N-bodies problem for mass points is described and its high accuracy is verified. The osculating elements are also accurately computed. This solution is implemented in the Gauss iterative algorithm for solving nonlinear least-squares problems. This algorithm is summarized and its efficiency for the inverse problem in celestial mechanics is checked on a 3-bodies problem. Then it is used to assess the accuracy to which a Newtonian calculation may reproduce the DE403 ephemeris, that involves general-relativistic corrections. The parameter optimization allows to reduce the norm and angular differences between the Newtonian calculation and DE403 by a factor 10 (Mercury, Pluto) to 100 (Venus). The maximum angular difference on the heliocentric positions of Mercury is ca. 220" per century before the optimization, and ca. 20" after it. The latter is still far above the observational accuracy. On the other hand, Mercury's longitude of the perihelion is not affected by the optimization: it keeps the linear advance of 43" per century. Key words: Mercury's perihelion. Parameter optimization. Mechanics of point masses.

astro-ph↗

arXiv2002

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-Poincaré 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.

gr-qc↗

arXiv2002

Remarks on the mathematical origin of wave mechanics and consequences for a quantum mechanics in a gravitational field

According to Schroedinger's ideas, classical dynamics of point particles should correspond to the " geometrical optics " limit of a linear wave equation, in the same way as ray optics is the limit of wave optics. It is shown that, using notions of modern wave theory, the " geometrical optics " analogy leads to the correspondence between a classical Hamiltonian H and a " quantum " wave equation in a natural and general way. In particular, the correspondence is unambiguous also in the case where H contains mixed terms involving momentum and position. In the line of Schroedinger's ideas, it is also attempted to justify the occurrence, in QM, of eigenvalues problems, not merely for energy, but also for momentum. It is shown that the wave functions of pure momentum states can be defined in a physically more satisfying way than by assuming plane waves. In the case of a spatially uniform force field, such momentum states have a singularity and move undeformed according to Newton's second law. The mentioned unambiguous correspondence allows to uniquely extend the Klein-Gordon relativistic wave equation to the case where a constant gravitational field is present. It is argued that Schroedinger's wave mechanics can be extended to the case with a variable gravitational field only if one accepts that the wave equation is a preferred-frame one. From this viewpoint, generally-covariant extensions of the wave equations of QM seem rather formal. Finally, it is conjectured that there is no need for a quantum gravity.

gr-qc↗

arXiv2002

Proper initial conditions for long-term integrations of the solar system

An optimization program is used to re-adjust the initial conditions, in order to reproduce as closely as possible the predictions of a complete ephemeris by using simplified equations of motion in the numerical integration. The adjustment of the initial conditions is illustrated in the transition from the DE406 complete long-range ephemeris to a Newtonian model considering only the Sun and the four major planets. It is also used to best reproduce this same DE406 ephemeris, based on post-Newtonian equations for a system of mass points and including the Moon and asteroids, by using a Newtonian calculation corrected by the Schwarzschild effects of the Sun and restricted to the ten major bodies of the solar system.

astro-ph↗

arXiv2001

Comparison between two methods of post-Newtonian expansion for the motion in a weak Schwarzschild field

The asymptotic method of post-Newtonian (PN) expansion for weak gravitational fields, recently developed, is compared with the standard method of PN expansion, in the particular case of a massive test particle moving along a geodesic line of a weak Schwarzschild field. First, the expression of the active mass in Schwarzschild's solution is given for a barotropic perfect fluid, both for general relativity (GR) and for an alternative, scalar theory. The principle of the asymptotic method is then recalled and the PN expansion of the active mass is derived. The PN correction to the active mass is made of the Newtonian elastic energy, augmented, for the scalar theory, by a term due to the self-reinforcement of the gravitational field. Third, two equations, both correct to first order, are derived for the geodesic motion of a mass particle: a "standard" one and an "asymptotic" one. Finally, the difference between the solutions of these two equations is numerically investigated in the case of Mercury. The asymptotic solution deviates from the standard one like the square of the time elapsed since the initial time. This is due to a practical shortcoming of the asymptotic method, which is shown to disappear if one reinitializes the asymptotic problem often enough. Thus, both methods are equivalent in the case investigated. In a general case, the asymptotic method seems more natural.

gr-qc↗

arXiv2001

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.

gr-qc↗

arXiv2001

On a scalar theory of gravitation

That preferred-frame theory accounts for special relativity and reduces to it if the gravitation field cancels. Starting from an interpretation of gravity as a pressure force, it is based on just one scalar field. This scalar gives the relation between the flat "background" metric and the curved "physical" metric, due to an equivalence principle between the absolute effects of motion and gravitation. The scalar is also a potential for the gravity acceleration vector. Motion is governed by an extension of the special-relativistic form of Newton's second law. This provides a new equation for continuum dynamics, that gives the gravitational modification of Maxwell's equations, consistent with photon dynamics. The same effects on light rays as in GR are predicted at the post-Newtonian approximation (PNA). An asymptotic PNA is being studied, in order to build a consistent celestial mechanics in the theory. The cosmic acceleration is predicted and nonsingular cosmological models are obtained.

gr-qc↗

arXiv2000

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.

astro-ph↗

arXiv2000

Asymptotic expansions for relativistic celestial mechanics

The method of asymptotic expansions is used to build an approximation scheme relevant to celestial mechanics in relativistic theories of gravitation. A scalar theory is considered, both as a simple example and for its own sake. This theory is summarized, then the relevant boundary problem is seen to be the full initial-value problem. It is shown that, with any given system of gravitating bodies, one may associate a one-parameter family of similar systems, the parameter measuring the gravitational field-strength. After a specific change of units, the derivation of asymptotic expansions becomes straightforward. Two hypotheses could be made as to which time variable has to be used in the expansion. The first one leads to an "asymptotic" post-Newtonian approximation (PNA) with instantaneous propagation, differing from the standard PNA in that, in the asymptotic PNA, all fields are expanded. The second hypothese could lead to an "asymptotic" post-Minkowskian approximation (PMA) allowing to describe propagation effects, but it is not compatible with the Newtonian limit. It is shown that the standard PNA is not compatible with the application of the usual method of asymptotic expansions as envisaged here.

gr-qc↗

arXiv2000

Weak-field approximation of a scalar theory of gravitation and some remarks on the propagation effects of gravity

A simple example is given of the implementation of the usual method of asymptotic expansions for weak gravitational fields. A scalar, preferred-frame theory of gravitation is considered, but the method is general. Two kinds of asymptotic expansion are a priori possible: "post-Newtonian" (PN) or "post-Minkowskian", the latter allowing to account directly for propagation effects. However, it is shown that only the PN asymptotic expansion is compatible with the Newtonian limit. It is also shown that, in the scalar theory, there is no non-Newtonian effect (in particular, no propagation effect) up to the second order, i.e., the order 1/c^2.

gr-qc↗

arXiv1999

Post-Newtonian Approximation of a Scalar Theory of Gravitation and Application to Light Rays

A scalar, preferred-frame theory of gravitation is summarized. Space-time is endowed with both a flat metric and a curved, "physical" metric. Motion is governed by a natural extension of Newton's second law, which implies geodesic motion only for a static field. The theory predicts Schwarzschild's exterior metric in the spherical static situation. It also predicts gravitation waves with the velocity of light. The equations of motion are recast into the "flat space - uniform time" form, and compared with the geodesic equations of motion. The principles of the post-Newtonian approximation of this theory are given, including the way to account for preferred-frame effects. This approximation is then developed more particularly for photons. It is found that the preferred-frame effects do not occur in this case, nor does the difference between Newton's second law and geodesic assumption. Thus, the post-Newtonian predictions of this theory for photons are indistinguishable from the standard post-Newtonian predictions of general relativity.

gr-qc↗