Is Spacetime the Cause of Inertia?

[PhizzicsPhan]

Brian Greene describes in The Fabric of the Cosmos how spacetime itself is now thought to be the cause of the inertial effects behind Newton's bucket experiment (rising water, etc.). That is, rather than the "fixed stars" being the cause, as was the commonly held notion before Einstein, spacetime itself, a 4D construct, is now thought to be the cause.

I see at least one problem with this notion, however: if we live in an increasingly expanding universe, as we apparently do, the very large majority of the duration of our universe will consist of an infinitesimally small matter density. This is the case because, as galaxies continue to hurtle away from each other, we reach over the course of billions and trillions of years a state in which all matter is eventually spread out fairly uniformly, and then the final heat death...

It's not a pretty picture, by any means, and it also seems to lead to a problem with the notion of spacetime itself as causing inertial effects. This is the case because if matter density over the entire course of the existence of our universe is on average infinitesimally small, the gravitational effects exerted by our 4D universe (inertia in this case) will also be infinitesimally small.

Any thoughts?

 

[Dale]

if matter density over the entire course of the existence of our universe is on average infinitesimally small, the gravitational effects exerted by our 4D universe (inertia in this case) will also be infinitesimally small

While this sounds nice, the math doesn’t bear it out, at least not for GR. Even a vacuum solution will lead to all of the usual observables in Newton’s bucket, so there is no minimum density required and the idea that the usual cosmological solution will have a low density portion does not suggest that inertia will disappear.