Undergrad Does the electron really spin 720 degrees?

[Chris Frisella]

That's an incomplete statement, hence potentially misleading.

First, let's call it "intrinsic angular momentum" rather than "particle spin".

To explain further, imagine a spatially extended field, hence having a spatially extended distribution of energy, stress and momentum. (Have you heard of the Energy-Momentum tensor?) Now pick an arbitrary point in space -- call it "a". Given the energy-momentum tensor of the field, we can compute the total angular momentum (denoted as "J") around "a" by a certain integral formula (which I won't write out since you don't like math). The result can change, in general, if you choose a different point "a".

Now imagine we're working in the rest frame of the system represented as that spatially extended field. "Intrinsic angular momentum" (denoted as "S") is defined as the angular momentum about any point on the field's centre of mass world line. In general, "S" is only a part of "J" -- the rest being called "orbital angular momentum" (denoted as "L"). I.e., $$J ~=~ S + L ~.$$ (Or is that too much math?)

That's too much sarcasm for sure.

Does "intrinsic angular momentum" influence a magnetic field?

 

[pat8126]

A photon has a spin of 1, while an electron is 1/2. I've heard it said that the electron needs to spin 720 degrees to complete a full cycle. Is there any proof that the electron is spinning 720 degrees and not just spinning 360 degrees, but at a lower harmonic of the photon-- 1/2 the photon's spin frequency?

Are you referring to an electron that is represented by a wave function or a discrete particle?

 

[PeroK]

We'll take this bit by bit. Particle spin is angular momentum, correct?

Here's a simple answer. If you consider a large object like the Earth, it has orbital angular momentum (from its orbit round the Sun) and spin angular momentum from its rotation about its own axis. But, these two are physically the same: the spin angular momentum of the Earth is just the orbital angular momentum of all the particles that make up the Earth as they rotate about the axis.

The spin angular momentum of an electron, however, is essentially different from its orbital angular momentum. It is NOT the orbital angular momentum of all the stuff that makes up an electron as it spins on its axis.

The electron's spin does, however, share mathematical properties with orbital angular momentum, but it's a fundamentally different brand of angular momentum from anything we see around us.

 

[Chris Frisella]

Are you referring to an electron that is represented by a wave function or a discrete particle?

I'm referring to the particle. Shouldn't any representation of the particle (wave function) share the same attributes of the particle itself...?

 

[Chris Frisella]

Here's a simple answer. If you consider a large object like the Earth, it has orbital angular momentum (from its orbit round the Sun) and spin angular momentum from its rotation about its own axis. But, these two are physically the same: the spin angular momentum of the Earth is just the orbital angular momentum of all the particles that make up the Earth as they rotate about the axis.

The spin angular momentum of an electron, however, is essentially different from its orbital angular momentum. It is NOT the orbital angular momentum of all the stuff that makes up an electron as it spins on its axis.

The electron's spin does, however, share mathematical properties with orbital angular momentum, but it's a fundamentally different brand of angular momentum from anything we see around us.

Thank you.
I understand the concept this far. Now what's needed is a clear bridge between the electron's spin and actual, tangible motion. I believe the electron's spin will cause the electron to be deflected if it is shot through an external magnetic field, yes?

 

[Nugatory]

I believe the electron's spin will cause the electron to be deflected if it is shot through an external magnetic field, yes?

An inhomogeneous external magnetic field... But with that qualification, yes.

The magnitude of the deflection will be the same no matter what the direction of that magnetic field is. This result is impossible to reconcile with any model of spin angular momentum being rotation about an axis.

 

[pat8126]

I'm referring to the particle. Shouldn't any representation of the particle (wave function) share the same attributes of the particle itself...?

In classical mechanics, the particle displays properties of a wave function in a field that is inherently different from a discrete bodily object.

Your original question, in which you spoke about frequency differentials, seems to make sense to me. Check out the following page: https://en.wikipedia.org/wiki/Wave_function

As far as a discrete bodily object, an electron is an abstraction much like a point on a circle and does not reflect physical reality.

 

[Chris Frisella]

An inhomogeneous external magnetic field... But with that qualification, yes.

Got it. Then here seems to be a connection between spin and tangible momentum.

 

[Nugatory]

Got it. Then here seems to be a connection between spin and tangible momentum.

More like a connection between force and momentum - which is just Newton's second law. The electron has a non-zero magnetic moment, so the inhomogeneous magnetic field exerts a force on it.

 

[strangerep]

That's too much sarcasm for sure.

OK -- sorry about that. Goodbye.

 

[pat8126]

The electron's spin [is] a fundamentally different brand of angular momentum from anything we see around us.

If one were to model an electron as a discrete bodily object, it seems that it does spin 2x around its axis in order to return to it's initial state. This animated GIF from the Wikipedia article tries to show that very fact.

https://en.wikipedia.org/wiki/Spin-½#/media/File:Spin_One-Half_(Slow).gif

So, it seems that the answer to the OP's initial question is YES - the electron really does spin 720 degrees.

 

[vanhees71]

No again! You cannot in any way interpret spin as the spinning of a rigid extended body. It's just not possible! And also in quantum theory a rotation around 360 degs is always the identity operation on the states. Note that the pure states are not given by the Hilbert-space vectors but by the corresponding rays! We explained this many times. There's no way to explain this differently than with the mathematics. Plain English or any other language is just not sufficient! There's only one language to express physics adequately, and that's mathematics.

 

[Nugatory]

There's only one language to express physics adequately, and that's mathematics.

And it's pretty clear that this thread has failed to provide a counterexample :)

Whether we should be satisfied with this state of affairs is a different question. Posts arguing that question have been moved to another thread: https://www.physicsforums.com/threads/when-natural-language-fails-to-explain.888239/

 

[Chris Frisella]

More like a connection between force and momentum - which is just Newton's second law. The electron has a non-zero magnetic moment, so the inhomogeneous magnetic field exerts a force on it.

The spin (up or down) determins the direction of deflection of the massive electron, thus a connection between spin and common motion, force, momentum etc.

 

[vanhees71]

What you get with a Stern-Gerlach experiment is the entanglement between the measured component of the total angular momentum of the particle (usully $J_z$ if you direct your magnetic field in $z$ direction) and position. In the original SG experiment they used (neutral) Ag atoms and thus the total angular momentum corresponds to the spin 1/2 of the one electron in the outermost shell. Thus, in this case, you have a separation of the two possible spin states $\sigma_z=\pm 1/2$ in two partial beams.

 

[PeroK]

The spin (up or down) determins the direction of deflection of the massive electron, thus a connection between spin and common motion, force, momentum etc.

The electron's charge may also determine how it is deflected. Or its mass in a gravitational field.

 

[vanhees71]

Gravity is so weak that you can neglect it in the SG experiment. I'm not aware that the SG experiment has been performed successfully with charged particles. Then the dominant effect is just cyclotron motion, and the effect due to the magnetic moment/spin is too small compared to this too. The original experiment was performed with silver-atom beams. There are also very accurate experiments with neutrons.

 

[PeroK]

Gravity is so weak that you can neglect it in the SG experiment. I'm not aware that the SG experiment has been performed successfully with charged particles. Then the dominant effect is just cyclotron motion, and the effect due to the magnetic moment/spin is too small compared to this too. The original experiment was performed with silver-atom beams. There are also very accurate experiments with neutrons.

I thought the OP's point that because spin affects motion, the electron must be physically spinning. I was simply pointing out that its charge and mass can also affect its motion, under other circumstances.

 

[Chris Frisella]

The electron's charge may also determine how it is deflected. Or its mass in a gravitational field.
...I thought the OP's point that because spin affects motion, the electron must be physically spinning.

Thank you for your response. I don't necessarily mean that it must be physically spinning, just that there is evidently a hard connection between spin and ordinary motion/momentum. I'm sure the charge of the electron is part of this deflection as well, but it's the spin that is determining the direction of deflection.


You can see an example of the experiment in this video. It shows the quantum mass deflecting up or down depending on its spin.

 

[vanhees71]

The point is that spin is associated with a magnetic moment $\vec{\mu} \propto \vec{s}$. The potential energy of a dipole in a magnetic field $\vec{B}$ is $\propto \vec{\mu} \cdot \vec{B}$, and thus the force on the particle $\propto \vec{\nabla}(\vec{\mu} \cdot \vec{B})$. Thus there's a force in an inhomogeneous magnetic field (already for a classical particle with magnetic moment). All this translates into the quantum case. The main difference is that the Stern-Gerlach experiment, based on these ideas, shows that the magnetic moment is quantized as predicted by the Standard Model, i.e., there's a connection of the magnetic moment of the elementary particles like an electron or muon with the spin, and the corresponding gyromagnetic ratio is one of the exactest predictions of the Standard Model (with some puzzle concerning the muon anomalous magnetic moment, which is subject to ongoing exciting high-precision measurements at Fermilab, who inherited the corresponding experiment from BNL).

 

[DarioC]

Chris: If you are still around I have an interesting experiment that you can do. It only requires a tennis ball and a magic marker.
DC

 

[Collin237]

This question really has to do with understanding the derivation of an electron needing to spin "720 degrees to return to its original state" as I've heard it described.

Actually, there is a way to define a set of angles that rotates half as fast as the usual ones and yet correctly keeps track of rotations in different directions, and which gets multiplied by -1 from a 360 degree rotation.

 

[Electron Spin]

That may be true, but it's hard to wade through the abstract math.

I understand my friend..When I twas' young I had a hard time with math too. Math is a tool for us and one must learn how to use these tools to understand the laws and nature, of nature..Sorry for the slight deflection of this fascinating Q.

Ya' know, Einstein wasn't that good with math by his own admission but he made up for it in his command of eloquent ' thought experimentals' ..

 

[DarioC]

Sooo---I didn't pique any interest on Chris's part. After reading more about 1/2 spin some time ago I picked up a tennis ball and by making two distinct marks on it and studying what happens with a complex rotation I seemed to have found that there is a way of rotating that requires 720 degrees to return to the original orientation. If there is any interest in this Macro/Classical process I will go into more detail.

Likely this has been observed by others many times, but I have not read of it.
DC

 

[Chris Frisella]

Sooo---I didn't pique any interest on Chris's part. After reading more about 1/2 spin some time ago I picked up a tennis ball and by making two distinct marks on it and studying what happens with a complex rotation I seemed to have found that there is a way of rotating that requires 720 degrees to return to the original orientation. If there is any interest in this Macro/Classical process I will go into more detail.

Likely this has been observed by others many times, but I have not read of it.
DC

You did actually pique my interest :-) How does this experiment go?

 

[DarioC]

OK. You take a tennis ball and mark it on "top" with a T. Then move down 90 degrees and mark it with an S (side) with an arrow pointing "up" from the top of the S.
My thought is that when the ball has the T up it is not the same status as when the T is on the bottom.

If you rotate the S around the ball (360 degrees) and at the same time move the T down 180 degrees to the bottom you will have a status that is not the same as when the T was on "top". The S arrow will be pointing down.

Then you rotate the ball 360 degrees, in the same direction, according to the S again, while bringing the T back to the top (90 degrees), you will have returned to the original status and it has taken 720 degrees of rotation of the S marker.

I appears that the rotation of the S marker is in the same plane for both rotations, though it is tricky and may not be. It is close at least. You can decide.

The easiest (only?) way to do this in practice, without going wacko, is to place the ball on a round hollow cylinder, like a metal ring, that will hold it in position when you are moving it around. I use a shot glass.

Does this have anything to do with 1/2 spin? Well, it fits the simplified definition given by Stephen Hawking.

It definitely is interesting, and fun.

An Edit: Hint-- with the S facing you, start the angle of rotation of the S at about 30 to 45 degrees up and to the right.

DC

 

[Chris Frisella]

Cool. That's like some rubix-cube action.

 

[DarioC]

Except that this is a continuous movement at one rotating angle rather than the step movement of say one rotation up and one rotation around of the rubix -cube.
Otherwise it would not have even a slight significance of coincidence to this subject.

Are you going to try the "experiment?"

 

[Chris Frisella]

Except that this is a continuous movement at one rotating angle rather than the step movement of say one rotation up and one rotation around of the rubix -cube.
Otherwise it would not have even a slight significance of coincidence to this subject.

Are you going to try the "experiment?"

True! In the absence of a ball to hand I have been doing it in my mind. It's interesting. I should get a real ball too.

 

[SirAlbertEinstein]

Maybe the physical analog is a rotation with a simultaneous precession, alluded to in some of the earlier answers. Which reminds me of what a professor told my class once about an electron in an MRI machine. For example, the MRI machine flips the electron from spin up to spin down, but it doesn't just flip, it rotates, basically, around two axes until it is spin down. (Imagine an arrow pointing up). But then again, after it's done rotating, it, theoretically, isn't back to the original state, as now it's flipped. But someone said earlier this isn't observable, and doesn't matter I guess. Or it does, who knows.