Is Spacetime the True Cause of Inertia? Revisiting Newton's Bucket Experiment

[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?

 

[bcrowell]

I think what you're referring to is basically the "Machian" attitude: http://en.wikipedia.org/wiki/Mach's_principle

Einstein was strongly influenced by Mach as he was developing general relativity. Too strongly, you could say, because it caused him to make various mistakes. For example, he was initially convinced that gravitational waves were unobservable, because they offended his Machian sensibilities. He was also dismayed by the Schwarzschild solution, because it allowed the existence of a universe containing only a single mass, with nothing else to act on it or be acted on by it.

Basically Mach's principle is more of a historical curiosity at this point than anything that is taken seriously as a definite physical principle. You're right that there is something anti-Machian about the future state of the universe as its expansion accelerates exponentially.

 

[PhizzicsPhan]

Yes, Einstein was a Machian in his early career - and he actually came to regret it later on. See Isaacson's excellent biography on this.

What I'm getting at with my question, however, is the more recent explanation for inertia, offered by Greene and other extant physicists, in terms of the totality of spacetime. Mach himself offered the fixed stars as the solution and Einstein/Minkowski 4D spacetime came to be seen as the better answer. But it seems to have problems of its own, as I've suggested above.