I'm going to answer your last question not for your benefit, because you didn't understand the answer the last few times, but because it's a fair question and maybe someone who tuned in late might benefit from the answer.
Reality is information and time is the rate of the flow of information. If the sun was knocked out of the sky, the reality of that event wouldn't reach us for 8 minutes. The max rate of information is c through time which manifests itself as the normal passage of time. Time can actually pass at any faster rate but to our perspective, the rate of time is maxed out at c. Because information is delayed, there are two types of time and two types of reality. Perspective time is each of our individual perspectives of reality delayed by the speed of information. Relativity says that is reality instead of defining reality as the causal source of perspective reality before it gets delayed.
Causal time is independent of the speed of light delay and so being instantaneous can only be post-processed unless the participants are co-located. Perspective time is how we experience causal time in its delayed form or in its instantaneous form if it's local. Causal time is independent of perspective and constant relative velocity so there is no time dilation in causal time. The time dilation that occurs in perspective time is independent of what's going on in causal time. Causal time ticks at the same rate within all frames and between all frames in constant relative velocity. There are two exceptions. The rate of causal time is not common between frames under different gravity or experiencing 2 different relative velocities such as when info delay of constant relative velocity occurs due to one's change of velocity. Under those two scenarios, causal time is ticking at two separate rates between the two participants.
The question is why would an imbalance in relative velocity cause causal time to tick at different rates between two participants? What is the link between velocity and time that would cause this? Nothing can travel faster than c and that includes the speed of information. That velocity is what creates both causality and time itself which manifests itself to us as the normal passage of time. Velocity controls the rate of that information transfer. The faster a ship goes out, the slower the rate of information that gets back to us and hence the slower we observe his time to be going from our perspective. This effect is reciprocal but is only perspective and not real from the causal reality definition. If he goes out at a constant velocity, the rate of time slowing from our perspective is also constant even though neither see their own time slowing because causal time is not slowing and they are co-located with that rate of time. Causal time rate is reality, not the illusion of perspective.
We can see the illusion of time slowing by receiving his televised picture, he would appear to move slowly to us. If he was coming towards us, the rate of information from him would be increased to a faster constant rate. His televised picture would show him moving through time at faster than normal rate like a fast forward DVD.
This Doppler shift ratio is just as much an illusion as time dilation but is not the same thing as time dilation. Everything is always moving at c according to this equation:
c2 = vx2 + vt2.
The faster you're observed to move through space, the slower you're observed to move through time. The time dilation is the other guy's observed velocity through time (vt= c/Y) while the Doppler shift ratio is what we observe as the other guy's half speed velocity of (vt). So numerically, if vx = .6c, time dilation (1/Y) = .8 so vt = .8c and the Doppler shift ratio is half speed of vt = .5 (according to relativity's velocity combo law).
So none of this has anything to do with real ageing, it's all illusion of perspective; the two people are actually ageing at the normal rate. But if one makes a change in their velocity, an imbalance is caused in their relative velocity until the reality of the change reaches the other party which then establishes a new relative velocity between the two. Constant relative velocity is what causes time dilation between the two participants in perspective time but it has no effect in causal time. An imbalance in the relative velocity has a delayed effect, in perspective time, on the time dilation between them. Since Alice is co-located with her change in velocity, there is no delayed effect on her. She immediately sees Bob's new time dilation and Doppler shift ratio from her perspective. Bob's still going at the old relative velocity so he still sees Alice's old time dilation and doppler shift ratio until the delay of info between them is resolved. Reality is information so Bob's perspective reality is out of sync with causal reality.
If Alice was a GPS satellite orbiting earth, her orbit would be a round trip journey. Bob would not see any blip in his perspective of Alice's dilated time at her turnaround back to him. Unseen to him, in the realm of causal reality, a correction is going on in their proper time rates. Alice is in fact ageing slower than Bob at a causal time rate that is not related to the time dilation factor, it is related to the Doppler shift ratio of her relative velocity to Bob which is the real relative velocity. Time is passing at twice normal rate for her while it still ticks at normal rate for Bob so she only ages 2 yrs for Bob's 4. Her velocity through time is actually 2c while Bob is still seeing it at .5c. This correction at the causal time level stops as soon as they re-establish a new relative velocity when the info reaches Bob that a change has been made. At this point, the Doppler shift ratio from Bob's perspective of Alice changes from .5c to 2c, they will now see each other go through time at double the normal rate but this is just an illusion of perspective time. In causal time, Alice was actually flying at double the speed of light through time for 4 of Bob's years (she did them in only 2 of hers).
Alice is unaware that she has been going at twice the velocity of light through time because she has only Bob to compare to. The moment she made her change, she saw his Doppler shift ratio switch to 2c from her perspective. The difference this time it was no longer perspective illusion but causal reality that she was going at 2c. She still saw herself as going at the normal time rate because her clock ticking would speed up along with her. Time itself had warped for her during this relatively short time in her journey.
Edited by ralfcis, Yesterday, 09:26 PM.