The above question came up on October 15, 2021, within a disussion https://www.researchgate.net/post/Field_energy_density_is_missing_in_General_Relativity_such_a_big_issue_is_preventing_a_unification_of_the_interactions/9 initiated by Stefano Quattrini on April 9, 2021, who answered:

"there is no need to consider the influence of the remote masses being their contribution negligible."

I answered as follows:

"I'm not so sure about that in view of formal relation ℏω = mc2 which lead me to reasonable values for the proton diameter and magnetic moment, see reference below, in parallel with formal escape velocity c2 = 2GMu/Ru out of the universe. Combining the above equations we get to ℏω0/m0 = 2GMu/Ru which via c2, ℏ and G apparently relates elementary (subscript 0) to universal (subscript u) parameters."

The question might be interesting in view of a recent discussion at Wikipedia under "Mach's Principle", https://en.wikipedia.org/wiki/Mach%27s_principle, see Talk Section under "Experimental Verification", about the possible significance of an experiment proposed by James C. Keith in 1963 and related experimental results.

Research Proposal Triple-gyro model for deduction of proton radius and magnetic moment

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