[Jaaanosik (OP)]

Hi all,
Is angular momentum frame dependent?
Before going into details how to check it out, I'd like to ask a questions what it would mean for physics,
Jano

[Halc]

Is angular momentum frame dependent?

It seems not. Take an example from relativity.  Earth rotates once every 23:56 hours, but in a frame where it is moving at .8c, it rotates once every 53:33 hours (slower) but has more mass, so the angular momentum seems unchanged.

[Jaaanosik (OP)]

Halc,
that's a good point.
What happens to a wheel when the rim of the wheel rotates at 0.7c and the wheel translates at 0.7c.
The wheel axle is 90 degrees to the velocity vector, the wheel is rolling and a trajectory of a point on the wheel rim is a cycloid in the outer reference frame.
The wheel is just rotating in the axle reference frame.
What happens to the angular momentum like here:



From Relativistic Hall Effect paper: https://arxiv.org/pdf/1112.5618.pdf
The angular momentum is symmetrical in the rest/axle frame (a) but it is not symmetrical in the outside frame (b).
What does it mean for physics?
Jano

[Kryptid]

I hope this doesn't lead to another discussion about reactionless drives.

[Jaaanosik (OP)]

Halc,
the first lines from the abstract:

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 angular momentum is the purpose of this paper.



The paper shows the delta between the angular momentum of the axle frame (a) and the outside frame (b).
The first one in (a) is symmetrical the second one in (b) is not symmetrical, there is a transverse shift.
That's what the paper shows.

... 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].

What are the implications for physics?
Jano

[Jaaanosik (OP)]

I hope this doesn't lead to another discussion about reactionless drives.

Hi Kryptid,
no, just the question, what does it mean for physics?
The angular momentum is frame dependent, as per the paper.
What does it mean for the Noether's theorem?
Jano

[Kryptid]

What does it mean for the Noether's theorem?

Nothing. Noether's theorem still applies.

[Malamute Lover]

I have been through the paper a couple of times and if I am reading it right, total AM (L) is still conserved but the distribution of intrinsic AM (r, 'spin')) and extrinsic AM (p, 'orbital') are frame dependent. But the AM conservation law applies only to L. Even in classical physics r and p are not individually conserved.

I think.

But then it has been a long hot day and I am after all older than at least some of the hills.

And I need  a nap.

[Jaaanosik (OP)]

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

[Malamute Lover]

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]

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.

[Jaaanosik (OP)]

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.

Let 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.

The (a) frame analysis - there is no change of the angular momentum.

But the diagram depicts center of mass/deformation, not change of those things.

The (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.

The +y side has bigger mass than the -y side in the (b) frame.
Let us imagine a rod on the axle with two weights at the end representing the wheel mass.
The W_+y weight is at the R_E location, on the +y side, the other W_-y weight on the -y side, the same distance from the axle.
W_+y  has bigger mass than  W_-y in the (b) frame. These masses represent the top and the bottom part of wheel, asymmetrical distribution.
W_+y  has equal mass to W_-y in the (a) frame, symmetrical distribution.
The acceleration is not supposed to change the angular momentum in the (a) frame.
The acceleration is supposed increase the angular momentum in the (b) frame because of the W_+y  and W_-y mass delta.

I am not equivocating velocity and the acceleration.
I am saying the velocity creates the delta in mass as per the paper.
Now we introduce the acceleration as a new thought experiment.
The delta in mass will increase the angular momentum of the wheel in the (b) frame but it is not suppose to do anything in the (a) frame.
Jano

[Jaaanosik (OP)]

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]

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.

Can the redistribution happen without new 4-accelerations in the (b) frame?
Can the -y spokes bend without new 4-accelerations in the (b) frame?
How is (a) frame going to see these 4-accelerations?
The (a) frame cannot see different 4-accelerations between +y and -y sides. The (a) frame is symmetrical.
The (b) frame sees these new 4-accelerations between +y and -y sides. The (b) frame is asymmetrical.

What does it mean for physics if two different frame observers do not agree on the accelerations???
Jano

[Kryptid]

What does it mean for physics if two different frame observers do not agree on the accelerations???

Nothing much. That's to be expected for relativity.

[Malamute Lover]

What 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.

[Jaaanosik (OP)]

What 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.

This requires a good analysis, here is a textbook:





The rotation creates equally spaced world lines in the (a) frame.





Here are the world lines as seen from frame (b), as per the paper:



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,
Jano

[Malamute Lover]

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,

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.

[Jaaanosik (OP)]

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,

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."

Nonetheless I fall to see that total angular momentum is not conserved.

Can you, please, elaborate how you see it?
Jano

[Malamute Lover]

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,

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."

The spokes of the wheel are traveling at different speeds as they go around. This is not an inertial frame of reference

.

Nonetheless I fall to see that total angular momentum is not conserved.

Can you, please, elaborate how you see it?
Jano

As I said earlier.
“

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

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. “

There is a tradeoff between intrinsic and extrinsic AM with the shift in energy centroid generating extrinsic AM compensating for the changes in intrinsic AM, just like the text of the paper says. Where does it say anything about non-conservation of AM? If that had been demonstrated by the paper, it would have been shouted long and loud as something totally new and ultra-important.

[Jaaanosik (OP)]

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

[Malamute Lover]

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

As already stated, the outside observer who sees (b) is not looking at an inertial reference frame. The spokes are going faster on top and slower on the bottom relative to overall motion.