Special & General Relativity Questions and Answers
How does general relativity incorporate rotation?
It seems that way.
If you spin a bucket of water, the surface of the water deforms because as Mach said it is rotating with respect to the frame of the distant fixed stars, then by relativity, we should be able to keep the bucked fixed and rotate the universe with the same angular velocity, and the water should still deform even though the bucket is not 'actually' rotating. Evidently, in the 1960's, theorists were able to give a partial answer to whether these two experiments gave the same outcome, and showed that the two 'experiments' in general relativity would give equal outcomes.
A second question was whether performing the rotating experiment in a completely EMPTY universe would show NO change in the surface of the water even with the bucket rotating. There is no meaningful way to test this, and so it is not a physical question.
Currently, a number of sophisticated experiments are planned involving rotating bodies in Earth orbit, to verify other physical outcomes predicted by general relativity for rotating reference frames and gravitational fields.
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All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the NASA Astronomy Cafe, part of the NASA Education and Public Outreach program.