Is rotational motion relative to space?

The same Wikipedia article everyone else is citing is a decent reference on this. Basically, we don't know, and probably never will, because we can't put an object in an otherwise empty universe.

Suppose you could, though. So we've got a planet in an otherwise empty universe. To test the hypothesis of absolute rotation, you could do various experiments on the planet's surface to measure the fictitious forces arising from being in a rotating reference frame. For example, you could set up Foucault's pendulum at various locations on the planet and measure the precession rate at each location. (I think you'd need at least 3 locations) From those results you could determine the planet's rotation axis and rotational velocity.

The Newtonian viewpoint holds that yes, rotation is relative to space. If this view is correct, and the isolated planet were rotating relative to space, you would see your pendulums (pendula?) precessing at a nonzero rate, and you could solve for the planet's rotational velocity.

On the other hand, the Einstein/Mach viewpoint holds that rotation is not relative to space, but rather is defined relative to the matter in the universe. If this viewpoint is correct, you would never see any precession of the pendulums because the bulk of the matter in this experimental universe is the planet itself, so it basically defines the frame of zero rotation. In our universe, of course, there is a much larger distribution of matter to define a nonrotating rotational reference frame. Mathematically, this results from a phenomenon in GR known as frame dragging.

The Newtonian/absolute view has the advantage of being kind of intuitive, but it does require that space defines some sort of absolute rotational reference frame. Given that we know all linear motion is relative, it seems odd (to me, and others) that rotational motion could be absolute. In addition, if rotation could be absolute, for any nonzero rotational velocity, a large enough distribution of matter in the universe would require the outer objects to be moving at the speed of light relative to a nonrotating reference frame. This could conceivably be allowed, it would just mean that no matter could be boosted into that nonrotating reference frame, but again, it seems odd. The Einstein/Mach view has the advantage that it makes this "faster-than-light rotation" extremely unlikely as a consequence of the structure of the theory alone.

This is an old question, but it might be possible to put the old saw to rest for good.

If you have a deSitter space, it can't be rotating--- deSitter space is unique. If you have a black hole in deSitter space, it can rotate (this is the deSitter Kerr solution recently discovered), but it is only one body rotation, the cosmological horizon can't rotate independently of the black hole horizon.

This might not be surprising, except that if you make the nonrotating deSitter black hole bigger and bigger, there is a point where the black hole and Cosmological horizon are symmetrical. In this case, you have two horizons. If you rotate one horizon, the other rotates in the opposite sense, so that only their relative rotation is meanigful. The two horizons are symmetric now, so you can't differentiate between their motions.

If you add matter in-between the two horizons, you will curve the universe inbetween, and if you put a lot of static dust in, you get to an Einstein static universe with two black holes at opposite ends. In this universe, the two horizons are clearly matter. So there is no boundary between matter and cosmological horizons, and it is a fair statement to equate all matter with some sort of horizon-object, so that the electron is like a little micrscopic black hole.

This is the point of view most consistent with string theory, since the strings in string theory are dual under strong-weak coupling dualities to objects which are clearly black holes in the classical limit, namely D-branes. The point of view that matter is the same as horizon puts Mach's principle to rest--- all motion is relative to distant "matter", either matter matter or horizon matter, which is also matter.

This statement is consistent with the holographic principle, and the holographic principle can be thought of as the ultimate in Mach's principle, since it says that all motion is relative to a distant holographic screen, so that the whole thing is moving relative to a distant horizon. This principle is more precise, more quantum, and more general than Mach's principle, and it is consistent with the solutions of GR in a space bounded by a horizon. I must say, however, that the deSitter formulation of string theory is not available right now, so that the full holographic principle is not completely known.

thank you for your question. Indeed, you are pointing in the directions of two big unifications made in physics: Linear motion and rest by Newton and acceleration by Einstein.

If it is convenient for you, I will devide your question into two parts concerning Newtonian and Einsteinian physics which will be related to who is observing the rotation.

First of all, if you are fixed to a point on the surface of the earth which is rotating, you will be able to measure it by means of fictitious forces acting on you, also in a non-relativistic Newtonian setup. But the interesting question is what happens if you are somewhere in space.

Then, assuming the earth as axisymmetric, Newtonian physics will tell you that there will be no difference to a non-rotating earth in the gravitational field. You will have to consider general relativity to answer this question. It turns out, that rotating bodies curl spacetime and you can even assign an angular momentum to it. By measuring this effect, which might be very hard, you would be able experimentally verify earth's rotation.

Sincerely,

Robert

PS.: For further information, see e.g. On the multipole moments of a rigidly rotating fluid body

PPS.: @David: If I understand your argumentation correctly, you state that earth's rotation would define the zero-rotation reference-frame. I must admit that this might not be correct. Think of the Kerr spacetime for a non-vanishing rotation of a black hole. This is a similar situation, you cannot find a coordinate system with vanishing angular momentum of the spacetime as a whole.