... The view from "B" that "A" "Appears" dilated is in fact just an illusion of motion. This view is supported by emperical data. To suggest that "A" actually changed tick rate and accumulated a different time as a physical reality is simply nutty. It would require that every clock in the universe have an infinite number of tick rates so as to be physically correct to all observers over all relative velocities...
(B was the clock that accelerated away from A which is still in the "common rest frame.")
... A clock remaining at rest has absolutely no cause factor to change. A mere relative velocity cause is ludricrus and physically impossible.
First let me agree with one of the ambiguous ways of interpreting you imprecise statements above:
It is true that the physical tick rate of both clocks A & B is unchanged by the existence of some other clock moving in another inertial frame. I.e. a just made pregnant lady can expect nine months to pass by her clock before the baby is born.
However assuming I am not in her frame but another inertial frame moving wrt hers I can measure that it takes her longer to make the baby. This is because I will use my clock, not hers to determine the rate the fetus is growing just as I will use my clock to determine the speed that her house is moving away from me. In fact I am very stubborn about this - I always compute ALL rates the same way no matter what they are or where they are or how they are moving wrt to me and my clocks.
I determine a rate of x change as follows:
The value of x at some initial time t1 is noted and is x(t1). Then later x(t2) is recorded. Then the rate of x change is [x(t2) -x(t1)] / (t2-t1)
The pregnant lady would do exactly the same but use her clocks. For example her time interval is (T2 -T1) and her X1 is my x1 event. To take a specific example, For both of us X1 & x1 are touching a lighted match to a fire cracker fuse, and for both of us, X2 & x2, are the fire cracker exploding. There are two identical firecrackers, one stationary in each frame. (I light mine, she lights hers. We do not even attempt to do this simultaneously as that will just lead to arguments in this discussion.)
I might add that if we ever had what you call a "common rest frame" it was for both of us many years ago and neither she nor I were old enough to have any clocks or firecrackers back then.* In fact the clocks and fire crackers have never been at rest in the common rest frame as all were only made a few weeks ago. I.E. NEITHER the clocks nor the firecracker were ever accelerated so they cannot be affected by acceleration that was in the distant past, long before they even existed.
You will agree that at least (T2 -T1)' > (t2-t1) or (T2 -T1)' < (t2-t1) as you do not deny "one way" time dilation, but refuse to be both are true
and that is correct as the prime I added to the right side quantities is to indicate that (T2 -T1)' is the time her fuse burns by my clocks and I cannot belief it both longer and shorter than the time (t2-t1), my identical fuse took to burn by my clock.
Exactly the same for her either: (T2 -T1) > (t2-t1)* or (T2 -T1) < (t2-t1)* but not both. Where an asterisk is added to time interval for my fuse to burn as measured by her clock.
SR states time is dilated in the frame moving wrt you. She and I both accept that. I.e. she believes (or measures) (T2 -T1) < (t2-t1)* and I believe (or measure) (T2 -T1)' > (t2-t1). Or in the less well defined words you use:
Both measure the others identical fuse as burning more slowly. You MacM assert that this is not physically possible. So you go on to conclude that since what SR asserts is nonsense, SR must be at least partially wrong.
I.e. you say it is not possible for her to measure my time interval (t2 -t1)* as longer than hers (T2 - T1); and also for me to measure her time interval (T2-T1)' is longer than mine (t2-t1). But it is as (t2 -t1)* IS NOT THE SAME AS (T2-T1)' Your lack of (actually your refusal to use) well defined symbols to aid clear thinking is at the heart of your belief that SRT is wrong, I think.
There is nothing impossible here; again:
(t2 -t1)* IS NOT THE SAME AS (T2-T1)'
It only seems to be the same when imprecisely expressed in your words as follows:
"Both CANNOT measure the others identical fuse as burning more slowly. THAT IS NONSENSE"
Probably all but you can see what the problem is: (Lack of precise terminology.)
Possibly even
QQ can or else he believes that (t2 -t1)* IS THE SAME AS (T2-T1)' since he believes time dilation is an inertal effect and in this example no clock or firecracker was ever subjected to any acceleration. I would like to know what he thinks.
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*Actually neither of use even existed back then (more than 150 years ago) when the acceleration took place - see post 425 for more details.