MacM: I do not give any particular numerical value for the relative speed of the frames. You are free to choose any you like. I.e. I use algebraic symbols for everything to cover ALL POSSIBLE CASES.
... Now let me repeat this in plain english. A & B are at rest in frame Eo,o. They both launch toward frame C which, you have failed to designate what that frame is with respect to frame E. Since it is not the same frame it must have relative velocity to E. Is it approaching or receeding and at what velocity.?
No, their relative speed is Vce. That and their relative geometries and their directions of motion is all given in post 118, in great detail and several times in different ways as follows:
... two inertial frames C & E, which have respective motion at speed Vce along a common “X-axis” line. The origin of E, designated as E(0,0), is already far to the right of the origin of C and the separation between these origins is increasing. All motions I will use are along this same X-axis line. …
And twice more again as:
...{1} Both A & B were stationary at the origin of frame E, I.e. were at E(0,0), so were co-moving away from C(0,0) at speed Vce. {2} Then both accelerated (in separate rockets, a & b) in the negative X direction (towards C’s origin) exactly the same until their C coordinates was very large and positive, for example the point C(100000, 0).
But as you did not like to read that much, so in post 198 I put much of this into one sentence of my three line scenario description as follows:
... “While at rest in E, they {clocks A &B} have speed of Vce away from the distant point C(0,0) in frame C's positive X direction.”
I do not give any particular numerical value for the relative speed of the frames or the scale units of X. You are free to choose any you like. Ie. That X=100000 could be 100000 miles, meters, light seconds, etc. I.e. I use algebraic symbols to cover ALL POSSIBLE CASES.
I admit that in post 198, unlike post 118, you must be able to think a little to fully understand the scenario geometry and history etc.
I.e. If the clocks are at rest in frame E, but have speed away from the origin of frame C equal to Vce, in C’s positive direction then:
(1) Like the resting clocks, frame E has speed away from the origin of frame C, the point C(0,0), also.
(2)The origin of frame E, E(0,0) is already to the right of C(0,0). (“speed
away from the origin of frame C” )
(3)The distance of E(0,0) from point C(0,0) is increasing (“moving in C’s the positive X direction.”)
(4) As the motion is along C’s X-axis even in frame E, this confirms the prior statement that ALL motion is along the X-axis direction common to both frames.
SUMMARY: E(0,0) is already “distant” and to the right of C(0,0) and this distance between the two frame origins is increasing with speed Vce.
Even this is just repeating the start of post 198 which was:
“I have …two references frames, C & E in relative motion along their common X-axis line with relative speed Vce.”
The later stated fact that when the clocks accelerate away from resting at E(0,0) they travel in “in the negative X direction (towards C’s origin)” also tells you the relative locations of the two frame origins.
You are just finding one cop out after another to avoid admitting your version of SR is self contradictory.
(as I proved mathematically in post 118 by following your procedures twice to get two different values for the same clock’s time dilation.)
You have not even told which of your two (approved in your post 93) conflicting proceedures is false and which is correct.
Nor do you deny that your logic is circular: I.e. we are discussing whether or not SR’s prediction that the tick rate of a clock depends upon which frame’s clocks are used to measure it. You, however, ASSUME it does not and postulate the existence of what you call the Physical Tick Rate or the universal Physical Time Dilation and tells us to calculate it with the clocks speed wrt their prior “common rest frame.” Postulating the answer to the question as your starting point in a discussion is not an argument for your POV – it is circular reasoning.