Does the electron really spin 720 degrees?

[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.

 

[Mark Harder]

It seems to me that the semantics is confusing everyone but the true experts, who freely manipulate the quantum variable called 'spin' and don't particularly worry about what that term means beyond that of a certain mathematical construct in the language of Hilbert space, operators and state functions and so forth . The rest of us are scratching our heads and wondering how an object can possesses a 'spin' and not actually spin. It's a fair response, you must admit. I'm grateful to whoever, was it Glashow?, coined the term 'quark'. Better to invent a nonsense term for something that makes no sense to pedestrians like me. IMHO, if you're going to say that a quantum object has no analogy in the macroscopic world, then don't use an macroscopic analogy like spin.
Is spin an object with phase in the sense that periodic functions can differ by some fraction of their period and return to ? In particular, if the phase changes by one period, the function is indistinguishable from the original. The function can be said to be transformed by elements of a Group, which must contain a transformation, the identity element of the Group, that leaves the object in its original state. That's a classical analogy, dealing with functions and groups. The quantum equivalent would be a state vector with 'spin' whose phase is transformed by an operator. That's strictly guesswork on my part, drawn from the attempts to come to terms with the concept that I read here. Feel free to correct, politely.

Perhaps we here in PhysicsForums should have a contest to see who comes up with the best substitute for quantum "spin". First word I came up with was "luck". Any takers?

 

[vanhees71]

You don't need to rename well-established and well defined things. Gell-Mann had the right to invent a name for "quarks", because he was the one who discovered them (first thinking of them as if they were just purely mathematical auxilliary constructs, and it took Feynman to convince him and the rest of the community of their "reality" in terms of his parton model of hadrons to describe deep-inelastic scattering).

The spin is a quantum concept. You cannot describe it in any other way than with quantum theoretical means, and the most clear way is to use the analysis of the (covering of) the rotation group, SU(2).

 

[Collin237]

Spin is not analogous to classical rotation, but it's convertible with it. They are both parts of the same conserved quantity, angular momentum, which is the Noether current of rotational symmetry. This was confirmed in 1910 by Einstein and de Hass in an actual laboratory experiment in 1910, before the math now known to correctly describe spin had even been proposed!

A word like "quark", as you said, appeared through the social act of naming, so it can be attributed to (or, depending on one's tastes, blamed on) the person who coined it. But discovering a phenomenon that only much later becomes a concept, as was the case with spin, is beyond the capability of society. So a fair description of spin cannot gloss over the natural justification for calling it what it demonstrably is.

 

[rrogers]

It seems to me that "spin" in this case can be mathematically modeled by a fiber extension to a manifold and then a nontrivial connection. Is this correct and can somebody give a reference (hopefully open-source) I can read?
As a possible separate question (?): I have mused that a standard physical "image rotator" is analogous to a spin 2 system. That is, the image rotates twice as fast as the rotator; this results from a rotating axis of inversion/mirror.

 

[Collin237]

What is an "image rotator"? I googled that phrase and all I could find was ads for a gallery carousel widget. I don't think that's what you're referring to.

If you mean a rotor (a quaternion interpreted geometrically), that's what I was referring to in #52. The ratio of rotations works the other way, and gives a rotor a spin of 1/2.

 

[rrogers]

What is an "image rotator"? I googled that phrase and all I could find was ads for a gallery carousel widget. I don't think that's what you're referring to.

If you mean a rotor (a quaternion interpreted geometrically), that's what I was referring to in #52. The ratio of rotations works the other way, and gives a rotor a spin of 1/2.

If the hall monitors move this; please leave a pointer since I think the material is worth knowing. In any case, a comparison with "spin 2" theory would be interesting; or if it's irrelevant I would like to know that as well.
All of the references below have the same thing in common: imagine a tube to look through, then imagine a line across the tube that is an axis of reversal, now rotate the line of reversal. Since the line has the same effect when in the "normal" position and when it's rotated 180 degC; the image must travel twice as fast. When I understood this while working on some optics I went to the tool shed and found a solid tube of clear plastic. Sure enough when you position your eye behind the tube so that the image is reversed (say left to right) then rotating the tube causes the viewed scene to travel twice as fast.
On a more professional level:
Here is a prism type:
https://en.wikipedia.org/wiki/Schmidt–Pechan_prism
Here is a mirror references: first wikipedia quote
"In the case of two mirrors, in planes at an angle α, looking through both from the sector which is the intersection of the two halfspaces, is like looking at a version of the world rotated by an angle of 2α"
https://en.wikipedia.org/wiki/Mirror_image
Or if you are a technical masochist (like myself):
https://www.colgate.edu/portaldata/imagegallerywww/98c178dc-7e5b-4a04-b0a1-a73abf7f13d5/ImageGallery/geometric-phase-of-optical-rotators.pdf
I haven't read it yet but it looks like my understanding.

 

[rrogers]

If the hall monitors move this; please leave a pointer since I think the material is worth knowing. In any case, a comparison with "spin 2" theory would be interesting; or if it's irrelevant I would like to know that as well.
All of the references below have the same thing in common: imagine a tube to look through, then imagine a line across the tube that is an axis of reversal, now rotate the line of reversal. Since the line has the same effect when in the "normal" position and when it's rotated 180 degC; the image must travel twice as fast. When I understood this while working on some optics I went to the tool shed and found a solid tube of clear plastic. Sure enough when you position your eye behind the tube so that the image is reversed (say left to right) then rotating the tube causes the viewed scene to travel twice as fast.
On a more professional level:
Here is a prism type:
https://en.wikipedia.org/wiki/Schmidt–Pechan_prism
Here is a mirror references: first wikipedia quote
"In the case of two mirrors, in planes at an angle α, looking through both from the sector which is the intersection of the two halfspaces, is like looking at a version of the world rotated by an angle of 2α"
https://en.wikipedia.org/wiki/Mirror_image
Or if you are a technical masochist (like myself):
https://www.colgate.edu/portaldata/imagegallerywww/98c178dc-7e5b-4a04-b0a1-a73abf7f13d5/ImageGallery/geometric-phase-of-optical-rotators.pdf
I haven't read it yet but it looks like my understanding.

Actually you can model spin 1/2 by attaching an arrowhead to the reversal line that is invisible to the observer but visible to a second observer. The second observer could see the arrowhead. The second observer would say that the first observer has to rotate the line/image twice to get back to the original "state"; even though the first observer would see no difference. BTW: I think I can formulate the whole process in matrix form; but haven't done it yet.

 

[yoron]

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.

Lovely answer. One might want to add that a electron also can be defined as a 'standing wave' around some nucleus to show how, well, ridiculous it becomes to call it a equivalence to a classical spin. At least from where I look at it.

 

[vanhees71]

No, that's also not an adequate picture of an electron, which is an electron; full stop. To our present knowledge it's an elementary particle described by a quantized Dirac spinor field in the Standard Model of elementary-particle physics. You cannot say anything else about it than that. For sure it's neither a classical point particle (which always is a macroscopic object whose extension is irrelevant for the situation to describe, i.e., it's sufficient to consider only its center of momentum and in this sense idealize it to a point obeying the laws of (relativistic) classical mechanics) nor a classical wave.

 

[yoron]

Heh, depends on where you look at it from, doesn't it?
Whatever a 'electron' now might be :)