5 Concluding Remarks.Of the possible mechanisms that could be responsible for time dilatation and the Acceleration Potential of D1, the only one for which a creditable mathematical process can be derived, is that in which the gravitational source creates a localised spatial expansion, via transition from the temporal dimension. In particular, it clearly promulgates satisfactorily outside the source with no discontinuity at the boundary, the physical surface of the source. This is a new concept for which no experimental nor observational support exists, and has therefore to be regarded as speculative. However, the manner in which the parameter g fits into the concept provides good circumstantial support to the idea, and indeed provides a physical meaning for the parameter g itself. The velocity vs appears on all radius vectors from the source, and as described appears because of the expansion of space emanating from it. As has been discussed, the only effects this process has on other material bodies is gravitational acceleration, and time dilatation. However, under certain conditions, it is possible that the spatial expansion process, over long enough periods of time, may have significant cosmological consequences. These will be discussed at length in a future paper. One other significant point is the similarity of the field equations of the new theory to those of Newtonian theory. This is due to the linearity of the space-time continuum in the new theory and its only difference to that of Newtonian theory being a relativistic one. In this paper the Acceleration Potential has been shown to be due to the spatial variability of the linear velocity of the spatial expansion wavefront generated by the gravitational source. Time dilatation is in turn caused by the variation in local temporal velocity, due to the presence of the spatial expansion and the criterion for existence in D1. However, because the spatial expansion wavefront is a spatially distributed variable, so is the time dilatation effect and this in turn affects the net gravitational acceleration experienced by a free body in D1. This effect is fully expressed in the equation for planar gravitational motion in D1, viz. [1], Eq(3.18). Thus the proper and complete cause of gravitational motion in D1, can now be formally stated as follows:- (i) The primary cause is a negative acceleration produced by the Acceleration Potential of the Domain, which is, in turn, the result of the spatial variability of the linear radial velocity of a spatial expansion generated within the source as a result of its motion in the temporal direction.
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P.G.Bass, August 2009
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