Local Gravitational Field Research Articles

A background-dependent approach to the theory of gravitation II. Relativistic gravitational equations

On the basis of the results of Paper I and guided by a Machian view of nature, we find new gravitational equations which are background dependent. Such equations describe a purely geometrical theory of gravitation, and their dependence on the background structure is through the total energy-momentum tensor on the past sheet of the light cone of each space-time pointx [θμνx, say], i.e., through the integral on the past sheet of the light cone ofx of the parallel transport of the energy-momentum tensor from the space-time point in which it is defined tox along the geodesic connecting the two space-time points. Following Gursey, we assume that the source of the De Sitter metric is not the cosmological term, but, rather, the energy-momentum tensor of a “uniform distribution of mass scintillations” [Tμνx, say].Tμνx, indeed, turns out to be equal to the metric tensor times a constant factor. As a consequence, in any local inhomogeneity A of a space-time whose background structure is determined by the Perfect Cosmological Principle,θμν turns out to be approximately equal to the metric tensor times a constant factor, providedT=gαβTαβ is sufficiently small and the structure of the past sheet of the light cones of the space-time points belonging to Λ is not too much perturbed by the local gravitational field. As a consequence, in Λ the new equations approximately reduce to Einstein's equations. If one considers a “superuniverse model” in which our universe is considered as a local inhomogeneity in a De Sitter background, then from the above result there follows a fortiori the agreement of the new gravitational equations with the classical tests of gravitation. Furthermore, the dependence on the background structure is such that the new equations (i) incorporate the idea that the frame has to be fixeddirectly in connection with cosmological observations, and (ii) are singular in the absence of matter in the whole space-time. Moreover, (iii) the coupling constant turns out to be dimensionless in natural units (c=1=ħ), and (iv) a local inertial frame in a De Sitter background is determined by the condition that with respect to it the background structure is homogeneous in space and in time and is Lorentz invariant.

Stellar occultation spikes as probes of atmospheric structure and composition

The characteristics of spikes observed in the occultation light curves of β Scorpii by Jupiter are reviewed and discussed. Using a model in which the refractivity (density) gradients in the Jovian atmosphere are parallel to the local gravitational field, the spikes are shown to yield information about (i) the [He]/-[H 2] ratio in the atmosphere, (ii) the fine scale density structure of the atmosphere and (iii) high-resolution images of the occulted stars. The spikes also serve as indicators for ray crossing. Observational limits are placed on the magnitude of horizontal refractivity gradients; these appear to be absent on scales of a few kilometers at altitudes corresponding to number densities less than 2 × 10 14 cm −3. Spikes are produced by atmospheric density variations, perhaps due to atmospheric layers, density waves or turbulence. To discriminate among these possibilities, future occultation observations should be made from a number of observation sites at two or more wavelengths simultaneously with high time resolution techniques. Given a large telescope and suitable observing techniques, useful information about Jupiter's atmosphere can be obtained from future occultations of early-type stars as faint as V ∼ + 6–7.

On the effect of spin on the gravitational field

Using a solution of Trautman's recently formulated Einstein-Cartan equations, it is shown that if an isolated body is embedded in an expanding universe consisting of a dust of spinning particles, then the local gravitational field of the body is influenced by spin, even when the cosmological constant is neglected.

Profile Analysis--A Geologically Oriented Gravity Interpretation: ABSTRACT

A byproduct of the examination of three different analytic methods of reducing gravity data to a form useful to the geologists is the presentation of the local gravitational field of one complete quadrangle in the Jurassic trend of Mississippi. The major salt dome minima are qualitatively confirmed by all three methods, although the quantitative effects vary. The more subtle effects of the Jurassic features are more susceptible to distortion by the process of removing the influence of regional density changes. The least distorting method of regional removal is shown to be the interlocking profile network. This technique obtains the most definitive resolution of the local gravitational effects of deep, low-volume structures. End_of_Article - Last_Page 2035------------

Neutrinos, gravity and cosmology

The observation of the soft cosmic neutrino and neutretto background, predicted by different cosmological theories, may be observed efficiently only with the help of reactions having no energy threshold. A new method is suggested making use of local gravitational fields.

Mathematics at Sheffield : Prof. A. G. Walker

DR. ARTHUR GEOFFREY WALKER has been appointed to the chair of mathematics in the University of Sheffield, in succession to the late Prof. P. J. Daniell. Dr. Walker has been a member of the Department of Pure Mathematics at Liverpool for the past ten years. He is thirty-seven years old and was educated at Watford Grammar School and at Balliol College, Oxford. On taking his degree in 1931, he went to Edinburgh and commenced research under Prof, (now Sir) Edmund Whittaker. This was a time of exceptional activity at Edinburgh. Prof. Whittaker was mainly interested in relativity and differential geometry, and his staff, which in the years 1927-32 included E. T. Copson, J. M. Whittaker, J. G. Semple, H. S. Ruse, W. H. McCrea and A. Oppenheim, all of whom have gone on to professorial chairs, for the most part followed his lead. To Walker, who had gained distinction in differential geometry in the Final Honours School at Oxford, the subject of Prof. Whittaker's lectures was particularly congenial, and he wrote several papers, the first of a long series on differential geometry, relativity and cosmology. In 1933 he returned to Oxford to take up a Harmsworth Research Scholarship at Merton College, to which he had been elected in the previous year. He worked with Prof. E. A. Milne on kinematical relativity, then at the beginning of its stimulating and controversial career. This subject has continued to engage Dr. Walker's attention ever since. He is a supporter of Milne's general point of view, but has developed a more general theory, which seems capable of accounting both for cosmological effects and for phenomena due to intense local gravitational fields such as that of the sun. Certain functional equations present themselves in this work, and he has investigated them from the point of view of pure mathematics in collaboration with his Liverpool colleagues F. W. Bradley, now professor of mathematics at the University of Alexandria, and Miss Joyce Batty.

Radial Velocities and the Curvature of Space-time

IN a letter to NATURE of April 26, Dr. Silberstein makes a proposal for determining the distance of a remote star by observing the displacement of the spectral lines at six months interval; he claims that this method will separate the ordinary Doppler effect of the unknown motion of the star from the distance-effect predicted by de Sitter. It seems to me clear that this proposal contains a fallacy. The material to be experimented on is a certain regular train of light-waves proceeding through the small region round the sun accessible to us; the star itself is inaccessible. The frequency of these waves is to be measured by two observers—for example, a January observer and a July observer. These observers differ only in their velocities V1 and V2 relative to the frame of reference; Dr. Silberstein neglects any effects of the short interval of time and of space between the two observations and of the distortion of the waves by the local gravitational field.

The E tv s Torsion Balance

The Eotvos Gravity Balance in the Science Museum, South Kensington, is described, and the theory of its operation considered. A full account is given of certain preliminary experiments made on the torsion wires, with a view to ascertaining the daily variation of the equilibrium position, due to strains set up in the wires during manufacture. Until this daily shift has been eliminated the instrument cannot be employed successfully. The experiments show that a preliminary treatment of the wires is desirable, and a test was also made of the baking method recommended by Eotvos for ageing the wires. This method was found to give the desired result, and after this treatment the reading of the instrument remained practically constant from day to day. Tables are given showing the variation in the reading of the instrument when its beam is rotated into different azimuths, and the constancy of these readings when repeated. The differences in the readings as the azimuth varies are sufficiently marked to indicate the changes in the local gravitational field of the laboratory, and further experiments are being carried out to determine these changes in detail, as a preliminary to field tests; it is hoped to communicate the results of these experiments at a later date.

Application of the E tv s Torsion Balance to the Investigation of Local Gravitational Fields

In a Paper read before this Society on February 9, the Eötvös Torsion Balance was described in detail, and the theory of its operation considered, the preparation of suitable torsion wires was mentioned, but no practical tests with the instrument were discussed.