Abstract

The view taken in this paper is that if we accept a theory where earth's gravitational field constitutes a preferred reference frame, it is reasonable to assume that this reference frame has at least some ?rotational? velocity near earth's surface. Under this view, the gravitational field of a given element of earth is considered to move with its mass center. The possibility is raised that the rotational velocity is below the value detectable from existing experiments because the effects of mass on opposite sides of the earth moving in opposite directions tend to cancel one another. Fundamental thoughts are presented for establishing a theory which predicts a field rotation which lags behind the rotation of the body producing it. A vector equation is then proposed for determining the velocity of a local preferred reference frame based on the motion of nearby matter. A computer program was developed to apply this equation to the rotating earth. The program allows the earth to be divided into 1 million elements and computes the unique velocity, density based mass, and distance from point of interest, for each element. As expected, the net field rotation at the poles is zero and increases as the equator is approached, with the rotation at any given latitude always being substantially less than the surface rotation at that latitude. Results also show that the rotation approaches zero as we move away from the rotating planet. The proposed vector equation is written to include an unknown function, F(R), describing how the influence of a given mass varies with distance, R, from the point of interest. Two specific functions are examined where the influence of earth dominates that of other mass in the universe. A third function, derived based on the variation of light speed within a gravitational field, is then examined. For this function, the influence of the sun and possibly of other mass in the universe cannot be neglected. Results obtained by applying these functions to the rotating earth are used to predict expected results for the Michelson-Gale experiment ?The Effect of the Earth's Rotation on The Velocity of Light? and for the Hafele-Keating experiment ?Around-the-world Atomic Clocks: Observed Relativistic Time Gains?. It is shown that the proposed vector equation can be made consistent with experimental results when an appropriate function, F(R), is selected. It is also shown the Michelson-Gale experiment would not detect a rotating gravitational field, regardless of the magnitude of the rotational velocity, if the rotational velocities in the upper and lower legs of the experiment were nearly equal.