Calling all physics heads

Factual Questions
1

I have a thought experiment I have posed before, but have never gotten a satisfactory answer to, so I’m throwing out to all dopers with strong physics skills.

Picture a universe with only two objects, both rings. Ring B is 2 meters in diameter, ring A is one meter, they have a common center, and lie in the same plane. They rotate with respect to each other and the axis of rotation for each is perpendicular to their common plane (same axis for both)

Now add two beings, one living on the outer suface of ring A and the other on the inner suface of ring B. They see each other go whizzing by 2 twice per second.

Now, give them both accelerometers. What do they each read?

This seems to me to be an indeterminate problem. There seem to be an infinity of self consistent answers, of which I’ll give four:

  1. The A-ian reads 0g and the B-ian reads 32.2g

  2. The B-ian read 0g and the A-ian reads -16.1g, negative by virtue of being on the outer surface of the ring.

  3. The A-ian reads -4.0g and the B-ian reads 8.0g

  4. The A-ian read -4.0g and the B-ian reads 72.5g
    These four solutions represent the answers expected by a third being outside the rings who represents a inertial frame of absolute rest who sees…

  5. The A ring motionless and the B ring spinning at 2 rps.

  6. The B ring motionless and the A ring spinning at 2 rps.

  7. The two rings spinning in opposite directions, each at 1 rps.

  8. Both rings spinning the same direction, the inner one at 1 rps and the outer at 3 rps.

What’s going on here? It seems any answer is self consistent as long as the rings’ relative rates of rotation differ by 2 rps.

The only answer I’ve heard that makes sense is very unsatisfying…that a universe has a certain angular momentum that is a first-principle value. It can be anything at all, but by leaving it out I have given an insufficient description of my universe. Once I specify a total angular momentum, only one answer is possible.

This strikes me as unsatisfactory becuase it imples there is a preferred reference frame - the one that gives the “right” angular momentum - which is a completely arbitrary value. Anybody got a better solution, or does General Relativity actually admit a preferred reference frame? (since we’re dealing with accelerations and I know special does not admit either accelerations or preferred reference frames).

2

I realize this isn’t the point of your experiment, but since I favor the Lense-Thirring explanation of inertia, (due to the fact that I arrived at the same conclusion independently and 80 years too late for the trip to Copenhagen)over the zero-point, the accelerometers would both read zero in the absence of ‘all of the mass’ of our Universe.

I’m afraid I haven’t found a good websource to cite, but if you find a good description of Lense-Thirring, you’ll have the answer to your questions about ‘preferred frame’.

3

Found a slew of pages with lay explanations of Lense-Thirring. I get it, and it does neatly dispose of my posed problem. Well, maybe not neatly, but I understand what they’re getting at. Actually, I doubt the accelerometers would both read zero unless we carefully chose the mass of the two rings, using math I probably never learned in the first place, but I can easily believe that “frame dragging” could lead to a unique solution without having to resort to an arbitrarily assigned total angular momentum.

Tomorrow I’ll try to figure out what each ring inhabitant would see looking at the other one given this particular effect. I probably won’t get it right, but that’s personally less troublesome than the origianl problem. A man’s got to know his limitations!

Thanks!

4

To save others searching, this page gives a nice simple explanation of the whole thing…even I understood it. :slight_smile: