In general-relativistic language, what exactly do you mean by “how fast the entire universe is rotating”?
I mean nothing. In GR, the very question is nonsense. The universe does not have a position, just relative positions of objects.
The universe does not have a velocity, just relative velocities of various objects. The universe does not have an acceleration, just relative accelerations of various objects. The universe does not have a rotational orientation, just relative rotational orientations of various objects. The universe does not have a rotational velocity, just relative rotational velocities of various objects.
There is no way in this universe to distinguish between a bucket rotating vs. the rest of the universe rotating around the bucket. There is also no such thing as how fast the universe “as a whole” is rotating.
I’m not sure if what you write makes sense. Take one simple example: a flat Minkowski spacetime, empty except for a few light particles (so that their influence on the metric is negligible). This means that special relativity applies, and it’s clearly consistent with GR.
Accelerated motions are not going to be relative in this universe, just like they aren’t in Newton’s theory. You can of course observe an accelerating particle and insist on using coordinates in which it remains in the origin (which is sometimes useful, as in e.g. the Rindler coordinates), but in this coordinate system, the universe will not have the above listed properties in any meaningful sense.
You write “In GR, the very question is nonsense. [0] The universe does not have a position, just relative positions of objects. [1] The universe does not have a velocity, just relative velocities of various objects. [2] The universe does not have an acceleration, just relative accelerations of various objects.” This passage incorrectly appeals to GR to lump together three statements that GR doesn’t lump together.
See http://en.wikipedia.org/wiki/Inertial_frames_of_reference and note the distinction there between “constant, uniform motion” and various aspects of acceleratedness. Your [0] and [1] describe changes within an inertial frame of reference, while [2] gets you to a non-inertial frame. Not coincidentally, your [0] and [1] are predicted by GR and are consistent with centuries of careful experiment, while [2] is not predicted by GR and is inconsistent with everyday observation with Mark I eyeballs. (With modern vehicles it’s common to experience enough acceleration in the vicinity of some low-friction system to notice that acceleration causes conservation of momentum to break down in ways that a constant displacement and/or uniform motion doesn’t.)
[2] is not predicted by GR and is inconsistent with everyday observation with Mark I eyeballs.
I ask, in return, that you read this. Eliezer Yudkowsky had argued that GR implies it’s impossible to measure the acceleration of the universe, and no one had objected. Now, EY is not the pope of rationality, but I suggest things aren’t as simple as you’re making them.
(With modern vehicles it’s common to experience enough acceleration in the vicinity of some low-friction system to notice that acceleration causes conservation of momentum to break down in ways that a constant displacement and/or uniform motion doesn’t.)
Your point just seems to be a version of the bucket argument: “acceleration must be real, because it has real, detectable, frame-independent consequences like breakage and pain and ficticious forces”. I think I posed the same challenge in an open thread a month or two ago. And as the link you gave says,
In Newton’s time the fixed stars were invoked as a reference frame, supposedly at rest relative to absolute space. In reference frames that were either at rest with respect to the fixed stars or in uniform translation relative to these stars, Newton’s laws of motion were supposed to hold. In contrast, in frames accelerating with respect to the fixed stars, an important case being frames rotating relative to the fixed stars, the laws of motion did not hold in their simplest form, but had to be supplemented by the addition of fictitious forces, for example, the Coriolis force and the centrifugal force. Two interesting experiments were devised by Newton to demonstrate how these forces could be discovered, thereby revealing to an observer that they were not in an inertial frame: the example of the tension in the cord linking two spheres rotating about their center of gravity, and the example of the curvature of the surface of water in a rotating bucket.
But 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. Therefore, if all of the universe were to accelerate uniformly, there would be no relative motion and therefore no experimental consequences, and we should regard the very idea as nonsense.
So if the universe were only you and your vehicle, you would not be able notice joint accelerations of you and the vehicle, only acceleration of yourself relative to the vehicle.
Now, you can disagree with this application of Mach’s principle, but the observations you describe do not contradict it.
I should also add one of the great insights I got out of Barbour’s book The End of Time (from which EY got his love of Mach’s principle and timelessness). The insight is that the laws of physics do not change in a rotating reference frame. Rather, there is a way you can determine if any given object is not in uniform motion relative to the rest of the universe, and this method also allows you to define an “inertial clock” which gives you an appropriate measure of time.
Most importantly, if you are spinning around, and there’s some other object accelerating relative to the rest of the universe, this method allows you to detect its acceleration, no matter how much or in what way your own frame is moving!
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.
I mean nothing. In GR, the very question is nonsense. The universe does not have a position, just relative positions of objects.
The universe does not have a velocity, just relative velocities of various objects.
The universe does not have an acceleration, just relative accelerations of various objects.
The universe does not have a rotational orientation, just relative rotational orientations of various objects.
The universe does not have a rotational velocity, just relative rotational velocities of various objects.
There is no way in this universe to distinguish between a bucket rotating vs. the rest of the universe rotating around the bucket. There is also no such thing as how fast the universe “as a whole” is rotating.
I’m not sure if what you write makes sense. Take one simple example: a flat Minkowski spacetime, empty except for a few light particles (so that their influence on the metric is negligible). This means that special relativity applies, and it’s clearly consistent with GR.
Accelerated motions are not going to be relative in this universe, just like they aren’t in Newton’s theory. You can of course observe an accelerating particle and insist on using coordinates in which it remains in the origin (which is sometimes useful, as in e.g. the Rindler coordinates), but in this coordinate system, the universe will not have the above listed properties in any meaningful sense.
You write “In GR, the very question is nonsense. [0] The universe does not have a position, just relative positions of objects. [1] The universe does not have a velocity, just relative velocities of various objects. [2] The universe does not have an acceleration, just relative accelerations of various objects.” This passage incorrectly appeals to GR to lump together three statements that GR doesn’t lump together.
See http://en.wikipedia.org/wiki/Inertial_frames_of_reference and note the distinction there between “constant, uniform motion” and various aspects of acceleratedness. Your [0] and [1] describe changes within an inertial frame of reference, while [2] gets you to a non-inertial frame. Not coincidentally, your [0] and [1] are predicted by GR and are consistent with centuries of careful experiment, while [2] is not predicted by GR and is inconsistent with everyday observation with Mark I eyeballs. (With modern vehicles it’s common to experience enough acceleration in the vicinity of some low-friction system to notice that acceleration causes conservation of momentum to break down in ways that a constant displacement and/or uniform motion doesn’t.)
I ask, in return, that you read this. Eliezer Yudkowsky had argued that GR implies it’s impossible to measure the acceleration of the universe, and no one had objected. Now, EY is not the pope of rationality, but I suggest things aren’t as simple as you’re making them.
Your point just seems to be a version of the bucket argument: “acceleration must be real, because it has real, detectable, frame-independent consequences like breakage and pain and ficticious forces”. I think I posed the same challenge in an open thread a month or two ago. And as the link you gave says,
But 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. Therefore, if all of the universe were to accelerate uniformly, there would be no relative motion and therefore no experimental consequences, and we should regard the very idea as nonsense.
So if the universe were only you and your vehicle, you would not be able notice joint accelerations of you and the vehicle, only acceleration of yourself relative to the vehicle.
Now, you can disagree with this application of Mach’s principle, but the observations you describe do not contradict it.
I should also add one of the great insights I got out of Barbour’s book The End of Time (from which EY got his love of Mach’s principle and timelessness). The insight is that the laws of physics do not change in a rotating reference frame. Rather, there is a way you can determine if any given object is not in uniform motion relative to the rest of the universe, and this method also allows you to define an “inertial clock” which gives you an appropriate measure of time.
Most importantly, if you are spinning around, and there’s some other object accelerating relative to the rest of the universe, this method allows you to detect its acceleration, no matter how much or in what way your own frame is moving!
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.