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In 1952 D. W. Sciama introduced a paper On the origin of inertia. It presents a method in which inertia could arise from other mass in the universe. It goes along these lines:

If you try to accelerate a mass, then from the point of view of that mass it is the rest of the universe that is accelerating in the opposite direction. Since an accelerating mass radiates gravitomagnetic radiation (just like an electric charge electromagnetic radiation), the radiation from the accelerating universe will exert an opposing force on that particle. That force is supposed to be ''the inertial force''. It depends on the mass distribution of the universe and it would not exist without other mass.

A very cool idea, whether you believe it to be the ''real cause of inertia'' of not. In fact, it cannot be entirely wrong, can it? From the point of view of the mass, the universe does seem to accelerate, so it will create gravitomagnetic radiation that exerts some force on the mass. Right? I am obviously using gravitoelectromagnetic(GEM) picture here to explain things. I am sure General relativity disagrees with the interpretation, although since GEM is linearized GR it cannot be too far off.

So my first question is: Is it not inevitable that the mass distribution of the universe has some effect on the inertia of the mass? For example, if I doubled the mass everywhere else in the universe, my inertia here on Earth would grow. And since GEM is an approximation of GR, then GR should say the same. But in GR the inertial mass is just gravitational mass which should not change, so what's going on? Does GR imply that I would ''feel more inertial'' if mass was added to the universe? I hope you can sort of read between my lines :).

My second question is more precise. It makes an analogue to electrodynamics: If the universe had a net charge, say positive, then would negative charges feel ''electric inertia'', and positive charges anti-inertia?

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  • $\begingroup$ As to your second question: Are you proposing some exotic matter or something else charged negatively under gravity? That'd be pretty exotic, indeed. $\endgroup$
    – Danu
    Commented Dec 1, 2015 at 16:29
  • $\begingroup$ @Danu No no. Just normal matter. In other words, suppose there were more protons than electrons in the universe. Then I ask: Is there an additional ''electric inertia''? It should be ''anti-inertia'' for positive charges, so that they would be easier to accelerate than if the universe was neutral. $\endgroup$
    – AnssiM
    Commented Dec 1, 2015 at 20:20

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When a local mass accelerates, it typically does so conserving stress-energy momentum tensor currents. That implies a local divergence-free property on energy-momentum tensor.

On the other hand, when you switch to the Machian viewpoint of "the whole universe is counteraccelerating" AFAICT you cannot postulate an equivalent local current conservation. This breaks down the assumed symmetry between the two viewpoints.

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