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Reading this last post led me to question whether the conversation between Doc Al and Russ_Watters ought not be left unanalyzed. I had finished reading the entire thead earlier and began to look backwards for something interesting to scrutinize.Doc Al said:Right. Don't confuse this "separation velocity" with a relative velocity.

As another example: Someone (observer A) observes two rockets (B and C) traveling in opposite directions, each with speed 0.9c. The "separation velocity" of the two rockets,as observed by A, is 1.8c. But the speed of C as observed by B (the velocity of C with respect to B) is only 0.994c.

There is a way for B and C to observe their relative separation velocity to be equal to the separation velocity measured by A who measure 1.8c, which is twice the velocity of each ship moving at .9c in opposite directions. I use c=1 the unit speed of light.

We start the measurement when B and C are 1/9 either side of the zero point A. At this instant B moving left and C moving right a photon is emitted parallel to each of the oppositely moving ships from A.The wave lengths L of each photon moving toward their respective ships is, L(B) not equal to L(C).

As B and C expand in distance from A the photons catch up with B and C after 1 second, measured in the stationary frame. Here each photon is reflected back to the origin arriving there at t = 2. At this time B and C are each 1.8 for c = 1, unit speed of light, on either side of A.

The reflected photon from B, or L(B) is allowed to proceed to C and the photon L(C) is allowed to proceed to B. From symmetry considerations each photon will arrive at their respective target ships when t= 4 8/10 or t = 48/10 seconds, if I haven't miscounted. B amd C having timed the emission of the photons can accurately determine when the alien photon wave length length arrives at the domestic detector, hence observers on each ship deduce that the expanding velocity of each ship is identically 1.8c, unambiguously.

Knowing their intrinsic speed, the B and C clocks on the ships can be calibrated to run identically with the stationary clocks. Here the expansion/relativity velocty are calculated in stationary and moving frame times.