 #76
DrGreg
Science Advisor
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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 comoving 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 spacetime into a oneparameter family of spacelike 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 comoving inertial frame
 within each such simultaneity plane, the Rindler spatial coordinates X, Y, Z coincide with the comoving 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 lefthand diagram illustrates the accelerated twin's point of view in the Twins Paradox. (The righthand diagram shows the inertial twin's point of view.)
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