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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?

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    $\begingroup$ Linear frame dragging is the similarly inevitable result of the general principle of relativity, applied to linear momentum. Although it arguably has equal theoretical legitimacy to the "rotational" effect, the difficulty of obtaining an experimental verification of the effect means that it receives much less discussion and is often omitted from articles on frame-dragging. Source:en.wikipedia.org/wiki/Frame-dragging $\endgroup$
    – user83548
    Dec 7, 2015 at 14:01

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Yes.

As pointed out in a comment, frame dragging occurs with linear effects too. My thought experiment on this is through a Mach - like view point. If you are inside at the middle of a very long pipe, which starts to accelerate, you will be dragged along. If the pipe stops accelerating at some fixed velocity, you will approach that velocity eventually.

So space couples not to mass but to matter. If it just coupled to mass, you would not be able to tell if your neutron rope was moving or not. It couples instead to the actual bits of matter.

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  • $\begingroup$ At the linearized level, though, we would expect there to be no gravitational field or gravitomagnetic field inside a long moving tube, in the same way there is no electric or magnetic field inside a long charged hollow tube that is moving along its length. Perhaps a long tube is not the best example for this phenomenon. $\endgroup$ Jan 11 at 19:54

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