# Rate of spin of a particle

1. Apr 14, 2005

### RandallB

Nuclear particle “SPIN” always comes in half units 2, 3/2, 0, even -1/2.
It’s an odd measure; not the rotation of a particle as if it were spinning through space in the same manner as earth spins as it rotates once a day.
But, named spin because it’s measuring a “quality” or “attribute” of a particle that seems like a rotation; or measure of angular momentum .

Now the question is – along with the ability to detect spin or angular momentum has anyone ever measured something they’d described as (or claimed as) spin rate or frequency of that spin (or angular speed of the angular momentum)?

If so, I’d guess that “rate” to be the same regardless of the spin number including 0 spin.
If anyone’s ever seen something described like that, I’d appreciate a reference source.

RB

2. Apr 14, 2005

### dextercioby

Explain more clearly what u understand by "spin rate or frequency of the spin"...

Daniel.

3. Apr 15, 2005

### marlon

Are you asking about how fast a particle would rotate around it's own uniaxial axis. If so, your question has no answer because this particle does not actually rotate around it's own axis. the concept of spin is ofcourse a real-time subject that has observable consequences like the Zeeman-effect. However, this rotation is just an abstract grouptheoretical concept that arises as a consequence of the involved symmetry : the spinor-symmetry.

Besides, spin is an INTRINSIC quantity of a particle. This means that spin does not change when performing coordinate transformation. Suppose the particle is actually rotating, then you'd be able to transform your frame of reference to a frame that rotates with the particle : the 'rotational speed or the spin (the two need to be connected)' would become ZERO. However this is not the case !!!

This is something like helicity in theoretical physics : helicity is NOT intrinsic !!!
This "left-handed" vs "right-handed" characterization is not meaningful for other particles, like electrons. An electron could have spin to the right and be traveling right and therefore be classified as right-handed. But from the reference frame of someone traveling faster than the electron, its velocity would be to the left, while its spin would be unchanged. This would mean that the electron is a left-handed particle with respect to that reference frame.

marlon

4. Apr 15, 2005

Staff Emeritus
I think it's not quite as abstract as all that. The wave state is represented by a multi-component object, a spinor, whose law of change under change of coordinates is through operations of the group. Thus a spinor is as well-defined as a tensor, in Minkowski spacetime.

5. Apr 15, 2005

### RandallB

Of course not!
Don't know how I could have made that any more clear in my question. You did a fine job of describing spin and various measures that have been made of it.
ALL as if ‘something’ was spinning though.
Left or Right handed (Backwards or Forwards with particle direction).
Or just plain Left or Right for a particle rotation perpendicular to its travel.
BUT ALL with the careful proviso that nothing is actually spinning or rotating!

In the same manner “Spin Frequency” would just be how fast the particle “appears" to rotate even though it does not spin.
Now if you want a better definition of “Spin Frequency”, you will need to give me a better definition of “Spin” that does not include anything that even looks like describing rotational spin.

Also note, I did not ask for nor expect a direct “Answer” to the question. Just to know if someone somewhere detected or suspected something that they – not you, not me – that they interpreted as being, or looking as if or maybe seemed like ‘spin frequency’.
I don’t care if they thought it was the artificial orbiting of a fictitious either or a undefined Heisenberg equation some how turning inside the particle or however they chose to describe it. That doesn’t matter to me.

If someone did see something of the sort, and had the guts to share it, I’d just like to see what they had to say. I’d be willing to look at it with an open mind, yet I’d understand if such a person might fear that most would not, and so be reluctant to talk about it.

6. Apr 16, 2005

### marlon

I think you misinterpreted my point. The point is that the spinor-behaviour of the wavefunction under specific coordinate-transformations is not the same as saying the object actually rotates. That is my point, that is what i called an abstract notion

marlon

7. Apr 16, 2005

### marlon

That is impossible because the 'rotational nature' of spin comes from the behaviour of the Dirac spinor under coordinate-transformations (which are called the rotations). I refer to my previous post that responds to selfAdjoint's reaction to my case.

Frequence cannot be defined because it is a concept that applies to rotating objects. Now, changing coordinations (represented by rotations) is NOT THE SAME as actually rotating. That is my entire point.

marlon

8. Apr 16, 2005

### arivero

Hmm you are aware it is units of $$\hbar$$, aren't you? I.e., it is 2h, 3h/2, 0h, -h/2... And of course, h has the same units that angular momentum. Moreover, spin shows to be an axial vector, just as angular momentum. So whant is the problem?

9. Apr 16, 2005

### RandallB

OK I’ll break it down in your terms.

'rotational nature' of spin comes from ..... coordinate-transformations” That ultimately give us “changing coordinations”.

That is coordinate coordination’s are changing. Each being unique lets call them each one a “Changed Coordinate Coordination” or CCC for short.

So we know we know that any CCC will not remain the same as it’s its nature (and name) to change to another CCC.
So we can split the question into two parts –

First: By what unit of measure (or any unit of measure you or someone would like to create) do you define the difference between one CCC to another second CCC?

Second: How much time does it take for a defined amount of CCC change to occur?

Time based on any defined observer frame common to both CCC coordination’s.

As to the “UNITS” of change between CCC’s – I have no idea what that might be hopefully it is not Degrees or Radians – the similarity to HZ that would imply would be to shocking to contemplate.

Or maybe in another way:
Does a unique Coordinate Coordination, based on current transformations used to evaluate spinor’s, considered to be repeated?
That is, does the identically Coordinate Coordination ever come back or get repeated?
If so, is there a known time interval to that repeat of a “rotations” view?

RB

10. Apr 16, 2005

### marlon

Again you are totally missing the point. There are no coordinates changing. A physical system is described by a wavefunction, right. Well what i am saying is that this wavefunction is INVARIANT for coordinate changes. To give a naive example : if you replace x by y, then the wavefunction will be the same. But this is just to denote the symmetry.Don't confuse this by saying the coordinates are actually changing because of some reason : they are not. Can you see that difference? This is the crucial part...

Now, the 'operation' for changing x with y is represented by a matrix and it is this matrix that forms a representation of the socalled 'rotation-group'. This is just a naive example, but something analoguous happens with spin. In stead of keep on talking about this, i suggest you look up the way grouptheory is implemented in QM.

regards
marlon

11. Apr 17, 2005

### marlon

12. Apr 18, 2005

### RandallB

Great thread -- I liked the post you pointed out, Thanks much.
But "humanino" did use the term rotation quite bit:
I added the single quotes to 'rotation' to indicate he didn't really mean turning.
Maybe we can clean it up just a bit:
Let's look at what he is saying another way as though me were taking a movie of our observations.
On our first frame we have a photo of our observable wavefunction.
Now for our second frame we get a photo though a mirror in our shot on the other side behind our subject!.
No changing that, Out of our control, we are stuck with whatever " Fermi-Dirac statistics & its reality of how it allows us to "see" and record our movie film observations.
And frame two of course comes out as the negative of our subject wavefunction!
Now our Third Frame is a shot that in addition to going through the mirror behind our subject waveform. The shot also goes through another mirror beside us! Both mirrors gives the 4 pi view or a (360)!
And so on for additional frames of our movie adding one more reflection each frame.
All the odd numbered frames are the same as the first frame not a reversec negative view.
All the even number shots the same as our second frame of the movie a neagative view.
IN FACT so identical, we realize the system might not be using a mirror next to us at all but just aligning directly back on our subject we cannot tell.
And we also realize we can not be sure that the first shot wasn't though the mirror behind the subject and the even number frames are the true "front" of our subject!
The rules of observing our waveform with "Fermi-Dirac statistics etc." just will not give us that detail. But it does confirm for us Spin is there! The implied "rotation" caused by the mirrors (or whatever) is not a real turning 'rotation'. But we can observe it! And measure it.

This turns us back to the original question, (without actually turning of course) which is still there, but maybe phrased better as:

Now that we have these observations captured (and detailed so well with grouptheory spinor math, etc.) on our imaginary strip of movie film.
Just how many frames per second were this observations made at?

Real simple - no rotation of HZ required - just observational frames per second.

Has anyone anywhere tried to quantify this?

RB