Will, C. M. 1981, Theory and Experiment in Gravitational Physics, (Cambridge: Cambridge University Press)  Home/Search   Document Not in Database   Summary   Related Articles   Check

....are at first disturbing because they indicate a violation of Lorentz invariance for the electromagnetic field in vacuum, which is commonly taken as a paradigmatic example of a Lorentz invariant system. Of course, in the general relativistic framework of [14] it is local Lorentz invariance [18] that is violated. Upon closer inspection, however, Lorentz invariance is not affected at a fundamental level. Between conducting plates, or in a background gravitational field, light does not propagate at the usual speed, simply because the boundaries (or the background) single out a preferred ....

C. M. Will, "Theory and Experiment in Gravitational Physics," Cambridge Univ. Cambridge, UK, Press, 1993.

.... et al. 1994; Konopliv et al. 1995) ii) The establishment of better values for gravitational and other astronomical constants, as well as testing of the hypothesis of their dependence on time which is predicted by a number of modern theories of gravity (Dirac, 1937; Anderson et al. 1986; Will, 1993). iii) The study of the dynamics and the evolution of the solar system, aimed at a better understanding of its metrological characteristics. This will help to solve some cosmogonical problems, such as: determining whether or not there is a second asteroid belt (the Kuiper belt) behind the ....

....et al. 1986) giving better numerical estimates of the quantity of dark matter in the solar system (Braginsky, 1994; Anderson, et al. 1995) and determining whether or not our Sun has a companion star. iv) Experimental tests of the modern gravitational theories in the WFSMA (Damour, 1983; Will, 1993; Lebach, et al. 1995; Anderson et al. 1996) including the establishment of upper limits on the amplitude and energy density of gravitational radiation (Anderson et al. 1986) The search for gravitational waves, their detection and studies of mechanisms of wave generation, as well as their ....

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Will, C. M.: 1993, Theory and Experiment in Gravitational Physics, (Rev. Ed.), Cambridge Univ. Press, Cambridge, England.

....is R ae = R ae . r is the covariant derivative operator. 2 can only be regarded as a major piece of missing information regarding the physics of the scalar field. Recently, it was found [31] that if OE is a non gravitational field in a curved spacetime, the Einstein equivalence principle (see [33] for a precise formulation and a discussion) forces the value of to be 1=6. This unintuitive result follows from the study of the Green s function representation of the solutions of the Klein Gordon equation 2OE Gamma ROE Gamma dV dOE = 0 ; 3) and from the requirement that, in the ....

....dOE = 0 ; 3) and from the requirement that, in the neighbourhood of any point of spacetime, the propagation of scalar waves resembles more and more closely the propagation in flat spacetime as the size of the neighbourhood becomes smaller and smaller. This is the Einstein equivalence principle [33] applied to the propagation of scalar waves. The quoted result (later confirmed in [32] holds for any metric and its derivation is completely independent of conformal transformations, or of the conformal structure of spacetime, or of the field equations of the theory of gravity [31] If the ....

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C. M. Will, Theory and Experiment in Gravitational Physics, revised edition (Cambridge Univ. Press, Cambridge, 1993).

....for the existence of long range vector fields. The parametrised post Newtonian formalism (PPN) phenomenologically quantifies possible deviations from general relativity. Such deviations are measured by a set of ten parameters:fl Gamma 1; fi Gamma 1; ff 1 ; ff 2 ; ff 3 ; i 1 ; i 2 ; i 3 ; i 4 [1]. To each of these parameters is associated a class of observable, non Einsteinian effects. The parameter ff 3 plays a special role in that it is associated both with a violation of the momentum conservation law, and with the existence of preferred frames (ff 3 j 0 in general relativity) The ....

.... momentum conservation law, and with the existence of preferred frames (ff 3 j 0 in general relativity) The most striking observable effect induced by a putative ff 3 6= 0 is the existence of a non zero self acceleration for a rotating body, perpendicular to its spin axis and absolute velocity [2, 3, 1]. As a consequence, the total acceleration of a body, which is a member of a gravitating system, can be decomposed as a = a Newt a nbody a ff 3 (1) 2 where a Newt is a two body Newtonian like 1=R 2 force (modified by possible equivalence principle violation effects) a nbody denotes ....

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Will, C. M. 1993, Theory and Experiment in Gravitational Physics, (Cambridge: Cambridge University Press)

.... could have naturally escaped detection so far, and what are the most promising experiments to look for them To complete the point of view adopted in these lectures the reader is urged to consult the (still relevant) Les Houches 1963 lectures of Dicke [1] and the specialized book of Will [2]. In Section 7 below we shall turn our attention to cosmological constraints on scalar fields having gravitationalstrength couplings to matter. 2 Methodologies for testing theories One can usefully distinguish two complementary approaches for testing the experimental validity of any given ....

....gravitation are defined by introducing, besides g , new, long range fields mediating the gravitational interaction. However, one should beware that, apart from tensor scalar theories, all the alternative gravitation theories that have been discussed in the specialized literature (notably Ref. [2]) suffer from various field theory pathologies: unboundedness from below of the energy, negative energy (ghost) excitations, algebraic inconsistencies among the field equations, discontinuities in the degree of freedom content, causality problems, etc. The number of non pathological field theories ....

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C.M. Will, Theory and Experiment in Gravitational Physics, 2nd edition (Cambridge University Press, Cambridge, 1992); and Int. J. Mod. Phys. D 1, 13 (1992) for an update.

.... on the background of quasars, pulsars and radio stars, as well as the verification of the zero points of the coordinates in the inertial reference frame ( 3] 10] 11] v) The experimental tests of the weak field and slow motion approximation (WFSMA) of modern theories of gravity ( 12] [13]) These studies will enrich our knowledge about our universe, its cosmological evolution, and the behavior of stellar systems in general. By presenting this list of problems, we would like to emphasize the importance of the Mercury Orbiter mission not only for the gravitational theory, but for ....

....surrounding indices denote symmetrization and square brackets denote anti symmetrization. 3 connected with ae by an equation of state. The quantity ae Pi is the density of internal energy of an ideal fluid. The definition of Pi is given by the equation based on the first law of thermodynamics ([13], 23] 26] 27] u n i Pi ;n p i 1 b ae j ;n j = 0; 2) where b ae = p Gammagaeu 0 is the conserved mass density. Given the energy momentum tensor, one may proceed to find the solutions of the gravitational field equations for a particular relativistic theory of gravity. The ....

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C. M. Will, Theory and Experiment in Gravitational Physics, (Rev. Ed.). Cambridge University Press, Cambridge, England (1993).

....is a field variable [11] Historically, most interest has been given to Brans Dicke (BD) gravity, in which the coupling function (OE) free function these theories have, is constant. To ensure that the weak field limit of this theory agrees with current observations, has to be big enough [12]. But in general, when varies, we need that 1 and Gamma3 d =dOE 0 when t 1, to allow the weak field limit of scalartensor gravitation accord well with general relativity (GR) tested predictions. Afterwards, soon was realized that these general scalar tensor theories would admit ....

....to incorporate gravity with other forces of nature [14] In general, almost all studies made on scalar tensor gravitation focus in the cosmological models they lead. This is in order to put several constraints upon the coupling function. Observational bounds, mainly coming from weak field tests [12] and nucleosynthesis [15 18] are more restrictive if exact analytical solutions are known for the cosmological equations. A few years ago, Barrow [19] Barrow and Mimoso [20] and Mimoso and Wands [21] derived algebraic numerical methods that allow Friedmann Robertson Walker (FRW) solutions to be ....

C. Will, Theory and Experiment in Gravitational Physics (Cambridge University Press, Cambridge, England, 1981)

....and Dirac s large number hypothesis as new ingredients. Ever since it first appeared, it has remained as a viable theory of classical gravity in that it passed all the available observational experimental tests provided a certain restriction on the generic parameter, of the theory is imposed [4]. Shortly after the appearance of their first work [1] one of the authors, C. Brans provided static, spherically symmetric metric and scalar field solutions to the vacuum BD field equations [2] Since the gravitational collapse and the subsequent black hole formation is generally of great ....

.... the parameter is positive since it has been prescribed so originally in the BD theory itself [1] namely according to Brans and Dicke, the positive contribution of nearby matter to the spacetime dependent Newton s constant demands be positive) and it also has been constrained so by experiments [4] (for 500, the theory is in reasonable accord with all available experiments thus far. In fact, there is another crucial reason why has to be positive from field theory s viewpoint. Namely, in order for the BD scalar field 2 Phi to have canonical (positive definite) kinetic energy, ....

See for example, C. M. Will, Theory and Experiment in Gravitational Physics, Revised Edition (Cambridge : Cambridge University Press, 1993).

....publications [12,13] are devoted to that subject. Below we describe briefly the technique we used to tackle the problem and the way we used EinS. 3. 2 Metric tensors and coordinate transformations We begin with the global PPN metric tensor of an isolated N body system in the form (see, e.g. [20]) 10 g 00 = Gamma1 2 c 2 w(t; x) Gamma 2 c 4 fi w 2 (t; x) O(c Gamma5 ) g 0i = Gamma 2(1 fl) c 3 w i (t; x) O(c Gamma5 ) g ij = ffi ij 1 2 c 2 fl w(t; x) O(c Gamma4 ) 1) where the gravitational potentials w and w i are defined as volume ....

....i . We have written the metric tensor of the global PPN reference system without specifying an explicit form of the energy momentum tensor. This is no more than a formal way to specify the global PPN metric tensor. The metric (1) 5) coincides with the version of the PPN formalism described in [20] as well as with the version discussed in [18] provided that only two parameters fl and fi are retained in both versions and the corresponding models for T fffi are substituted into (1) 5) Effectively, we consider only those theories of gravitation which produce the metric (1) 5) in the ....

Will, C. Theory and experiment in gravitational physics, revised ed. Cambridge University Press, Cambridge, 1993. 20

....limb of the Sun and it decreases with the inverse impact parameter of the (unperturbed) light ray from the Sun. This implies that the light deflection (more precisely the gravitational time delay) in the field of the Sun is measurable even for radio sources lying closely to 180 ffi from the Sun [1,2]. For the analysis of high precision optical astrometric measurements at the milliarcsecond level (e.g. HIPPARCOS) GRT became an indispensable tool [3] For planned space interferometry with microarcsecond accuracies (DIVA, GAIA, SIM, FAME, etc. relativity will play a crucial role and the whole ....

....second reason for this effacement is the principle of equivalence. In its weak form, applicable to Newtonian celestial mechanics, it asserts the equivalence of inertial mass with gravitational mass that has been tested by experiments with a relative precision of about 10 Gamma11 (see e.g. Will [1] for more detail) As explained in great detail, e.g. in [20 22] the treatments of both sub problems in the classical post Newtonian approach are unsatisfactory. One usually considers the N body 4 problem in some asymptotically flat space time that can be covered with one single global ....

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C.M. Will, Theory and Experiment in Gravitational Physics, Cambridge University Press, Cambridge (1993).

....i ,U ij ,W ,W i ,W ij 167 ( Gammag) t 0i c 1 R i ,U ,U ij 16 c Gamma1 R i ,U ,U i ,U ij ,W ,W ij 157 ( Gammag) t ij c 2 R i 2 c 0 R i ,U ,U i ,U ij 151 c Gamma2 R i ,U ,U i ,U ij ,W ,W i ,W ij 1268 pseudotensor (see, e.g. Section 4. 4 of [16]) The complete expressions for the pseudotensor for the metric (2) are available from the author. 3.3 Local reference systems in the PPN formalism Another interesting problem is a definition of the local reference system of a massive body in the PPN formalism. The problem can be described in the ....

Will, C. Theory and experiment in gravitational physics, revised ed. Cambridge University Press, Cambridge, 1993. 5

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Will, C. M. 1981, Theory and Experiment in Gravitational Physics, (Cambridge: Cambridge University Press)

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Will, C. M. 1981, Theory and Experiment in Gravitational Physics, (Cambridge: Cambridge University Press)

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Will, C. M. 1981, Theory and Experiment in Gravitational Physics, (Cambridge: Cambridge University Press)

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Will, C. M. 1981, Theory and Experiment in Gravitational Physics, (Cambridge: Cambridge University Press)

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Will, C. M. 1981, Theory and Experiment in Gravitational Physics, (Cambridge: Cambridge University Press)

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Will, C. M. 1981, Theory and Experiment in Gravitational Physics, (Cambridge: Cambridge University Press)

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Will, C. M. 1981, Theory and Experiment in Gravitational Physics, (Cambridge: Cambridge University Press)

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Will, C. M. 1981, Theory and Experiment in Gravitational Physics, (Cambridge: Cambridge University Press)

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Will, C. M. 1981, Theory and Experiment in Gravitational Physics, (Cambridge: Cambridge University Press)

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Will, C. M. 1981, Theory and Experiment in Gravitational Physics, (Cambridge: Cambridge University Press)

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Will, C. M. 1981, Theory and Experiment in Gravitational Physics, (Cambridge: Cambridge University Press)

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Will, C. M. 1993, Theory and Experiment in Gravitational Physics, (Cambridge: Cambridge University Press).

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C. Will, Theory and Experiment in Gravitational Physics. Cambridge University Press, 1993.

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C. M. Will, Theory and Experiment in Gravitational Physics (Cambridge Univ. Press, Cambridge, 1993). Translated by V. Astakhov

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