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Is angular momentum frame dependent?
We consider the relativistic deformation of quantum waves and mechanical bodies carrying intrinsic angular momentum (AM). When observed in a moving reference frame, the centroid of the object undergoes an AM-dependent transverse shift...
... The antisymmetric AM tensor can be represented by a pair of three-vectors, Lαβ = (H,L), where L = r×p is the axial vector of the AM, whereas H = pct − (ε/c) r is the polar vector marking the rectilinear trajectory of the particle [13].
I hope this doesn't lead to another discussion about reactionless drives.
What does it mean for the Noether's theorem?
Let us apply an acceleration on the axle like this:The (a) frame analysis - there is no change of the angular momentum.The (b) frame analysis - there is a change of the angular momentum because the axle is not in the center of mass.The wheel is a 'pendulum', the mass is shifted in the +y axis direction,Jano
This situation is quite similar to the spin Hall effect in various systems, where variations in the intrinsic AM(spin) are compensated at the expense of the centroid shift generating extrinsic AM.[…]However, in addition to the shape deformations, a rotating body also acquires mass deformations. The y >0 and y <0 sides of the wheel have different velocities in the moving frame and their constituent particles acquire different local γ-factors. Owing to this, the y >0 particles become heavier than the y <0 particles. [page 2 of the article, the same page as the spoked wheel picture]
Angular momentum seems constant (not dependent on chosen axis of rotation) in an inertial frame where the center of mass is stationary. So Earth, in its own inertial frame has X angular momentum even if the axis is considered somewhere else. This is not true if Earth is moving, so Earth moving linearly at 30 km/sec has less angular momentum around its center of gravity than it does around any other point, like the sun for instance.That makes angular momentum frame dependent.Quote from: Jaaanosik on 29/07/2020 23:06:41Let us apply an acceleration on the axle like this:You are equivocating acceleration and velocity. That doesn't work. The deformation in the picture is due to linear velocity, not at all due to acceleration.QuoteThe (a) frame analysis - there is no change of the angular momentum.But the diagram depicts center of mass/deformation, not change of those things.QuoteThe (b) frame analysis - there is a change of the angular momentum because the axle is not in the center of mass.Does not directly follow. Momentum is not depicted at all in the pictures, but if the momentum vector is applied to the right-side (original) picture, it would be located somewhere other than the axle, but its magnitude and direction (the two elements that matter for a vector) would not necessarily be different.
Let us apply an acceleration on the axle like this:
The (a) frame analysis - there is no change of the angular momentum.
The (b) frame analysis - there is a change of the angular momentum because the axle is not in the center of mass.
Quote from: Jaaanosik on 29/07/2020 23:06:41Let us apply an acceleration on the axle like this:The (a) frame analysis - there is no change of the angular momentum.The (b) frame analysis - there is a change of the angular momentum because the axle is not in the center of mass.The wheel is a 'pendulum', the mass is shifted in the +y axis direction,JanoQuoteThis situation is quite similar to the spin Hall effect in various systems, where variations in the intrinsic AM(spin) are compensated at the expense of the centroid shift generating extrinsic AM.[…]However, in addition to the shape deformations, a rotating body also acquires mass deformations. The y >0 and y <0 sides of the wheel have different velocities in the moving frame and their constituent particles acquire different local γ-factors. Owing to this, the y >0 particles become heavier than the y <0 particles. [page 2 of the article, the same page as the spoked wheel picture]The spokes on the top are denser, as seen in the picture and heavier. The energy centroid is higher than the geometric centroid. Looks to me like overall angular momentum is conserved, but redistributed.
What does it mean for physics if two different frame observers do not agree on the accelerations???
Quote from: Jaaanosik on 30/07/2020 04:49:53What does it mean for physics if two different frame observers do not agree on the accelerations???Perfectly normal.A passenger on a rocket ship experiences constant acceleration. An observer in an inertial frame of reference sees that because of time dilation, the rocket ship acceleration is dropping over time. They disagree about acceleration exactly as expected.Something to also keep in mind is that the passenger on the rocket ship experiences acceleration while the observer only infers it.
The world lines lose the symmetry in (b), they are asymmetric.This is the problem, two different frames show different analysis.They do not agree on the world lines. This is not good.They do not agree on physics,
Quote from: Jaaanosik on 30/07/2020 19:57:09The world lines lose the symmetry in (b), they are asymmetric.This is the problem, two different frames show different analysis.They do not agree on the world lines. This is not good.They do not agree on physics,Two different reference frames seeing things differently is what relativity is all about.
Nonetheless I fall to see that total angular momentum is not conserved.
Quote from: Malamute Lover on 30/07/2020 20:08:58Quote from: Jaaanosik on 30/07/2020 19:57:09The world lines lose the symmetry in (b), they are asymmetric.This is the problem, two different frames show different analysis.They do not agree on the world lines. This is not good.They do not agree on physics,Two different reference frames seeing things differently is what relativity is all about. How can this be reconciled with this: "The laws of physics take the same form in all inertial frames of reference."
QuoteNonetheless I fall to see that total angular momentum is not conserved. Can you, please, elaborate how you see it?Jano
This situation is quite similar to the spin Hall effect in various systems, where variations in the intrinsic AM(spin) are compensated at the expense of the centroid shift generating extrinsic AM. […] However, in addition to the shape deformations, a rotating body also acquires mass deformations. The y >0 and y <0 sides of the wheel have different velocities in the moving frame and their constituent particles acquire different local γ-factors. Owing to this, the y >0 particles become heavier than the y <0 particles. [page 2 of the article, the same page as the spoked wheel picture
I see the problem this way. The frame (a) sees the rim of the wheel symmetrically. See the figures 13.14 and 13.15.The frame (b) sees the rim of the wheel asymmetrically. See the figure 2 of the paper.Both are the inertial frame observers.The (a) and (b) observers are not on the rim itself though.If there is an accelerated observer on the rim of the wheel then this local observer will measure either symmetrical centripetal acceleration as predicted by (a) frame or asymmetrical acceleration where the spacing between 'the rim blocks' changes as predicted by (b) or ... completely something else that neither reference frame predicted.Jano