I could hardly have said it better myself. The ability to use a locally flat coordinate system at a point (regardless of the value of the Riemann tensor at that point) is all that
you could never tell the difference between firing your rocket to accelerate through flat spacetime, and firing your rocket to stay in the same place in curved spacetime.
means.
I don't see how it could mean that. Rockets are extended objects, as are people. While we can always find coordinates that make the metric Minkowski at a single point, it is not true that we can always find coordinates that make the metric Minkowski over a finite region, no matter how small.
While we can always find coordinates that make the metric Minkowski at a single point, it is not true that we can always find coordinates that make the metric Minkowski over a finite region, no matter how small.
Indeed; this is why the concept of an "inertial frame" does not exist in general relativity, except in the infinitesimal limit.
But as long as we're going to permit ourselves to speak about the motion of an entire rocket or person, rather than the motion of its parts (thus in effect modeling the object as a point-particle), we can equally well describe the same rocket or person as being at rest.
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).
This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was My Childhood Role Model, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
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