GR & 3rd Law: A Thought Experiment

[my_wan]

I like simple physical setups to articulate and generate good thought experiments.

Setup:
Consider a hole cut in a flat sheet of material with these conditiond;
Bottom portion is perfectly circular with 150 degrees of arc.
End points are represented by x=+n, y=0 and x=-n, y=0.
x=0, y=0 represents the midpoint. The length L is +n to -n.
To complete the hole define the points in a straight line starting at each point on the surface of the 150 degree arc passing through the point of origin, x=0, y=0 and endng at distance L from the starting point on the arc.

Setting it in motion:
Provide a motor that maintains constant rpm at the point of origin.
Place a rod of length L contained by the hole and spun by the motor.
Note: The rod must be allowed to shift back and forth on the motor shaft but forced to spin with the motor. Rotation torch is assumed to be canceled by other means, counter rotating pairs, etc.

Question setup:
At first glance it wouldn't be hard to imagine that since a greater length of rod is always in the +y direction that a positive momentum is created for the system in that direction. Obviously this appears to be ruled out by the 3rd law, like lifting yourself up in a bucket. Now we consider that GR demands this system to generate gravitational radiation in a particular direction.

Questions:
(1) If the 3rd law holds under classical analysis of this situation wouldn't that mean that under GR there would be at least some momentum imparted to it in a given direction?
(2) If the gravitation radiation is found to cancel out the momentum wouldn't that mean that under a purely classical analysis it would show a violation of the 3rd law, or at least invalidate the classical concept of an enclosed system.

Given the symmetries of relativity I can imagine situations were the answer is no to both questions. I would appreciate any insight you have on it.

Thanks,

 

[Creator]

... Rotation torque is assumed to be canceled by other means, counter rotating pairs, etc.

Now we consider that GR demands this system to generate gravitational radiation in a particular direction.

,

I can't really envision what your device looks like from your description. However, it seems to me...

GR would also predict gravitational radiation from the 'counter rotating pairs' (that cancel the torque) which is equal & opposite momentum to that emitted by your rod device so there is no directional asymmetry in the radiative momentum transfer.

Creator

 

[my_wan]

Maybe my description wasn't clear enough. The statement about rotation was just about practical problems not about actual operation or physics, like nectlecting air resistance when calcing acceleration due to G. In other words the rotational torch is to be ingnored. Only the excess mass of the spining rod always being in the +y direction is considered.

The hole itself has a shape somewhat similar to an egg with point of rotation for the rod closer to the rounder lower part of the egg. It would be reasonable to assume a shape with the nessisary characteristics would not be possible, which is why I give such a precise prescription for it. It is in fact possible to design and operate this apparatus.