# Frame dragging and absolute rotation

1. Jan 21, 2010

### nottay

I'm trying to wrap my head around how rotational frame dragging affects the centrifugal force of a massive, rotating body and was hoping someone could explain this concept to me better. If I am confused on any of the points below please let me know.

It is my understanding that there is no such thing as an absolute reference point even in terms of rotating reference frames in GR and rotational frame dragging is the result of each rotating body trying to coerce its surrounding space-time field that its rotating reference frame is the correct one. Absolute rotation is a result of all the matter in the universe influencing their space-time and defining what bodies are rotating and how much.

My question is, if there is a massive body rotating at high speeds with no other mass close by, will it eventually (thru frame dragging) re-orient the space-time field around it in such a way that it will no longer be rotating from its point of view and experience no centrifugal force?

I've created a thought experiment which will hopefully make my question clearer:

Lets say the entire universe is comprised of only three masses and space-time. The first mass is very massive, comprising 95% of all the matter in the universe but is not very dense and doesn't collapse under the effect of its own gravity. The second mass has very low mass and located far enough away from the first mass that any gravitational attraction to the first mass is cancelled out by the cosmological constant in such a way that these two masses always remain the same distance from each other and do not rotate relative to their space-time field or each other. The third mass makes up the other 4.99% of the universe and collides with the first mass off-center at high speed and is absorbed into the mass by the impact causing the combined mass to rotate relative to the space-time field. An observer on the second mass with a very powerful telescope sees the impact and notes that the rotation of the body is causing it to bulge about its axis of rotation due to the centrifugal force of its rotation. So as time passes the observer watches as the rotating body drags the space-time field around it through rotational frame dragging. My question is whether the frame dragging would eventually cause the entire "universe" to rotate with the body therefore eliminating the centrifugal force in such a way that the observer on the second mass would eventually see the bulge disappear and the first mass be transformed back into a perfect sphere by gravity?

I really hope this makes sense :)

2. Jan 21, 2010

### bcrowell

Staff Emeritus
That's not actually true. You can detect whether you're rotating by referring to a gyroscope, for instance.

3. Jan 26, 2010

### nottay

I know rotation can be detected by a number of different tests but doesn't relativity imply that there shouldn't be such a thing as absolute rotation if all frames of reference are equal? I'm referring to Mach's principle and the idea that a rotating body experiences centrifugal force due to the inertia of the rest of the matter in the universe as implied in his quote:

"You are standing in a field looking at the stars. Your arms are resting freely at your side, and you see that the distant stars are not moving. Now start spinning. The stars are whirling around you and your arms are pulled away from your body. Why should your arms be pulled away when the stars are whirling? Why should they be dangling freely when the stars don't move?"

4. Jan 26, 2010

### bcrowell

Staff Emeritus
GR doesn't satisfy Mach's principle. Who is the quote from?

5. Jan 26, 2010

### nottay

The quote is from Ernst Mach. So if the centrifugal force isn't caused by a body rotating in reference to the matter around it then what determines the absolute rotation? I find it hard to believe that there is simply a preferred reference point when it comes to rotation.

6. Jan 28, 2010

### PhilDSP

Frame dragging may be caused by the time lag of EM propagation, mighten it?. When a charged particle "moves", even rotates, the EM fields that any particular point feels will be different from that it would feel if it weren't rotating or moving. That brings about non-locality.

The Kramers–Kronig relations are one place where that non-locality is identified. The Jackson textbook on EM has a very nice introduction and explanation.