I don't think Eliezer is right when he says that Mach's principle (the way he interprets it) is widely accepted. It's true that the general theory of relativity is formulated so that there is no privileged coordinate frame. However, Mach's principle goes beyond this, saying that there is no privileged state of motion. On the usual interpretation of GR, this latter claim is false. Inertial motion can be distinguished from other states of motion, in a coordinate-independent way. Inertial worldlines are just the ones that follow geodesics.
Now Eliezer points out that by changing the space-time curvature, we can change inertial motion to non-inertial motion. This is true, but relativists don't usually treat curvature the way they treat coordinate frames. A coordinate frame is conventional, something that we apply to the universe for convenience. Space-time curvature, on the other hand, is out there. There is a genuine fact of the matter about the curvature of space-time. And it follows that there is genuine fact of the matter about which worldlines are inertial.
Maybe Eliezer is right that we should treat curvature as conventional, but this is not the way most relativists think of it. Also, it doesn't seem like a very compelling position. If curvature is conventional, then so is the space-time metric, which means so is geometry. This leads to a thorough-going Poincare-esque instrumentalism, which is a consistent world-view but one that I find unattractive. And knowing what Eliezer says about quantum mechanics, I suspect he would find it unattractive as well.
Putting aside the specific definition of "Mach's principle" (which seems to mean different things to different people), as well as sociological questions about what relativists usually do or don't do, the way I understand it is as follows (and I would welcome corrections from anyone in a position to offer them):
In general relativity, spacetime is a Lorentzian manifold -- that is, a manifold modeled on Minkowski space, which is just like Euclidean space except with a funny inner product such that the "norm" is constant on hyperboloids in...
Today's post, Mach's Principle: Anti-Epiphenomenal Physics was originally published on 24 May 2008. A summary (taken from the LW wiki):
Discuss the post here (rather than in the comments to the original post).
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