" So in the end in the battle between Newton and Einstein, who is right? In every day life, they both are. The speeds at which life goes by are so slow that it has only been in recent history that we have been able to detect the differences. Newton viewed space-time as being flat, unchanging and very boring, but that is not at all the case in Einstein’s world. To Einstein, space-time is very dynamic, changing depending gravity and velocity."
Newtonian Physics vs. Special Relativity (futurism.com)
I've got to think about this some more but, my present understanding is that the watches in Uncle Ken's thought experiment do not just appear to run differently, they actually do run differently. The formula that Uncle Ken keeps quoting (rt=d) is Newtonian physics. I believe that time dilation operates the same in Newtonian physics as it does in Einsteinian physics, but the differences are so small as to be imperceptible for all practical purposes. It might be easier to visualize if we look at it from an expanded cosmic perspective.
In the classic thought experiment involving two twins, one who takes a long journey at a significant fraction of the speed of light, the traveling twin does not just appear to age more slowly than the twin who stays home, he actually does biologically age more slowly. When he returns home his rate of aging returns to the rate of his twin, but his currant age does not revert to the current age of his twin, he will always be younger than his twin unless his twin undertakes an identical journey while he stays home this time.
Speaking of links, did you even read this one?
Special relativity indicates that, for an observer in an inertial frame of reference, a clock that is moving relative to them will be measured to tick slower than a clock that is at rest in their frame of reference. This case is sometimes called special relativistic time dilation. The faster the relative velocity, the greater the time dilation between one another, with time slowing to a stop as one approaches the speed of light (299,792,458 m/s).
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I have been reading all the articles in the "Draft" series with interest. Some of it is familiar from stuff you posted in our old email days, but some gaps are being filled in this time, which is good.
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