Determine the velocity of an inertial frame using only three recorded time-of-flight events wert motion of a single light pulse.

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The question then is, does this measurement of velocity constitute a prohibited condition anticipated by any postulate[1] of SRT?

“It is impossible to measure or detect unaccelerated translatory motion in free space”?

From the schematic of the system in Figure 1 measuring the velocity of the inertial frame A is clearly a very simple system. The A frame velocity is determined by a measurement of the distance a pulse of light travels in specific recorded time events. There are only three of these events: 1. the time the pulse was emitted from the A frame at t0, 2. the time the pulse arrived back at the A frame after reflection from the inertial frame transponder, Tp at t1, and 3. The arrival back at the A frames of the light pulse re-emitted at t1.

The total light path has been segmented into two parts, (d1 + d2) and (d3 + d4). Remember the direction of the light pulse is unimportant, it is the total light path traveled that is measured.

The distance difference, (d1 + d2) - (d3 + d4) is the distance the frame traveled during the total time-of-flight traveled by the light pulse that is (d1 + d2) and (d3 + d4).

Picture the frame moving in the direction of the pulse moving away until the distance (d1 + d2) was traveled (project a straight line without the reflection). Attaching the final pulse trajectory to the end of the (d1 + d2) and heading toward the oncoming A frame, the collision of the pulse and the A frame determines the total distance traveled by the pulse and t2 duly notes this event.

The definition of velocity is,

V = [Xn+1 − Xn]/[ tn+1 − tn] (1)

The data base of experimental data is contained in the three time events, t0, t1, and t2. Expressing the dn in time and speed parameters with unit speed of light c = 1, then ,
(d1 + d2) - (d3 + d4) = [(t1 − t0) − (t2 − t1)] = Va(t2 − t0) or,
VA(t2 − t0) = 2t1 − (t2 + t0) hence,

VA = [2t1 − (t2 + t0)]/(t2 − t0) (2)
QED.

There is no referenced inertial frame to which the A frame VA is measured, or needs to be measured from; there is no “absolute velocity reference frame, implied or expressed, where Vf = 0”. Remember, the VA was not determined by a stop watch and meter stick. The VA is a calculated term using the known speed of light, the time-of-flight of the pulse trajectory segments, and the definition of velocity. Can the origin of the light pulse be located and returned to? Yes, but there should be a valid reason for such a future activity – sentimental reasons ought not to be consider a valid reason. If the VA becomes suspect, measure the velocity again.

V = (Xn+1 – Xn)/(tn+1 – tn). (1)

I found this postulate in [1] Chapter 11, Relativistic Flight Mechanics, “The Handbook of Astronautical Engineering”, 1st Edition, Ed. H. H. Koelle, fwd. W. von Braun, McGraw (1961)