Perhaps the root of our disagreement is that you think (?) that the GR field equations constrain their solutions to conform to Mach’s principle, while I think they admit many solutions which don’t conform to Mach’s principle, and that furthermore that Vladimir_M is probably correct in his sketch of a family of non-Mach-principle solutions.
EY’s article seems pretty clear about claiming not that Mach’s principle follows deductively from the equations of GR, but that there’s a sufficiently natural fit that we might make an inductive leap from observed regularity in simple cases to an expected identical regularity in all cases. In particular EY writes “I do not think this has been verified exactly, in terms of how much matter is out there, what kind of gravitational wave it would generate by rotating around us, et cetera. Einstein did verify that a shell of matter, spinning around a central point, ought to generate a gravitational equivalent of the Coriolis force that would e.g. cause a pendulum to precess.” I think EY is probably correct that this hasn’t been verified exactly—more on that below. I also note that from the numbers given in Gravitation, if you hope to fake up a reasonably fast rotating frame by surrounding the experimenter with a rotating shell too arbitrarily distant to notice, you may need a very steep quantity discount at your nonlocal Black-Holes-R-Us (Free Installation At Any Velocity), and more generally that apparently solutions which locally hide GR’s preferred rotational frame seem to be associated with very extreme boundary conditions.
You write “under Mach’s principle (the version that says only relative motion is meaningful, and which GR agrees with), these consequences of acceleration you describe only exist because of the frame against which to describe the acceleration, which is formed by the (relatively!) non-accelerating the rest of the universe.” I think it would be more precise to say not “which GR agrees with” but “which some solutions to the GR field equations agree with.” Similarly, if I were pushing a Newman principle which requires that the number of particles in the universe be divisible by 2, I would not say “which GR agrees with” if there were any chance that this might be interpreted as a claim that “the equations of GR require an even number of particles.” Solutions to the GR field equations can be consistent with Mach’s principle, but I’m pretty sure that they don’t need to be consistent with it. The old Misner et al. Gravitation text remarks on how a point of agreement with Mach’s principle “is a characteristic feature of the Friedman model and other simple models of a closed universe.” So it seems pretty clear that as of 1971, there was no known requirement that every possible solution must be consistent with Mach’s principle. And (Bayes FTW!) if no such requirement was known in 1971, but such a requirement was rigorously proved later, then it’s very strange that no one has brought up in this discussion the name of the mathematical physicist(s) who is justly famous for the proof.
(I’m unlikely to look at The End of Time ’til the next time I’m at UTDallas library, i.e., a week or so.)
Refer to the Rovelli paper mentioned in this discussion:
MP7: There is no absolute motion, only motion relative to something else, therefore the water in the bucket does not rotate in absolute terms, it rotates with respect to some dynamical physical entity. True. This is the basic physical idea of GR.
This is a much stronger claim than the one you pretended I was making, that GR agrees my selected Mach’s principle—rather, the pure relativity of universe is the basic idea of GR, not something simply shared between Mach’s principle and GR (like with your modulo 2 example).
And (Bayes FTW!) if no such requirement was known in 1971, but such a requirement was rigorously proved later, then it’s very strange that no one has brought up in this discussion the name of the mathematical physicist(s) who is justly famous for the proof.
Perhaps the root of our disagreement is that you think (?) that the GR field equations constrain their solutions to conform to Mach’s principle, while I think they admit many solutions which don’t conform to Mach’s principle, and that furthermore that Vladimir_M is probably correct in his sketch of a family of non-Mach-principle solutions.
EY’s article seems pretty clear about claiming not that Mach’s principle follows deductively from the equations of GR, but that there’s a sufficiently natural fit that we might make an inductive leap from observed regularity in simple cases to an expected identical regularity in all cases. In particular EY writes “I do not think this has been verified exactly, in terms of how much matter is out there, what kind of gravitational wave it would generate by rotating around us, et cetera. Einstein did verify that a shell of matter, spinning around a central point, ought to generate a gravitational equivalent of the Coriolis force that would e.g. cause a pendulum to precess.” I think EY is probably correct that this hasn’t been verified exactly—more on that below. I also note that from the numbers given in Gravitation, if you hope to fake up a reasonably fast rotating frame by surrounding the experimenter with a rotating shell too arbitrarily distant to notice, you may need a very steep quantity discount at your nonlocal Black-Holes-R-Us (Free Installation At Any Velocity), and more generally that apparently solutions which locally hide GR’s preferred rotational frame seem to be associated with very extreme boundary conditions.
You write “under Mach’s principle (the version that says only relative motion is meaningful, and which GR agrees with), these consequences of acceleration you describe only exist because of the frame against which to describe the acceleration, which is formed by the (relatively!) non-accelerating the rest of the universe.” I think it would be more precise to say not “which GR agrees with” but “which some solutions to the GR field equations agree with.” Similarly, if I were pushing a Newman principle which requires that the number of particles in the universe be divisible by 2, I would not say “which GR agrees with” if there were any chance that this might be interpreted as a claim that “the equations of GR require an even number of particles.” Solutions to the GR field equations can be consistent with Mach’s principle, but I’m pretty sure that they don’t need to be consistent with it. The old Misner et al. Gravitation text remarks on how a point of agreement with Mach’s principle “is a characteristic feature of the Friedman model and other simple models of a closed universe.” So it seems pretty clear that as of 1971, there was no known requirement that every possible solution must be consistent with Mach’s principle. And (Bayes FTW!) if no such requirement was known in 1971, but such a requirement was rigorously proved later, then it’s very strange that no one has brought up in this discussion the name of the mathematical physicist(s) who is justly famous for the proof.
(I’m unlikely to look at The End of Time ’til the next time I’m at UTDallas library, i.e., a week or so.)
See also the conversational thread which runs through http://lesswrong.com/lw/qm/machs_principle_antiepiphenomenal_physics/kb3 http://lesswrong.com/lw/qm/machs_principle_antiepiphenomenal_physics/kb8 http://lesswrong.com/lw/qm/machs_principle_antiepiphenomenal_physics/kba
Refer to the Rovelli paper mentioned in this discussion:
This is a much stronger claim than the one you pretended I was making, that GR agrees my selected Mach’s principle—rather, the pure relativity of universe is the basic idea of GR, not something simply shared between Mach’s principle and GR (like with your modulo 2 example).
I did—Barbour.