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I have a question about a gravitational thought experiment. In relation to GR there is some attention paid to the torque exerted on the local space by a spinning mass, although I think only a sphere is considered and therefore the torque on the surrounding space resolves to a very small number. Also, the torque created by a spinning mass is only thought to be produced by planet size masses. Although, my question involves very small test masses.

The question involves an idealized experiment of a small spinning disk(rotor) several inches in diameter made of a very dense metal positioned below a balance beam, also several inches in diameter. In this “Perfect World” experiment all extraneous variables are accounted for and negated(such as the spin direction of the earth and the direction of it’s magnetic field, etc.) and the disk and balance beam are isolated from each other with no direct contact. Although, the disk spins in close proximity below the balance beam.

If the balance beam moves in the same direction as the spin of the rotor during initial acceleration of the rotor, would this finding be consistent with GR? I’m fairly new to the nuances of GR and I don’t think Newtonian gravity takes into account rotation of the masses under study?

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I am not sure understand your set up but whatever it is you won't measure anything related to the rotational or torsion effect you are referring to in GR.

First, assuming by a balanced beam is something free to rotate (from some torsional force), the mass of the the rotating disc is just not enough to make it detectable. The effect your talking about is called the frame dragging effect. It's been measured with very rough accuracy of 15% by the Gavity B satellite probe going around the earth's using 4 gyroscopes, reported in 2008, and improved some after averaging the results of the 4 in 2011.

See https://en.m.wikipedia.org/wiki/Gravity_Probe_B

It took years to get close to that Perfect World measurement you hypothesize. To understand some of the sources of noise that give you a hint of the scale of the measurement problem, initial results had noise that was of about the same size as the effect being measured, and it wa determined after much work that it was due to some lack of evenness of the paint used, on what was otherwise the most perfectly spherical gyroscopes ever made (by then). Those gyroscopes were in 2 degree Kevin liquid Helium to reduce the thermal noise.

Perfect World measurements do not exist. If you have no noise (and disturbances) you can measure anything, no matter how small. You cold measure the changed gravity due to an ant in a planet in the andromeda galaxy. It's not as bad for this case, but it's pretty bad.

Anyway, the numbers measured were rotation rates on the order of 30 mas/year. A mas is a milliarcsec.

Your rotating disc would have to go maybe 30 or 40 orders of magnitude faster than the rotating earth to have the same angular momentum (you can calculate it, I did a quick estimate on my head) as the earth, which is what determines that frame dragging effect. That'd be faster than light going around the earth. And that would still give you that terrible measurement problem.

It is expected that frame dragging has an effect around black holes and neutron star, and it is thought that it may contribute to black holes spinning mass around and creating the jets familiar for quasars. It'll certainly drag you along if you in-fly into a rotating black hole

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