I just added an answer to an elder discussion,
https://www.researchgate.net/post/Is_rest_mass_of_a_body_equivalent_to_local_accumulated_gravitational_potential_originating_from_remote_masses_of_the_universe
"When it is not accidental that potential energy of a mass m at the level of local cumulative gravitational potential originating from remote masses of the universe equals E = mc^2, shouldn't it be worthwhile to reconsider Mach's principle ?"
https://web.archive.org/web/20230120174916/https://www.researchgate.net/project/Local-effects-of-remote-masses
According to Newton's shell theorem and the on average homogeneity of mass distribution in the universe, there should be no significant gravitational influence from distant masses. So the answer must be no, Ernst Mach can't be right !
Berndt Barkholz: "Newton's shell theorem"
Please note that we are not talking about forces, ie gravitational potential gradients, but just about the cumulative gravitational potential itself.
Dear Johan K. Fremerey ...
...there is no force and thus no time gradient -> no effect on anything ! Due to the shell theorem there can't be any gravitational potential !
{However... there is a very small time-gradient caused by the average density of the universe which is responsible for the observed red-shift of far away stars and galaxies}
Dear Berndt Barkholz,
you obviously make no difference between potential and potential gradient.
What local phenomenon could possibly be affected by a not existing gravitational interaction from light-years distance ?
Where do we find a gravitational potential, but no time-gradient ?
Berndt Barkholz: "a not existing gravitational interaction"
Due to 1/r2 dependence from distance r gravitational potential gradients of distant masses in fact have negligible influence on local phenomena. The gravitational potential from remote masses, however, does not vanish as it goes with 1/r. It rather accumulates to about 108 times our Sun's gravitational potential at the Earth's distance which holds us in orbit.
We should be aware that potential gradient cannot exist without a potential, and we should search for possible influences of gravitational potential on local phenomena rather than a priori denying the ideas of Mach, Keith and others.
https://web.archive.org/web/20230120174916/https://www.researchgate.net/project/Local-effects-of-remote-masses
An analogy: in the case of a large gathering of people, we would perhaps not only talk about the effect of local crowds, but also about their overall effect.
Peter Enders: "What exactly is "Newton's shell theorem"?"
See https://en.wikipedia.org/wiki/Shell_theorem
Johan K. Fremerey
Thank you for pointing to the Wikipedia entry! In the 1999 translation of the 3rd ed., it is Theorems 31 (including F~1/r^2) and 30in Book I, Section 12, p. 591. -- If the distribution of masses around the Earth, say, beyond our sun system, is spherically symmetric, then their net static gravitational force exerted upon the Earth vanishes. However, they do act upon accelerated bodies through the gravitational vector potential (cf. Heaviside's application of Maxwell's equations to gravity, the gravito-electromagnetic equations), see Dennis Sciama's 1953 calculations. (Unfortunately, I don't know his general-relativistic treatment announced in that article.)
Peter Enders: "they do act upon accelerated bodies"
This seems to comply with the ideas of Mach, and what James C. Keith found out in his proposal of a high-speed rotor experiment, see references below.
Johan K. Fremerey
Thank you for the links. Unfortunately, they refer to contributions beyond my current interests of explorations.
This has not be realized in general relativity, except in the light cone but it is trivial. I think neither Newton nor Mach is right, because it is an anthropocentric view. We have not to explain inertia, since motion is not with respect to us.
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