Couldn’t you tell whether your planet is revolving or rotating using a Foucault’s pendulum? I’m not sure whether you can get all the information about the planets’ relations with a complex set of Foucault’s pendula or not, but you could get some.
The Foucault pendulum is able to measure earth’s rotation in part because of the frame established by the rest of the universe. But in the scenario I described, the frame dragging effect of one or both planets blows up your ability to use the standard equations. Would the corrections introduced by including frame-dragging show a solution that varies depending on which of the planets is “really” moving?
Also, I think your answer is a map-territory confusion. While GR does not distinguish certain types of motion from each other, and while GR seems to be the best model of macroscopic behavior we have, to claim that this means that there is really no fact of the matter seems a little overconfident.
It’s the other way around. The fact that there is no test that would distinguish your location along a dimension means that no such dimension exists, and any model requiring such a distinction is deviating from the territory.
Yes, GR could be wrong, but for it to be wrong in a way such that e.g. you actually can distinguish acceleration from gravity would require more than just a refinement of our models; it would mean the universe up to this point was a lie.
Yes, GR could be wrong, but for it to be wrong in a way such that e.g. you actually can distinguish acceleration from gravity would require more than just a refinement of our models; it would mean the universe up to this point was a lie.
This isn’t really true. In GR, you can in principle always distinguish acceleration from gravity over finite stretches of spacetime by measuring the tidal forces. There is no distribution of mass that would produce an ideally homogeneous gravitational field free of tidal forces whose effect would perfectly mimic uniform acceleration in flat spacetime. The equivalence principle holds only across infinitesimal regions of spacetime.
This isn’t really true. In GR, you can in principle always distinguish acceleration from gravity over finite stretches of spacetime by measuring the tidal forces. …
Yes, I was just listing an offhand example of an implication of GR and I didn’t bother to specify it to full precision. My point was just that in order for a certain implication to be falsified (specifically, that there is no fact of the matter as to e.g. what the velocity of the universe is), you would need the laws of the universe to change, not just a refinement in the GR model.
The Foucault pendulum is able to measure earth’s rotation in part because of the frame established by the rest of the universe. But in the scenario I described, the frame dragging effect of one or both planets blows up your ability to use the standard equations. Would the corrections introduced by including frame-dragging show a solution that varies depending on which of the planets is “really” moving?
I must admit I’m a little baffled by this. I’m pretty ignorant of GR, but I was strongly under the impression that
(a) the frame dragging effect was miniscule, and
(b), that Foucault’s pendulum works simply because there is no force acting on the pendulum to change the plane of its rotation. Thus, a perfect polar pendulum on a planet in a universe with no other bodies in it will never have any force exerted on it other than gravity and will continue to swing in the same plane. If the planet is rotating, an observer on the planet will be able to tell this by observing the pendulum, even in the absence of any other body in the universe. Similarly, in the above paradox, an observer can tell whether their planet is revolving around the other planet while remaining oriented towards it because the pendulum will rotate over the course of a “year”.
To appreciate how differently things are when you remove the rest of the universe, consider this: what if the universe is just one planet with the people on it? How will a Foucault pendulum behave in that universe? Shouldn’t it behave quite differently, given that the rotation of the planet means the rotation of the entire universe, which is meaningless?
To appreciate how differently things are when you remove the rest of the universe, consider this: what if the universe is just one planet with the people on it?
As Prase said above, that depends on the boundary conditions. As the clearest example, if you imagine a flat empty Minkowski space and then add a lightweight sphere into it, then special relativity will hold and observers tied to the sphere’s surface would be able to tell whether it’s rotating by measuring the Coriolis and centrifugal forces. There would be a true anti-Machian absolute space around them, telling them clearly if they’re rotating/accelerating or not. This despite the whole scenario being perfectly consistent with GR.
The Foucault pendulum is able to measure earth’s rotation in part because of the frame established by the rest of the universe. But in the scenario I described, the frame dragging effect of one or both planets blows up your ability to use the standard equations. Would the corrections introduced by including frame-dragging show a solution that varies depending on which of the planets is “really” moving?
It’s the other way around. The fact that there is no test that would distinguish your location along a dimension means that no such dimension exists, and any model requiring such a distinction is deviating from the territory.
Yes, GR could be wrong, but for it to be wrong in a way such that e.g. you actually can distinguish acceleration from gravity would require more than just a refinement of our models; it would mean the universe up to this point was a lie.
SilasBarta:
This isn’t really true. In GR, you can in principle always distinguish acceleration from gravity over finite stretches of spacetime by measuring the tidal forces. There is no distribution of mass that would produce an ideally homogeneous gravitational field free of tidal forces whose effect would perfectly mimic uniform acceleration in flat spacetime. The equivalence principle holds only across infinitesimal regions of spacetime.
See here for a good discussion of what the equivalence principle actually means, and the overview of various controversies it has provoked:
http://www.mathpages.com/home/kmath622/kmath622.htm
Yes, I was just listing an offhand example of an implication of GR and I didn’t bother to specify it to full precision. My point was just that in order for a certain implication to be falsified (specifically, that there is no fact of the matter as to e.g. what the velocity of the universe is), you would need the laws of the universe to change, not just a refinement in the GR model.
I must admit I’m a little baffled by this. I’m pretty ignorant of GR, but I was strongly under the impression that
(a) the frame dragging effect was miniscule, and
(b), that Foucault’s pendulum works simply because there is no force acting on the pendulum to change the plane of its rotation. Thus, a perfect polar pendulum on a planet in a universe with no other bodies in it will never have any force exerted on it other than gravity and will continue to swing in the same plane. If the planet is rotating, an observer on the planet will be able to tell this by observing the pendulum, even in the absence of any other body in the universe. Similarly, in the above paradox, an observer can tell whether their planet is revolving around the other planet while remaining oriented towards it because the pendulum will rotate over the course of a “year”.
To appreciate how differently things are when you remove the rest of the universe, consider this: what if the universe is just one planet with the people on it? How will a Foucault pendulum behave in that universe? Shouldn’t it behave quite differently, given that the rotation of the planet means the rotation of the entire universe, which is meaningless?
As Prase said above, that depends on the boundary conditions. As the clearest example, if you imagine a flat empty Minkowski space and then add a lightweight sphere into it, then special relativity will hold and observers tied to the sphere’s surface would be able to tell whether it’s rotating by measuring the Coriolis and centrifugal forces. There would be a true anti-Machian absolute space around them, telling them clearly if they’re rotating/accelerating or not. This despite the whole scenario being perfectly consistent with GR.
Rotation of the planets doesn’t mean rotation of the universe, don’t forget there are not only the planets, but also the gravitational field.