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Clocks in the vicinity of earth as observed by GPS (Global Positioning System), do not seem to vary with their distance from the sun. This phenomenon has been described as the "noon-midnight" problem and was discussed by Hatch (2004). Clocks on the earth or in orbit around the earth are closer to the sun at noon than at midnight, however, the difference in gravitational potential from the sun does not result in different clock rates. The relativistic gravitational forces in the throughout (???) the near earth system are very nearly the same as at the orbital radius. This paper is a detailed analysis which shows that the observations are a result of relativistic equivalence and that the change in distance effects are nearly canceled by the corresponding change in orbital velocity. Previous authors have suggested that the solution to the problem is the equivalence principle but, to my knowledge, no thorough mathematical analysis has been presented.

If two inertial systems or reference frames in the vicinity of the same mass gravitational reference are moving in a straight line relative to each other at least one of them must be accelerating relative to that gravitational reference. Since the universe is defined by its mass objects it is the contention of this presentation that Lorentz transformations cannot be applied to "non-accelerating reference frames" moving at constant velocity relative to each other anywhere in the universe. 1t further shows that the Lorentz transformations are not covariant but are on way relationships relative to fixed gravitational reference points in space. The empirical evidence that appears to support the covariance of the Lorentz transformations also support the one way hypothesis since the experiments and observations were mostly made in the Earth' s gravitational field.

If the Schwarzchild solution for Einstein's field equations were modified very slightly black hold theory and the big bang theory would have to change completely while all of the observed anomalies predicted by his solution at long distances from a central mass object would still be correctly predicted. If one takes the position that the proximity of a mass object is not "empty space" then the requirement that the metric be invariant under the time reversal, t -> -t, does not hold there. The result is a new metric which approaches the Schwarzchild metric as the distance from a central mass object increases. One consequence of this modification is that if a mass object smaller than its event horizon existed. its event horizon would be at MC/c² rather than 2MC/c² and nothing could get inside it because G becomes zero at the horizon and is negative inside it. There are no singularities. Depending on how one looks at it, time either stops or the velocity of light goes to zero at the event horizon.

Futurics, V19, N3-4, pp. 24-28 (1995).