Imagine a windowless hollow cylinder, with an observer sitting inside on the curved wall. Something is pulling the observer against that wall. The observer can also walk easily along the inner circumference of the cylinder, but does not explore walking in any axial direction of the cylinder.
What gives rise to the observer's acceleration towards the wall?
Rotation. Naturally, the most likely explanation for the observer's attraction to the wall would be that the hollow cylinder is a rotating space station. However, could there be another explanation?
Gravity well. For example, assume a massive ring made from Neutronium is stationary and axisymmetric with the cylinder. The massive ring is surrounding the also stationary (non-rotating) space station at an appropriate distance. Would that not create a gravity gradient that would give rise to the same attractive force? Notice, the gravity gradient in the plane of a massive ring is generally attractive towards the ring, except at the exact center of the ring.
Relativistic frame dragging. Assume that a massive hollow spherical shell (perhaps also made from Neutronium) is surrounding the cylindrical space station. The space station is located at the center of the spherical shell. The gravity gradient inside a spherical shell is zero, so if both the space station and the surrounding shell are stationary (non-rotating wrt to distant stars), the observer should not experience any acceleration towards the wall. However, what if the surrounding massive spherical shell was rotating fast enough, with the axis of rotation aligned with the axis of the cylindrical space station, to cause perceptible relativistic frame dragging inside the space station? Would the observer be able to distinguish this situation from the first?
The observer is allowed to build a smaller cylinder inside the space station, outfitted with an acceleration sensor, to counter any suspected rotation of the space station. In scenario 1, counter-rotation of the experimental cylinder should reduce the measured radial acceleration, and possibly cancel it out entirely. In scenario 2, radial acceleration can be enhanced, but not reduced. But what would the observer discover in scenario 3?