IRREVERSIBLE TRAJECTORY
(SGM Prediction)
If the Newton-Einstein harmonic motion prediction is correct, the test object's trajectory would perfectly illustrate the symmetry of time's arrow. It would not be possible to tell whether a video recording of the motion was played back in the forward or backward direction.
On the other hand, if the SGM non-oscillation prediction is correct, the test object's trajectory would perfectly illustrate time's asymmetry. A video recording of the motion would look physically correct only when played back in the forward direction.
The reason is simple: Time only increases because space and matter also only increase. The arrow of time goes with the arrow of space and the arrow of matter; in effect, they all point outward. This is the essence of gravity.
A further corollary corresponding to this trajectory is the SGM's prediction that a clock at the center of the large mass has the same maximum rate as a clock at infinity.
Also, if borne out by experiment, this trajectory would be cogent evidence that there are four dimensions of space.
The reversibility of time and the corresponding oscillation prediction follow not only according to the standard conceptions of gravity in particular, but more generally, from the energy conservation law. Which means, of course, that the SGM prediction involves a violation of this law: the increase of mass and space make it appear, at first, that the test object accelerates toward the center. But consider: if the test object is an accelerometer, its reading remains zero as it falls. Whereas accelerometers attached to the large mass all have positive readings. If these accelerometers are telling the truth* about their state of motion, then the energy conservation law is incorrect. Rather than insist that energy must be conserved (and that the accelerometers are lying) or not, the scientific method demands that we discover the truth by experiment.
The energy conservation law is practically sacred, as it has been repeatedly confirmed by experiments--in the case of gravity, near or beyond the surfaces of large bodies. But none of these experiments have sought to find out whether the law remains true in the case of free fall into the center of a massive body. Perhaps faith in the sacred law will prove to be well founded. But that faith is no replacement for an empirical fact.
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*In General Relativity one is encouraged to have one's acceleration and to call it static too. A General Relativist may agree that the accelerometers are telling the truth; but he or she will also call the field of the spherical mass static. This contradictory approach is seemingly justified by saying the positive accelerometer readings indicate acceleration with respect to the nearby geodesics (free fall trajectories) in the field. This raises the question, what must the massive body be doing to produce so many positive accelerometer readings? How does a static body manage this amazing feat? My guess is that it is impossible for a static body to do such a thing; positive accelerometer readings do not indicate a state of staticness; they indicate a state of real, absolute acceleration. Matter is not static; it is in a state of perpetual outward motion. Which of these approaches is correct, again, needs to be decided by experiment.