Inertia & Accelerated Expansion: How Does Machian Explanations Fit In?

[e2m2a]

I understand that some old Machian interpretations of inertia require a closed universe. Now that it has been confirmed that the universe is expanding forever and is not closed, how does Machian explanations of inertia fit in with this?

 

[haushofer]

Why exactly should the universe be closed for 'some Machian interpretations'? Could you give some references? :)

 

[Chronos]

Inertia is irrelevant. Nothing actually moves with respect to its own inertial reference frame during expansion irrespective of whether the universe is open or closed.

 

[Carrock]

...Now that it has been confirmed that the universe is expanding forever and is not closed, how does Machian explanations of inertia fit in with this?...

Still plenty of theories predicting finite expansion eg https://arxiv.org/abs/1409.7073

Could you give some references? :)

 

[e2m2a]

In Einstein's Meaning of Relativity , he stated: "1. From the standpoint of the theory of relativity, the condition for a closed surface is very much simpler than the corresponding boudary condition at infinity of the quasi-Euclidean structure of the universe.

2. The idea that Mach expressed, that inertia depends upon the mutual action of bodies, is contained, to a first approximation, in the equations of the theory of relativity; it follows from these equations that inertia depends, at least in part, upon mutual actions between masses. As it is an unsatisfactory assumption to make that inertia depends in part upon mutual actions, and in part upon an independent property of space, Mach's idea gains in probability. But this idea of Mach's corresponds only to a finite universe, bounded in space, and not to a quasi-Euclidean, infinite universe. From the standpoint of epistemology it is more satisfying to have the mechanical properties of space completely determined by matter, and this is the case only in a space-bounded universe..."

Again, my question is, based on the empirical astronomical data that the universe is expanding forever at an accelerated rate, does this completely negate Mach's principle as Einstein interpreted it?

 

[Jonathan Scott]

Kenneth Nordtvedt has pointed out that linear frame-dragging effects in GR appear to be consistent with a Machian explanation of inertia, and (as can be found for example in MTW) rotational frame-dragging effects are also apparently consistent with a "sum for inertia" concept. However, there is no exact Machian explanation of inertia in GR and it seems unlikely that one can be found because it would apparently require G to vary according to the distribution of nearby masses. (Personally I think it is very weird that GR gets so close but can't close the gap). In both cases, the effect relates to the distribution of masses in the observable universe only.

If you want a strong Machian explanation of inertia, you are outside the scope of General Relativity, so what you get depends on what alternative theory you use. Unless you've got peer-reviewed references, that's probably outside the scope of Physics Forums.