You are right that there are other choices of accelerated coordinate system. And it is debatable as to exactly what the accelerated observer's "point of view" is. Nevertheless it is conventional to consider the co-moving inertial frame to represent the "instantaneous" view, and Rindler coordinates are the only coordinates (I think) that are compatible with this view in the sense that:I didn't mean that it's impossible to define a coordinate system that takes the accelerated observer's world line to be its time axis. (I said something to that effect in another thread, and you were right to correct me then). What I meant is that it doesn't make much sense to think such coordinates as representing the accelerating observer's point of view. I'm sure there are lots of ways to slice up space-time into a one-parameter family of space-like hypersurfaces that we can (if we want to) think of as representing space at different times. Why should the choice defined by Rindler coordinates be the "correct" choice?
- the observer is at fixed spatial coordinates X = Y = Z = 0
- at X = 0 (but not at other positions), T is the proper time of the observer
- every surface of constant T coincides with the plane of simultaneity of the corresponding co-moving inertial frame
- within each such simultaneity plane, the Rindler spatial coordinates X, Y, Z coincide with the co-moving inertial frame's spatial coordinates
That, in my view, makes Rindler coordinates a more "natural" choice than any others. Of course all "points of view" are a mathematical construct, even in inertial frames. They don't reflect what you see with your eyes; the frame point of view is something you have to calculate retrospectively from observations made after the events being measured, and it depends on what conventions you choose to adopt to perform the calculation.
And I think Rindler coordinates would answer the question put in post #65: they give us a way of seamlessly (up to continuous first derivative) interpolating between the two points of view of inertial motion before and after acceleration. The attached left-hand diagram illustrates the accelerated twin's point of view in the Twins Paradox. (The right-hand diagram shows the inertial twin's point of view.)
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