Translational Motion Vs. Rotational Motion

[jpescarcega]

Howdy. It has become clear to me that translational motion is not taken into account in general relativity because it is subjective, and that rotational motion is taken into account in GR in places such as the Kerr Metric. What makes rotational motion so absolute? Couldn't an observer's measurement of the rotational frequency of an object be different from another observer's measurement, (making rotational frequency subjective)?

Thank you all in advance for the time you put into this. It is appreciated.

 

[PeterDonis]

It has become clear to me that translational motion is not taken into account in general relativity because it is subjective

It's not subjective, it's coordinate-dependent. GR handles coordinate-dependent translational motion just fine, so I don't understand why you would think it's not taken into account.

rotational motion is taken into account in GR in places such as the Kerr Metric

I'm not sure I would call this "rotational motion"; I would call it a rotating source of gravity, which is more specific. "Rotational motion" could also mean a satellite circling a planet, or a centrifuge rotating but not producing any significant gravity (over and above the "pseudo-gravitational field" due to its rotation). GR covers all of these things, but it's worth some effort to keep them distinguished conceptually.

What makes rotational motion so absolute?

Some aspects of it are absolute (i.e., invariant--the same for all observers) and some are not. See below.

Couldn't an observer's measurement of the rotational frequency of an object be different from another observer's measurement

Yes. But other aspects of rotation are not coordinate dependent. For example, the proper acceleration felt by an observer at the rim of a centrifuge is an invariant; all observers agree on what that proper acceleration is. They might disagree on other coordinate-dependent numbers that go into formulas for calculating that proper acceleration, but all those numbers will vary with changes in coordinates in such a way as to keep the actual observable, the proper acceleration, the same.

 

[bcrowell]

Einstein begins his original paper on general relativity[1] with an example involving two planets that discusses essentially this point. He expected that in general relativity, rotational motion *would* be relative, so that GR would fulfill Mach's principle. Once the full implications of the theory were worked out, it became clear that GR wasn't as Machian as he had hoped. There are other theories of gravity, such as Brans-Dicke gravity, that are more Machian than GR. The actual universe appears empirically to be non-Machian in the sense that to fit solar-system data using BD gravity, you need a value of an adjustable parameter that makes it as non-Machian as vanilla GR. See https://www.physicsforums.com/threads/does-machs-principle-work-both-ways.515077/#post-3409514 .

[1] A. Einstein, "The foundation of the general theory of relativity," Annalen der Physik, 49 (1916) 769; translation by Perret and Jeffery available in an appendix to the book at http://www.lightandmatter.com/genrel/ (PDF version)