Rotating Disks: Particle Movement & Spin

[Jeronimus]

When we rotate a disk, can this process be fully explained by looking worldlines of the particles the rotating disk is composed of, hence their x,y,z,t position "as time passes", or do particles have some kind of "facing direction", hence also spin(not the quantum mechanical notion of spin) while the disk is rotating?

An analog would be a planet rotating around the sun. It could rotate in such a way, that one side of the planet would always be facing north(once we defined where north is) or alternatively, the planet could rotate in such a way that the side which formerly was facing north always, would point towards all directions on the plane when doing a full orbit around the sun.

What would be the quantum mechanical view on this? Is there any notion of "facing towards" in QM?

 

[pervect]

A single, classical point particle doesn't - as far as I know at least - have any need for spin. If you consider a classical particle with some non-zero finite extent, it does make sense to talk about the particles spin. I believe one would consider such an extended particle as a collection of worldlines, one for each point, rather than as a single worldline. There's some fairly advanced mathematics that describes the spin of such a collection (usually called a congruence) of worldlines. The name for this spin-related property of the collection/congruence is the "vorticity tensor".

 

[Jeronimus]

A single, classical point particle doesn't - as far as I know at least - have any need for spin. If you consider a classical particle with some non-zero finite extent, it does make sense to talk about the particles spin. I believe one would consider such an extended particle as a collection of worldlines, one for each point, rather than as a single worldline. There's some fairly advanced mathematics that describes the spin of such a collection (usually called a congruence) of worldlines. The name for this spin-related property of the collection/congruence is the "vorticity tensor".

So, let's assume we could place a muon exactly at the center of a tiny high velocity spinning disk. Such a muon would not be able to tell any difference compared to a muon on a similar disk which is not spinning, right?

Has any experiment coming close to that been performed, where a small disk containing some radioactive material set to spin extremely fast, to check if the material exactly in the middle would decay at the same average deltaT as the material exactly at the center of a similar non-spinning disk?

 

[haael]

In absence of interactions, particles only change positions. You can imagine them as tiny gyroscopes that maintain direction.

In contrast, in magnetic materials particles (atoms) also change spin, because of the magnetic interaction.

 

[Jeronimus]

In absence of interactions, particles only change positions. You can imagine them as tiny gyroscopes that maintain direction.

In contrast, in magnetic materials particles (atoms) also change spin, because of the magnetic interaction.

An atom however is not an elemental particle. It is divisible still. I am concerned about elemental particles that are supposedly indivisible, like electrons, muons etc. Do those have some kind of "facing direction" which can change, hence them spinning around even when placed exactly at the center of a fast rotating disk, or not?
I am not talking about the QM notion of spin which seems to be something completely different. Yet i am also interested if in QM there is a notion of an elemental particle having a "facing direction".

Furthermore, IF elemental particles would have a facing direction, and when placed at the center of a fast rotating disk, hence changing their facing direction, would there be any kind of experiment to show a difference? The experiment above i proposed, might not show any difference at all if changing the facing direction does not affect the decay time of muons, but maybe it does?

 

[haael]

An atom however is not an elemental particle. It is divisible stil.

The same holds for any part of the system. Any atom, any molecule, any elementary particle and any isolated part of the system, no matter how big or small will maintain its own angular momentum unless there is an interaction that causes it to change or align with the rest of the system.

Do those have some kind of "facing direction" which can change, hence them spinning around even when placed exactly at the center of a fast rotating disk, or not?
I am not talking about the QM notion of spin which seems to be something completely different. Yet i am also interested if in QM there is a notion of an elemental particle having a "facing direction".

The only "facing direction" elementary particles have is the spin, or rather polarization vector. Spinless particles don't have any and are symmetrical.

Furthermore, IF elemental particles would have a facing direction, and when placed at the center of a fast rotating disk, hence changing their facing direction, would there be any kind of experiment to show a difference?

Yes, there is an experiment that can show whether the spin of the particle in the center is coupled to the rest of the disk.

If you have some disk of some moment of inertia and you put an uncoupled particle in the center that can rotate freely with respect to the disk, then nothing will change. But if you make this particle coupled (i.e. with magnetic field) so its spin is always aligned with the rest of the disk, the moment of inertia will change.

 

[Jeronimus]

But if you make this particle coupled (i.e. with magnetic field) so its spin is always aligned with the rest of the disk, the moment of inertia will change.

Based on this, if we were able to get some muons at rest relative to our frame and would then proceed to use a magnetic field as a means to get them spinning really fast, hence changing the moment of inertia those muons have, if i understood this correctly.
Would we then see any change in their decay time, or does the value of the moment of inertia they have not affect this is at all?

 

[haael]

use a magnetic field as a means to get them spinning really fast, hence changing the moment of inertia those muons have

Muons are "spinning" by default, that means they have spin. What you achieve with magnetic field is precession.

Would we then see any change in their decay time, or does the value of the moment of inertia they have not affect this is at all

Muons moment of inertia doesn't change. It's the system as a whole that has different moment of inertia.

As whether muons decay time changes - I don't know, but probably yes. When we enable magnetic field, muons are no longer free particles. They interact with the magnetic field, their paths become curved, their spins go into precession. You will have to check the literature if their decay time effectively changes thanks to the interaction.

 

[pervect]

So, let's assume we could place a muon exactly at the center of a tiny high velocity spinning disk. Such a muon would not be able to tell any difference compared to a muon on a similar disk which is not spinning, right?

Has any experiment coming close to that been performed, where a small disk containing some radioactive material set to spin extremely fast, to check if the material exactly in the middle would decay at the same average deltaT as the material exactly at the center of a similar non-spinning disk?

A muon isn't a classical particle - it's quantum mechanical in nature. I had to look up whether it was a fermion or a boson. Wiki says it has spin 1/2, making it the former.

I recall from one of my texts (Wald) that GR has some issues with handling fermions in the semi-classical approximation (semi-classical because GR is basically a classical theory, but we can treat the curvature of space-time classically and ask what happens to quantum particles due to the curvature).

While I know that there are some issues with fermions in GR, I don't really know what the issues are, or all the various possible resolutions of them. I do recall reading that the issues inspired Einstein-Cartan theory, but that starts to get rather far afield, as it's a different and more complex theory than GR.

As far as experimental tests go, I'm not aware of any. I very much doubt that any of the issues involve would affect radioactive decay measurably, however.

 

[Jeronimus]

As far as experimental tests go, I'm not aware of any. I very much doubt that any of the issues involve would affect radioactive decay measurably, however.

I would really like to find an experiment done with a radioactive fast rotating disc. Thinking this further, it appears to me that you would not even have to just check exactly the middle of the disc. If rotating a disc causes particles to spin on top of just changing direction, and if spin itself would affect the radioactive decay time, then it would show on all particles, not just the middle one, with the middle one spinning the fastest or so i believe.

In any case, we would get different results for the decay times, should spin affect those, than if we were to calculate the decay times independent on the particles spin.

 

[A.T.]

the middle one spinning the fastest

Why?

 

[pervect]

Most of the confusion about spining disks comes from people who attempt to understand then without previous understanding of the relativity of simultaneity. For instance, they'll assme that it's possible to synchronize clocks in a rotating frame, and do not understand or listen to explanations about why that's not possible.

As far as peer reviewed theories go, we do have theories that are not GR that suggest that under the right conditions, spin could have important effects upon gravity. But these differences come up in the context of what happens in the neighborhood of a singularity of a black hole, not in the context of radioactive decay on a spining disk.

As an aside, some of the issues with fermions probably wouldn't arise in most cases of radioactive decay, the weak force in particular is mediated by a boson.

 

[Jeronimus]

Why?

Good question :D

I am not sure what led me to type that an elemental particle in the middle of the disc would spin faster, ignoring that for elemental particles you probably cannot apply any notion of "facing direction" anyway.
What i meant was the ratio between the spin and velocity of the particle, which would increase the further you move towards the middle of the disc. Hence if there is any kind of spin which would affect the decay time of an elemental particle, the deviation from the values we would get by treating this as if particles would only change position and some kind of spin affecting the decay time, would increase or so i believe.