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Mayeul Arminjon

Publications and source records attributed to Mayeul Arminjon.

At least 19 recordsLinked to original sources
arXiv2026

Equations of motion of the mass centers in a scalar theory of gravity with a preferred frame

The theory considered interprets gravity as a pressure force. Thus, the scalar gravitational field defines the gravity acceleration field. However, it also determines the relation between the flat ``background metric'' and a curved ``physical metric''. Here we derive the equations of motion of the mass centers of a system of weakly gravitating bodies in the second version of that theory. We use the framework which was built and used for the first version. Namely, we use an asymptotic scheme of post-Newtonian (PN) approximation to derive the local (field) PN equations, and by integration inside the bodies we deduce from those local equations the equations of motion of the mass centers, using also an asymptotic framework for the good separation between the different bodies.

physics.gen-ph↗
arXiv2025

Progress in evaluating a possible electromagnetic interaction energy in a gravitational field

The Lorentz-Poincar\'e interpretation of special relativity (SR) keeps the classical concepts of separated space and time, at the price of postulating an indetectable preferred inertial frame or ``ether". But SR does not contain gravity. The presence of gravity could make the ether detectable. This is one idea behind the ``scalar ether theory of gravitation" (SET), which coincides with SR if the gravity field vanishes, and passes a number of tests. However, the coupling of SET with the Maxwell electromagnetic (EM) field needs to use the theory's dynamical equation for the energy tensor in a non-trivial way. It cannot be assumed that the energy tensors of the charged matter and the EM field add to give the total energy tensor, source of the gravitational field. Thus, an additional, ``interaction" energy tensor ${\bf T}_\mathrm{inter}$ has to be postulated. Asking that ${\bf T}_\mathrm{inter}$ is Lorentz-invariant in the situation of SR, fixes its form. It depends only on a scalar field $p$. ${\bf T}_\mathrm{inter}$ is an exotic kind of matter and is distributed in the whole space, hence it could contribute to dark matter. For a weak gravitational field, $p$ obeys a first-order partial differential equation (PDE) involving the EM field and the Newtonian potential. However, the EM field varies on the scale of the wavelength, which is extremely small. To get the field $p$ in a galaxy, some averaging has to be done. After several attempts based on the homogenization theory, a simpler way has been found recently: If the macro-averages of $p$ and the EM field vary smoothly, it can be shown that the PDE for $p$ remains valid in the same form with spacetime-averaged fields. The current stage of calculations will also been shown.

physics.gen-ph↗
arXiv2023

Interstellar radiation as a Maxwell field: improved numerical scheme and application to the spectral energy density

The existing models of the interstellar radiation field (ISRF) do not produce a Maxwell field. Here, the recent model of the ISRF as a Maxwell field is improved by considering separately the different frequencies at the stage of the fitting. Using this improved procedure: (i) It is checked in detail that the model does predict extremely high values of the spectral energy density (SED) on the axis of a galaxy, that however decrease very rapidly when $\rho $, the distance to the axis, is increased from zero. (ii) The difference between the SED values (with $\rho =1\,$kpc or $8\,$kpc), as predicted either by this model or by a recent radiation transfer model, is reduced significantly. (iii) The slower decrease of the SED with increasing altitude $z$, as compared with the radiation transfer model, is confirmed. We also calculate the evolutions of the SED at large $\rho $. We interpret these evolutions by determining asymptotic expansions of the SED at large $z$, and also ones at large $\rho $.

physics.gen-ph↗
arXiv2023

Towards testing a dark matter candidate that emerges from the scalar ether theory

According to a scalar theory of gravity with a preferred frame, electromagnetism in the presence of a gravitational field implies that there is an additional energy tensor, which might contribute to dark matter. The expression of this tensor is determined by a mere scalar $p$, that depends on the EM field and (for a weak field) on the Newtonian gravitational field. We briefly recall why this tensor arises and how the EM field in a galaxy can be calculated. The data fields that enter the PDE for the scalar field $p$ oscillate very quickly in space and time, as does the EM field. This prevents integration of that PDE at the relevant galactic scale. Therefore, a homogenization of that PDE has to be operated. We discuss in some detail three possible ways of applying the homogenization theory to that PDE: time, space, or spacetime homogenization. The second and third ways may lead to feasible, albeit heavy calculations.

physics.gen-ph↗
arXiv2023

Interaction energy between a charged medium and its electromagnetic field as a dark matter candidate

In the scalar theory of gravitation with a preferred reference frame, a consistent formulation of electrodynamics in the presence of gravitation needs to introduce an additional energy tensor: the interaction energy tensor. This energy is gravitationally active and might contribute to the dark matter, because it has an exotic character and it is not localized inside matter. In order to check if that energy might form representative dark halos, one has to model the interstellar radiation field in a galaxy as a complete electromagnetic field obeying the Maxwell equations. A model has been built for this purpose, based on assuming axial symmetry and on recent results about axisymmetric Maxwell fields. Its predictions for the variation of the spectral energy density inside our Galaxy are relatively close to those of a recent radiation transfer model, except on the symmetry axis of the Galaxy, where the present model predicts extremely high values of the energy density.

physics.gen-ph↗
arXiv2021

Spectral energy density in an axisymmetric galaxy as predicted by an analytical model for the Maxwell field

An analytical model for the Maxwell radiation field in an axisymmetric galaxy, proposed previously, is first checked for its predictions of the spatial variation of the spectral energy distributions (SEDs) in our Galaxy. First, the model is summarized. It is now shown how to compute the SED with this model. Then the model is adjusted by asking that the SED predicted at our local position in the Galaxy coincide with the available observations. Finally the first predictions of the model for the spatial variation of the SED in the Galaxy are compared with those of a radiation transfer model. We find that the two predictions do not differ too much. This indicates that, in a future work, it should be possible with the present model to check if the "interaction energy" predicted by an alternative, scalar theory of gravitation, contributes to the dark matter. Keywords: Disk galaxy; interstellar radiation field; axial symmetry; electromagnetic field; Milky Way.

physics.gen-ph↗
arXiv2021

An analytical model for the Maxwell radiation field in an axially symmetric galaxy

The Maxwell radiation field is an essential physical characteristic of a galaxy. Here, an analytical model is built to simulate that field in an axisymmetric galaxy. This analytical model is based on an explicit representation for axisymmetric source-free Maxwell fields. In a previous work, the general applicability of this representation has been proved. The model is adjusted by fitting to it the sum of spherical radiations emitted by the composing "stars". The huge ratio distance/wavelength needs to implement a numerical precision better than the quadruple precision. The model passes a validation test based on a spherically symmetric solution. The results for a set of "stars" representative of a disk galaxy indicate that the field is highest near to the disk axis, and there the axial component of ${\bf E}$ dominates over the radial one. This work will allow us in the future to check if the interaction energy predicted by an alternative theory of gravitation might be a component of dark matter. {\bf Keywords:} Disk galaxy; Maxwell equations; axial symmetry; exact solutions; numerical model; dark matter.

physics.gen-ph↗
arXiv2020

An explicit representation for the axisymmetric solutions of the free Maxwell equations

Garay-Avendaño \& Zamboni-Rached (2014) defined two classes of axisymmetric solutions of the free Maxwell equations. We prove that the linear combinations of these two classes of solutions cover all totally propagating time-harmonic axisymmetric free Maxwell fields -- and hence, by summation on frequencies, all totally propagating axisymmetric free Maxwell fields. It provides an explicit representation for these fields. This will be important, e.g., to have the interstellar radiation field in a disc galaxy modelled as an exact solution of the free Maxwell equations. Keywords: Maxwell equations; axial symmetry; exact solutions; electromagnetic duality

physics.class-ph↗
arXiv2018

On the equations of electrodynamics in a flat or a curved spacetime and a possible interaction energy

We investigate which are the independent equations of continuum electrodynamics and what is their number, beginning with the standard equations used in special and in general relativity. We check by using differential identities that there are as much independent equations as there are unknowns, for the case with given sources as well as for the general case where the motion of the charged medium producing the field is unknown. Then we study that problem in an alternative theory of gravity with a preferred reference frame, in order to constrain an additional, "interaction" energy tensor that has to be postulated in this theory, and that would be present also outside usual matter. In order that the interaction tensor be Lorentz-invariant in special relativity, it has to depend only on a scalar field $p$. Since the system of electrodynamics of the theory is closed in the absence of the interaction tensor, just one scalar equation more is needed to close it again in the presence of $p$. We add the equation for charge conservation. We derive equations that will allow one to determine the field $p$ in a given weak gravitational field and in a given electromagnetic field. Keywords: Maxwell equations, special relativity, general relativity, alternative theory of gravitation, preferred reference frame

physics.gen-ph↗
arXiv2018

Is spacetime as physical as is space?

Two questions are investigated by looking successively at classical mechanics, special relativity, and relativistic gravity: first, how is space related with spacetime? The proposed answer is that each given reference fluid, that is a congruence of reference trajectories, defines a physical space. The points of that space are formally defined to be the world lines of the congruence. That space can be endowed with a natural structure of 3-D differentiable manifold, thus giving rise to a simple notion of spatial tensor --- namely, a tensor on the space manifold. The second question is: does the geometric structure of the spacetime determine the physics, in particular, does it determine its relativistic or preferred-frame character? We find that it does not, for different physics (either relativistic or not) may be defined on the same spacetime structure --- and also, the same physics can be implemented on different spacetime structures. Keywords: Affine space; classical mechanics; special relativity; relativistic gravity; reference fluid.

gr-qc↗
arXiv2018

Charge conservation in a gravitational field in the scalar ether theory

A modification of the Maxwell equations due to the presence of a gravitational field was formerly proposed for a scalar theory with a preferred reference frame. With this modification, the electric charge is not conserved. The aim of the present work was to numerically assess the amount of charge production or destruction. We propose an asymptotic scheme for the electromagnetic field in a weak and slowly varying gravitational field. This scheme is valid independently of the theory and the "gravitationally-modified" Maxwell equations. Then we apply this scheme to plane waves and to a group of Hertzian dipoles in the scalar ether theory. The predicted amounts of charge production/destruction discard the formerly proposed gravitationally-modified Maxwell equations. The theoretical reason for that is the assumption that the total energy tensor is the sum of the energy tensor of the medium producing the electromagnetic (e.m.) field and the e.m. energy tensor. This means that an additional, "interaction" tensor has to be present. With this assumption, the standard Maxwell equations in a curved spacetime, which predict charge conservation, are compatible with the investigated theory. We find that the interaction energy might contribute to the dark matter.

physics.gen-ph↗
arXiv2017

On continuum dynamics and the electromagnetic field in the scalar ether theory of gravitation

We summarize a recent work on the title subject, skipping the detailed calculations but introducing the basic points with enough detail. The theory considered is formulated in a preferred reference frame in a four-dimensional spacetime endowed with a curved "physical" metric. The dynamics of a test particle is defined by an extension of the special-relativistic form of Newton's second law. This determines the dynamical equation verified by the energy-momentum tensor ${\bf T}$ of a "dust" continuum, also in the presence of a non-gravitational external force. The dynamical equation for ${\bf T}$ thus obtained is assumed valid for a general continuous medium or a system of fields. When the non-gravitational force is the Lorentz force, this equation in turn determines the Maxwell equations in a gravitational field for the present theory. They are consistent with the dynamics of photons i.e. with the geometrical optics of the theory. Except for a constant gravitational field, they seem to imply some local production or destruction of electric charge. The possible amounts are yet to be assessed.

physics.gen-ph↗
arXiv2016

Continuum dynamics and the electromagnetic field in the scalar ether theory of gravitation

An alternative, scalar theory of gravitation has been proposed, based on a mechanism/interpretation of gravity as being a pressure force: Archimedes' thrust. In it, the gravitational field affects the physical standards of space and time, but motion is governed by an extension of the relativistic form of Newton's second law. This implies Einstein's geodesic motion for free particles only in a constant gravitational field. In this work, equations governing the dynamics of a continuous medium subjected to gravitational and non-gravitational forces are derived. Then, the case where the non-gravitational force is the Lorentz force is investigated. The gravitational modification of Maxwell's equations is obtained under the requirement that a charged continuous medium, subjected to the Lorentz force, obeys the equation derived for continuum dynamics under external forces. These Maxwell equations are shown to be consistent with the dynamics of a "free" photon, and thus with the geometrical optics of this theory. However, these equations do not imply local charge conservation, except for a constant gravitational field. Keywords: Alternative theories of gravitation; preferred reference frame; curved spacetime; Maxwell equations; charge conservation

physics.gen-ph↗
arXiv2016

On the definition of energy for a continuum, its conservation laws, and the energy-momentum tensor

We review the energy concept in the case of a continuum or a system of fields. First, we analyze the emergence of a true local conservation equation for the energy of a continuous medium, taking the example of an isentropic continuum in Newtonian gravity. Next, we consider a continuum or a system of fields in special relativity: we recall that the conservation of the energy-momentum tensor contains two local conservation equations of the same kind as before. We show that both of these equations depend on the reference frame, and that, however, they can be given a rigorous meaning. Then we review the definitions of the canonical and Hilbert energy-momentum tensors from a Lagrangian through the principle of stationary action in a general spacetime. Using relatively elementary mathematics, we prove precise results regarding the definition of the Hilbert tensor field, its uniqueness, and its tensoriality. We recall the meaning of its covariant conservation equation. We end with a proof of uniqueness of the energy density and flux, when both depend polynomially of the fields. Keywords: energy conservation; conservation equation; special relativity; general relativity; Hilbert tensor; variational principle

gr-qc↗
arXiv2016

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.

physics.gen-ph↗
arXiv2015

Defining the space in a general spacetime

A global vector field $v$ on a "spacetime" differentiable manifold $\mathrm{V}$, of dimension $N+1$, defines a congruence of world lines: the maximal integral curves of $v$, or orbits. The associated global space $\mathrm{N}\_v$ is the set of these orbits. A "$v$-adapted" chart on $\mathrm{V}$ is one for which the $\mathbb{R}^N$ vector ${\bf x}\equiv (x^j)\ (j=1,...,N)$ of the "spatial" coordinates remains constant on any orbit $l$. We consider non-vanishing vector fields $v$ that have non-periodic orbits, each of which is a closed set. We prove transversality theorems relevant to such vector fields. Due to these results, it can be considered plausible that, for such a vector field, there exists in the neighborhood of any point $X\in \mathrm{V}$ a chart $χ$ that is $v$-adapted and "nice", i.e., such that the mapping $\bar{χ}: l\mapsto {\bf x}$ is injective --- unless $v$ has some "pathological" character. This leads us to define a notion of "normal" vector field. For any such vector field, the mappings $\bar{χ}$ build an atlas of charts, thus providing $\mathrm{N}\_v$ with a canonical structure of differentiable manifold (when the topology defined on $\mathrm{N}\_v$ is Hausdorff, for which we give a sufficient condition met in important physical situations). Previously, a local space manifold $\mathrm{M}\_\mathrm{F}$ had been associated with any "reference frame" $\mathrm{F}$, defined as an equivalence class of charts. We show that, if $\mathrm{F}$ is made of nice $v$-adapted charts, $\mathrm{M}\_\mathrm{F}$ is naturally identified with an open subset of the global space manifold $\mathrm{N}\_v$.

math.GM↗
arXiv2015

On the Hamiltonian and energy operators in a curved spacetime, especially for a Dirac particle

The definition of the Hamiltonian operator H for a general wave equa-tion in a general spacetime is discussed. We recall that H depends on the coordinate system merely through the corresponding reference frame. When the wave equation involves a gauge choice and the gauge change is time-dependent, H as an operator depends on the gauge choice. This dependence extends to the energy operator E, which is the Hermitian part of H. We distinguish between this ambiguity issue of E and the one that occurs due to a mere change of the "represen-tation" (e.g. transforming the Dirac wave function from the "Dirac representation" to a "Foldy-Wouthuysen representation"). We also assert that the energy operator ought to be well defined in a given ref-erence frame at a given time, e.g. by comparing the situation for this operator with the main features of the energy for a classical Hamilto-nian particle.

gr-qc↗