Solving the Spaceship Paradox: A New Explanation

[PAllen]

Please note that in the case at hand, the constant radar length measured by an inertial observer in the starting rest frame is not a rest length. The objects are accelerating in this frame, not at rest. The rest length of the object is length measured in its instantaneous rest frame (which is ambiguous here, because each end has a different family of instantaneous rest frames). However, whether you pick front or back instantaneous rest frames, you get increasing rest length for the congruence under consideration.

Thus, it does seem you have it backwards. Whether using radar distances or some other 'reasonable' definition of distance, rest length/distance is increasing. Distance (between ships) measured in the initial rest frame remains constant.

 

[Mentz114]

...Two distant events are simultaneous for a give observer A making radar measurements if the proper time along A's world line of the midpoint of the signal round trips is the same.

That's clear enough.

The rest length of the object is length measured in its instantaneous rest frame (which is ambiguous here, because each end has a different family of instantaneous rest frames).

The ambiguity here is troubling. Maybe what I have been calling 'rest length' is more like a local ruler length. More to think about.

However, whether you pick front or back instantaneous rest frames, you get increasing rest length for the congruence under consideration.

I'll have to check that for radar measurements.

Good answers, and thanks for the reference. I have read that but not since I started on about radar in this thread.