I like simple physical setups to articulate and generate good thought experiments.(adsbygoogle = window.adsbygoogle || []).push({});

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,

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# GR and the 3rd law

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