Imagine there is a tall tower erected at the equator, a pulse of light is beamed from the top of the tower to the ground. Do I need to consider frame dragging? After all the spacetime is being tucked along as the Earth rotates and there is a similar experiment serving as a control at the poles. In this case only the surface gravity matters or I should include frame dragging too?
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$\begingroup$ Bear in mind that although the top & base of the (rigid) tower have the same angular velocity they don't have the same linear velocity. $\endgroup$– PM 2RingCommented Dec 16, 2023 at 11:02
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In your mentioned case, you do need to consider frame dragging, because the Earth's rotation will affect the spacetime around the tower. The light pulse will not travel in a straight line but will be slightly deflected by the frame-dragging effect. The deflection will depend on the direction of the light pulse relative to the Earth's rotation. If the light pulse is beamed toward the east, it will move faster than if it is beamed toward the west, as seen by a distant observer.
A similar experiment at the poles would not experience frame dragging, because the poles are not rotating concerning the distant observer. The light pulse would travel in a straight line from the top of the tower to the ground, regardless of the direction it is beamed. The only effect that would matter in this case is the surface gravity, which would slightly bend the light pulse towards the Earth.
