GR Acceleration

[Shaw]

I'm curious to know if General Relativity theory has an answer to this question:

Space is not an abstract concept (it has volume and contains energy), so if an observer cannot tell if he is accelerating and the Universe is at rest, or if he is at rest and the Universe is accelerating (corollary to Mach's observation on velocity), then can one also say that if inertial forces result from acceleration in space, can they conceivably also result from the acceleration of space itself?

[yogi]

Einstein was convinced that this would be the case - if a mass were somehow retained in some absolute location and the entire universe accelerated relative to the mass, then the stationary mass would experience the same reactionary force as if it were accelerated
relative to space.

[pervect]

I'm curious to know if General Relativity theory has an answer to this question:

Space is not an abstract concept (it has volume and contains energy), so if an observer cannot tell if he is accelerating and the Universe is at rest, or if he is at rest and the Universe is accelerating (corollary to Mach's observation on velocity), then can one also say that if inertial forces result from acceleration in space, can they conceivably also result from the acceleration of space itself?

The problem is that an observer can tell if he is accelerating.

Mach's principle is not a part of General Relativity, so I would say that your question doesn't have an answer in the framework of GR, because it makes assumptions that are not part of the framework of GR. In fact, some versions of Mach's principle are ruled out by GR. You'd have to be a bit more specific about your statement of Mach's principle for me to tell if your interpreation of it is one of those that's inconsitent with GR or not.

The usual failulre of Mach's principle occurs with is a rotating universe - GR allows the universe to have a non-zero total angular momentum, many interpretations of Mach's principle don't allow this.