Absolutely rotationless reference frames?

[gmax137]

I just came across this thread
https://www.physicsforums.com/threads/inertia-and-machs-principle.916815/#post-5779364
that may be of interest to the OP.

 

[Buckethead]

No, angular momentum is frame invariant. Imagine two frames which are rotating about the same axis at the same rate. Even though no points in either frame are moving with respect to each other, experiments can be done to show that the frames are rotating and measure how much angular momentum they have.

Please don't forget about frame dragging. If an object is not exhibiting proper acceleration and is in a frame that is experiencing frame dragging and is also separated by an object (on the same rotational axis as above) such that the second object's frame is not being dragged, then it is possible that both objects can be rotating relative to each other while neither is experiencing proper acceleration.

 

[facenian]

This isn't how I understand angular momentum. In my eyes, it is simply defined as the sum of the cross product of position and momentum for all mass elements in the system. If we change frames (maybe change the location of the origin, maybe have the new frame move at a constant speed relative to the old, maybe give the frame a constant rotational speed) then we will generally find different angular momenta for the same system, because the position and momentum vectors will change with the frames.

You are right. It is easy to check that, when applying a Galilean transformation, the angular momentum defined with respect to a certain frame is not invariant when passing to another reference system that is moving with respect to the first one.

With regard to the initial question space and time in Newtonian mechanics are absolute concepts. In particular space is said to be absolute in a very particuar and philosophically uneasy manner because, althoug relative constant motion can not be detected with respect absolute space, acceletation and consecuently rotational motion can and this is precisely what gives meaning to absolute space. Newton was very soon criticized for this defect in his theory.
On the other hand, although Special Relativity overthrew Newton's absolute time ,it did not change the concept of absolute space.

 

[Dale]

@facenian If you take a blank sheet of paper and draw a straight line and a curved line then you can say that the straight line is straight and the curved line is curved without placing any coordinates on the paper. There is no "absolute vertical" nor "absolute horizontal" implied by the fact that the curved and straight lines are distinguishable.

 

[facenian]

@Dale I'm not sure if I have understood you point. Absolute space in the Newtonian sense does not mean that there is an absolute vertical or horizontal direction neither it means that straight lines are diferent from curved lines only because the existence of absolute space. The problem resides with motion itself because from a kinematical point of view only relative motion is meaningful and this is so even in Newtonian mechanics "but only" for a certain class of rectilinear motion which determines the class of inertial frames. The problem stems from the words "but only". It Is this fact that gives rise to "Absolute Space" because rectilinear acceleration(and rotation) with respect to absolute space can be dectected without reference to any other frame(or body) with respect to which motion is measured.