You really don't understand acceleration do you? Your velocity is dependent on the distance between you and the other ship. You don't believe in a absolute velocity, remember? How can you claim an acceleration when your velocity clearly remains at zero as your clock elapses time?
Except that it doesn't. The inertial frame associated the vehicles initially do not change when the vehicles accelerate. Instead the vehicles move through a sequence of frames, finishing in a final inertial frames once they stop accelerating. They are always at the same distance from one another but they know there has been a change of velocity, they measured the acceleration. In the original initial frame they are now moving at some speed. In their new inertial frame they are not, but in that frame they were moving initially.
Your assertion that the velocity always stays zero is not true. The 'relative velocity' is not between the vehicles but between the vehicles and some frame. Which frame doesn't matter, it shouldn't matter.
Time and time and time again you show you don't know what a frame is in kinematics. The problem isn't with the notion of relative velocity, it is with your understanding of it. The vehicles cannot say what their velocities are absolutely but they don't need to. Instead they can say what their velocities are (say) V
relative to some inertial frame. They are not required to pick the inertial frame they are in at that moment, they can pick any inertial frame.
Let's consider the Newtonian concept of frames, without the need for an absolute reference frame. Frames are choices of coordinates. In Frame 1 a car is at $$x = x_{0}$$ at time t, having started at position $$x_{0}$$ and not moving in those coordinates. The car now accelerates with acceleration a for time T, starting at t=0. It will end up at speed aT. It covered a distance $$\frac{1}{2}aT^{2}$$ in that time so it'll be at position $$x(t) = \frac{1}{2}aT^{2} + (aT)(t-T)$$. We are still working in the original inertial frame, since we're describing the motion in terms of the original (x,t) coordinates. We could now say "I want to work in the new inertial frame, where the car is now at rest". Then we need to do the Galilean transform x' = x-vt = x - (aT)t[/tex] and we'll shift our time coordinates too, $$t' = t-T$$. Reversing these relationships we have $$t = t' + T$$ and $$x = x' + (aT)t = x' + (aT)(t'+T)$$.
Then $$x(t) = \frac{1}{2}aT^{2} + (aT)(t-T)$$ becomes $$x' - (aT)(t'+T) = \frac{1}{2}aT^{2} + (aT)t'$$ so $$x' = -(aT)(t'+T) + \frac{1}{2}aT^{2} + (aT)t' = -\frac{1}{2}aT^{2}$$. No t' dependence, the car is stationary in the new frame (as required by its definition!). Adding in a second car doesn't change this, it would just have a position L more than the first car. They would both experience acceleration, pendulums would swing, they are always a constant distance apart. The cars can measure the acceleration and at the end they have a non-zero speed with respect to the initial inertial frame and conversely at the start they have a non-zero speed with respect to the final inertial frame. No need to talk about absolute frames and your assertions about there being a problem measuring this is nonsense.
The relativistic version of what I described uses Lorentz transforms, not Galilean ones, but the methods and qualitative results are identical. The problem is that you don't grasp how 'frames' work within relativity (or even basic Newtonian mechanics). The mathematics involves for such an understanding at taught to 15 year olds, so it isn't like this is some horrifically complex abstract concept.
Time and time and time again the problem is with you, not anyone else.
