Firstly I will admit I do not understand the real cause of rotational frame dragging and some of the math heavy explanations are too complicated for me. To me frame dragging looks like unsubstantiated analogy with friction. So in order to better understand the mechanism, I would like to know if frame dragging applies to linear motion too.
Image an infinite cable made of neutron star matter. A gyroscope is orbiting the cable on a stable orbit, pointing perpendicular to the cable length. Now I start to pull the cable along its length axis. Would the gyroscope start to precess due to distortion of the space along the cable?
If I did this experiment in a huge jar of honey, the linear motion of the cable would cause the honey to "drag"particles along the way. Would the same happen with empty space?