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Motion of a Test Particle According to the Scalar Ether Theory of Gravitation and Application to Its Celestial Mechanics

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Motion of a Test Particle According to the Scalar Ether Theory of Gravitation and Application to Its Celestial Mechanics Z. Naturforsch. 2019; aop Mayeul Arminjon* and Rainer Wolfgang Winkler Motion of a Test Particle According to the Scalar Ether Theory of Gravitation and Application to its Celestial Mechanics https://doi.org/10.1515/zna-2018-0470 1 Introduction and Summary Received October 17, 2018; accepted December 9, 2018 There are two empirically indistinguishable interpreta- Abstract: The standard interpretations of special relativ- tions of special relativity: the Lorentz–Poincaré (L-P) inter- ity (Einstein–Minkowski) and general relativity (GR) lead pretation, which sees the relativistic effects as following to a drastically changed notion of time: the eternalism from the “true” Lorentz contraction of all objects in their or block universe theory. This has strong consequences motion through the ether, and the standard (Einstein– for our thinking about time and for the development of Minkowski) interpretation [1, 2]. The latter is currently pre- new fundamental theories. It is therefore important to ferred, despite the fact that the L-P interpretation is com- check this thoroughly. The Lorentz–Poincaré interpreta- patible with the classical notion of time and has definite tion, which sees the relativistic effects as following from advantages regarding the physical understandability, in a “true” Lorentz contraction of all objects in their motion particular regarding the causal explanation of the rela- through the ether, uses a conservative concept of time tivistic effects such as time dilation [1, 3]. (The L-P interpre- and is in the absence of gravitation indistinguishable from tation of special relativity is also known under the name the standard interpretation; but there exists currently no “Lorentz ether theory,” which we consider inappropriate accepted gravitation theory for it. The scalar ether theory because it hides (i) the decisive contributions of Poincaré of gravitation is a candidate for such a theory; it is pre- and (ii) the full compatibility of this interpretation with the sented and discussed. The equations of motion for a test physics of special relativity.) An important argument for particle are derived; the case of a uniformly moving mas- the standard (Einstein–Minkowski) relativity is that gen- sive body is discussed and then specialized to the case eral relativity (GR) is an extension of it and is not compat- of spherical symmetry. Formulas for the acceleration of ible with the L-P interpretation [4]. In standard relativity, test particles are given in the preferred frame of the ether the concept of time is completely different from what we and in the rest frame of the massive body that moves with experience: there is no observer-independent flow of time, velocity V with respect to the ether. When the body rests in and there is no simple concept of present. Instead, the = −2 the ether (V 0), the acceleration is up to order c iden- idea of eternalism (the block universe theory) appears to 6= tical to GR. The acceleration of a test particle for V 0 is be the notion of time that best corresponds with standard given; this makes it possible to fit observations in celestial relativity. These are significant changes to our understand- mechanics to ephemerides with V as a free parameter. The ing of the world, which we should challenge if we wish to current status of such fits (although to ephemerides and make sure that they are really correct. We will therefore not to observations) is presented and discussed. examine in this article a theory of gravity that is consistent with the L-P interpretation. That theory interprets gravity Keywords: Alternative Theories of Gravitation; Celestial as Archimedes’ thrust exerted by a perfect fluid or “ether” Mechanics; Lorentzian Metric; Preferred Reference Frame; on the matter particles – those being viewed as extended Test Particle. objects, more precisely as organized flows in that same fluid. Archimedes’ thrust is due to the (macroscopic) pres- sure gradient in the postulated fluid. This interpretation of gravitation and its natural coupling with the L-P inter- pretation of special relativity have been discussed in detail in [5]. In short, the L-P interpretation of special relativ- *Corresponding author: Mayeul Arminjon, University of Grenoble ity sees the metrical effects (space contraction and time Alpes, CNRS, Grenoble INP, 3SR Lab., F-38000 Grenoble, France, E-mail: [email protected] dilation) as absolute effects of the uniform motion. When Rainer Wolfgang Winkler: Schäufelweg 4, D-81825 Munich, combined with the interpretation of gravity as being due Germany, E-mail: [email protected] to the pressure gradient of the ether, this leads to attribute Brought to you by | provisional account Unauthenticated Download Date | 1/14/19 6:16 PM 2 | M. Arminjon and R. W. Winkler: Motion in the Scalar Ether Theory of Gravitation similar metrical effects to the gravitation. One thus builds The experimental check of such an alternative theory of a relativistic theory of gravitation with a preferred refer- gravitation involves of course many points, a good number ence frame, based on a unique scalar field [6], hence the of which have been already checked, see, among others, name “scalar ether theory” or SET.¹ The preferred refer- [6, 15, 16]; for a summary, see [17], Section 1. (As noted ence frame E of the theory is the frame that moves with there, this scalar theory differs from all known scalar the- the macroscopic (or averaged) velocity field of the fluid ories.) In particular, the celestial mechanics has also been ether considered by that theory. In other words, the aver- checked for this theory [15, 18], but this was for an ear- age velocity field of the ether with respect to E is zero by lier version of the theory (“v1,” see [16] and references definition of that frame [5]. The global frame E is a natu- therein), which had to be modified to the current version ral inertial frame. Hence, the existence of global inertial (“v2,” see [6]). The aim of the present research is to begin frames is unproblematic for this theory. (Global inertial the check of the celestial mechanics of the “new” version, frames occur of course in Newton’s theory but also, to a v2. That beginning consists essentially in assuming for certain extent, in the celestial mechanics based on GR, simplicity that the mass centres of the N bodies move as through the use there of the harmonic gauge condition [9], test particles in the gravitational field of the other bodies. which can be interpreted as defining a generalization of In this framework, the main task of the present work was the Newtonian global inertial frames [10].) Special relativ- to derive a tractable equation of motion for a test particle ity is the limiting situation in which the pressure gradi- in SET. ent is negligible, thus making the ether (macroscopically) In Section 2, we present the main equations of the the- homogeneous. In summary, that theory has a physical ory. We note there that a general expression of the acceler- interpretation for gravity and extends the L-P interpreta- ation of a test particle obtained for v1 holds true for v2, and tion of relativity to the heterogeneous ether implied by we show the spatial covariance of the equations. Section 3 gravity. derives a simple and exact expression of the acceleration The other motivation for that theory is to avoid some in the most general case. In Section 4 we prove that, in problems that are suffered by GR, despite its experimental the case where the gravitational field is produced by a success. uniformly moving massive body, the source of that field (i) In SET, the gravitational collapse does not lead to a can be defined in the uniformly moving frame as a time- singularity [11]; neither does the past state of very independent scalar field. We obtain then the explicit exact high density implied by the cosmic expansion [12]. solution for the gravitational field (50). That case is fur- (ii) In SET, the spacetime manifold is given, and there is ther specialized in Section 5 by assuming that the mas- no need for any gauge condition. sive body has spherical symmetry. We provide there the (iii) Because that theory has a preferred reference frame, expression of the acceleration both in the preferred frame its coupling with quantum theory is easier than for and in the moving frame. Section 6 discusses the applica- GR; e.g. the energy operator of the Dirac equation tion to the effective calculation of an ephemeris.² We show does not have any nonuniqueness problem [13]. that the approximation done in the present work to calcu- (iv) In SET, the cosmic expansion is necessarily accel- late the post-Newtonian (PN) correction, that each planet erated, without the need to introduce any dark moves as a test particle in the field of the spherical Sun, energy [12]. plus the fact that comparison is made with an ephemeris (v) In order to formulate a consistent electrodynamics based on GR, necessarily lead to the result found that the in the presence of gravitation for that theory, one velocity of the barycentre is unrealistically small. There- had to postulate an interaction energy, and that fore, the next steps should be (i) to derive fully consistent energy turns out to be a possible candidate for dark equations at the PN level that take into account the self matter [14]. fields (as was previously done for v1 [18]) and, most impor- tantly, (ii) to adjust the theory on “direct” data, as little affected as possible by a reduction using GR. 1 Note that extensions of GR having a preferred reference frame have been proposed, in particular the “Einstein-aether” theory. That the- ory adds a vector field (the 4-velocity of the preferred frame) into the Hilbert-Einstein action [7, 8] and has thus a “dynamical” preferred 2 In order to test this theory in celestial mechanics, it is preferable frame.
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