Very massive objects cause the so called 'frame dragging' that can increase the speed of a beam of light to a total aggregate speed faster than the speed of light in normal circumstances so my question is: can a very massive fast object drag the'frame' along its trajectory so a theoretical space ship, chasing it, would have its speed increased due to this possible linear 'frame dragging'?
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1$\begingroup$ I would think so. Just difficult to study because first you need to find a massive object moving at relativistic speeds, then you need to catch it intercepting something which only happens briefly, or find something following it which is super unlikely, and if you do probably really is a spaceship ;) $\endgroup$– DKNguyenCommented Apr 25, 2021 at 21:37
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$\begingroup$ Not my area of expertise, but just a thought: consider the problem in the very fast massive object's frame. For example, the earth is moving rapidly relative to the galactic rest frame, and something falling in the same direction of that motion through the galaxy can be viewed as "chasing the earth". There is a speeding up that occurs, but it's the normal gravitational acceleration we have an intuitive feel for. I don't think this is what is called frame dragging. I could be wrong though. $\endgroup$– AndrewCommented Apr 26, 2021 at 15:04
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1$\begingroup$ From wiki en.m.wikipedia.org/wiki/Frame-dragging "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 (but see Einstein, 1921).[5]" $\endgroup$– shai horowitzCommented May 1, 2021 at 19:30
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1$\begingroup$ related (possible duplicate) "Does frame dragging apply to linear motion?" physics.stackexchange.com/q/220473/226902 - moreover, about "rotation" frame dragging: physics.stackexchange.com/q/156439/226902 $\endgroup$– QuilloCommented Apr 8, 2022 at 13:26
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2 Answers
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I don't see why the linear effect shouldn't be there. After all, you can envision the rotation as a following up of infinite linear motions. At any instant, a body in circular motion is composed of bodies with linear motion. If you envision two massive plates moving parallel through space. The plates are kept at rest wrt each other. Between the plates, there is no gravitation due to mass, but you will be dragged along in a direction parallel to the plates if you find yourself in between them (or outside them but in between you'll experience no "normal" gravity). You will end up with the same velocity as with which the plates are moving. This goes to show that space is connected to matter and not to mass, which is just a property of matter. If only mass were the cause of curvature, then no framedragging was present.
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$\begingroup$ If the "moving" object is sufficiently massive, I believe this could impart a net motion in the direction of its travel; this is essentially the "gravity assist" maneuver that humans have used for space probes, right? $\endgroup$– geshelCommented Apr 27, 2021 at 1:12
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1$\begingroup$ @geshel Gravity assist has nothing to do with frame dragging. The velocity you acquire in gravity assist is only due to gravity. If you find yourself between the two moving plates, there is no ordinary gravity field, only a frame-dragging effect, which carries you along in a direction parallel to the plates. $\endgroup$ Commented May 1, 2021 at 17:04
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Consider an infinitely long cylinder that moves at some speed: does it drag test particles along?
We can move to the view from an observer moving along the cylinder at the same speed as the cylinder. The observer sees a static Levi-Civita spacetime outside the cylinder: $$ ds^2 = r^{8\sigma^2-4\sigma}(dr^2+dz^2) + D^2 r^{2/4\sigma}d\phi^2 -r^{4\sigma} dt^2 $$ where $\sigma$ and $D$ are constants, with $\sigma$ behaving like a mass density. Note that for a particle in this spacetime there is no acceleration along the z direction (e.g. the orbiting geodesics have constant angular velocity and remain in a plane). So there is no frame dragging in this view.
Moving back to the "stationary" view where we see the cylinder and previous observer sweep past, since it is related to our view by a Lorenz transformation along the cylinder, we reach the same conclusion. A bunch of particles orbiting in sync (say one with period twice the other) will have synced orbits in any of the other frames.
Compare this to Bonnor beam spacetimes, where parallel beams of light do not attract each other.
answered Aug 14 at 14:00