It could be argued that the moved clock had to be accelerated to be moved so that the overall process was not a constant velocity situation. That is not the contention of relativity, however, which states that the moved clock does run slower and relies on the fact of acceleration to make the distinction as to which clock was moved and which stayed at rest.
(5) Consider three clocks, #1, #2, and #3, at constant velocities
v1, v2, and v3. According to relativity the time of clock #3 is contracted by some amount relative to Clock #1. Likewise Clock #3 is time contracted relative to Clock #2, but by some different amount. But, Clock #3, with a time contraction relative to Clock #1 in an amount based on the velocity difference between Clock #1 and Clock #3, and with a time contraction relative to Clock #2 based on the velocity difference between Clock #2 and Clock #3, cannot be actually contracted two different amounts at the same moment. Since the contraction must be actual, not solely observational, an absurdity results.
The solution to this problem is simple. All clocks are actually, as observed from the prime frame of reference, contracted according to their absolute velocity relative to that frame, not according to their velocity relative to another moving clock. In addition, an observer at a moving clock observes somewhat different results than those actual absolute contractions because his standards of measurement have also been contracted by his own motion [even though they
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appear unchanged to him]. This produces an observed, but not actual modification of the absolute, actual contraction.
[Of course, if one of the moving clocks is moving at a modest velocity the difference between its at rest dimensions and its actual contracted ones is so small that the observations from that slow-moving clock would be essentially equivalent to from at rest, the very case set out for planet Earth in (3) above.]
In his original paper on relativity Einstein contended that there was no way that an observer experiencing acceleration could distinguish between whether his system was actually accelerating in a region free from gravitation or was actually at rest in a gravitational field. In fact, that contention is incorrect and the distinction can be made by local measurement, as is now known. The distinction occurs because gravitation follows an inverse square law in practice in the real universe and gravitation is inherently radial relative to the gravitating mass.
One could say that Einstein was largely correct but for partially incorrect reasons. The same can be said of the effect of absolutivity on cosmology and space-time physics. The results obtained by traditional 20th Century physics and the theories leading to them are largely correct. Absolutivity only restores the medium and the prime [but not "preferred", special, nor having different physical laws] frame of reference.
The fact that until recently we could detect no absolute velocity and that even now it is only detectable with special scientific effort does not mean that all motion is relative, it only means that we have not developed the means for ready detection of absolutivity. There have been many other things that were undetectable in the past but that are not so now: germs, distant stars, x-rays, atoms, etc.
The Theory of Relativity has required mind-twisting adjustments to way of thinking, adjustments away from the reasonable and "apparent" to a mass of paradoxes and their proposed resolutions. Absolutivity retains contact with reality both in describing physical reality accurately and by doing so in a fashion much more consistent with reasonableness.
With absolutivity the principle of invariance becomes simple, practical and apparent in addition to being necessary as it always was. There is only one "system", the universe with some parts moving in various ways and some parts at rest and that one system has, of course, one overall set of physical laws throughout. Before absolutivity, invariance was necessary but was crying for an explanation, a cause. One can see no particular reason why invariance should be necessarily automatically true in the universe of the Theory of Relativity. Absolutivity solves the problem by showing the natural inevitability of invariance.
Why does this new medium succeed when all prior attempts to define an "aether" without contradictions failed? The reason is the nature of the electro-magnetic wave medium, as follows.
Electro-magnetic field is cyclically changing electric and magnetic field. It is caused by changing motion of electric charge. The changes are changes in the always-present static field of electric charge. The variations in the static field are relative to its average value, the static field amount in the absence of motion of charge. The magnetic field is a further variation in the static field, a distortion of it due to the effect of charge motion.
Static electric field is normally thought of as just that, static. But, if electro-magnetic waves are merely variations in that field and yet they propagate at the speed of light, then the static electric field must be a propagation of some thing at the speed of light,
c. Such a propagation model of static electric field is essential. Otherwise communication at speeds in excess of the speed of light could take place by making static field changes. See Inertial Mass, Its Mechanics - What It Is; How It Operates 2.
That propagation, the static electric field, is the medium, the "aether", and it is relative to the universe' prime frame of reference, that of the "Big Bang", that of where its source charges originated, where they were before motion carried them elsewhere. That propagation emanates from each charge, originally from the origin of the "Big Bang" and now from wherever each
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charge is. It, itself carries the controlling parameters
μ and ε. See Gravitational Mass, Its Mechanics - What It Is; How It Operates 3.
It is now time to address the apparent paradox that was left as a question at the beginning of this discussion. The apparent paradox had two elements.
First
A charge at rest relative to the Earth's surface exhibits to us, who are also at rest relative to the Earth's surface, no magnetic field even though the charge is clearly in motion with the Earth's surface rotating about the planet's axis, revolving about the sun and moving relative to and with the galaxy.