Spin Explained for the "Wikipedia Physicist" - No QM Needed!

[Char. Limit]

What is Planck-close, though? Are you talking about h?

 

[apeiron]

What is Planck-close, though? Are you talking about h?

Yes, I did mean Planck-scale, so values yo-yoing around that limit on locatedness.

 

[Char. Limit]

Heisenberg said you can't exactly locate anything. Thus, the electron's position is a permanent unknown.

 

[alxm]

Heisenberg said you can't exactly locate anything. Thus, the electron's position is a permanent unknown.

That's a misstatement of the uncertainty principle. And what's it got to do with the topic?

 

[Char. Limit]

A poster was talking about the position of the electron... ah, never mind. I even forgot to consider "and momentum" in my reasoning. I think I'm not thinking well at 12:30 A.M.

 

[peteratcam]

Just my two cents:

Spin is intrinsic angular momentum - in some regards a completely classical concept, although very hard to imagine because it is very unfamiliar in the classical context. (For the experts, nothing prevents you doing a classical field theory with dirac spinor fields - the representation structure of the Poincare symmetry is the same as ever)

Because the world is quantum mechanical, the possible values of this intrinsic angular momentum are quantised. The quantisation structure is as follows:
The total intrinsic angular momentum squared is always found to be s(s+1)\hbar^2. (hbar has units of angular momentum) where the value of s depends on which particle you are studying, but is always an integer or half integer.
For the electron, proton, neutron, s = 1/2. People will say 'the electron is spin 1/2' which means, the total intrinsic angular momentum is
\hbar\sqrt{\frac{1}{2}(\frac{1}{2}+1)}
Obviously it is easier to refer the the value 's', and just say spin 1/2 (since physicists always know how to relate the value of 's' back to the measured angular momentum). The value 's' is called the spin quantum number.

(A good quantum number is a symbol (not necessarily a number) which labels quantum mechanical stationary states according to the value of a conserved quantity).

Charge is also a quantum number, but it is complicated to explain why.

If something has a 'magnetic moment' it means it behaves like a tiny bar magnet. If you know about solenoids, hopefully you'll remember that when charge moves in a circle, it creates a magnetic field - when a charge has some angular momentum it creates a magnetic field.

It's not obvious, but this property is true of intrinsic angular momentum also. The intrinsic angular momentum of the electron creates a magnetic field - the magnetic moment of the electron.

In general, there will be some relation between the intrinsic angular momentum of some particle, and the magnetic moment it has, but this is complicated to work out. The relation is the g-factor.

 

[Char. Limit]

This also explains it to me very well. Thanks.

The property is true of intrinsic angular momentum because the particle itself has a charge, right?

 

[dextercioby]

Just my two cents:

Spin is intrinsic angular momentum - in some regards a completely classical concept, although very hard to imagine because it is very unfamiliar in the classical context. (For the experts, nothing prevents you doing a classical field theory with dirac spinor fields - the representation structure of the Poincare symmetry is the same as ever)

There's no reason to talk of spin in the context of classical physics. Of all the fields we know, only 2 (em and gravitational) have a classic-level existence (they are the only interactions with infinite range). They're interaction fields to be more precise.

If you apply the Noether theorem to the e-m Lagrangian for the restricted Lorentz invariance, you get the angular momentum tensor composed of 2 parts: the orbital one and the "intrinsic" one. The "intrinsic" can be thought of "spin" only when discussing the quantization of the e-m field. Without the quantization, one doesn't have the <particle> interpretation any classical field (as I said above, there are only 2 classical fields altogether), thus can't talk about the spin of a particle, or total spin of a system of particles.

As I said in another thread, there's no spin outside flat space relativity, there's no spin outside quantum mechanics.

 

[alxm]

The property is true of intrinsic angular momentum because the particle itself has a charge, right?

No, charge is a separate property. Neutrons have no charge and half spin. So do neutrinos. Photons have no charge and integer spin.

 

[peteratcam]

This also explains it to me very well. Thanks.

The property is true of intrinsic angular momentum because the particle itself has a charge, right?

I think this is the state of affairs, although high energy physics is not my thing, so I hope someone will correct me if they know otherwise:
If a particle has charge, and has spin, then it will have a magnetic moment.
If a particle has charge and no spin, then it will not have a magnetic moment.
If a particle has no charge, but does have spin, then it might have a magnetic moment.

 

[peteratcam]

There's no reason to talk of spin in the context of classical physics. Of all the fields we know, only 2 (em and gravitational) have a classic-level existence (they are the only interactions with infinite range). They're interaction fields to be more precise.

As I said in another thread, there's no spin outside flat space relativity, there's no spin outside quantum mechanics.

In the context of classical physics, I agree. But in the context of understanding classical field theory in Minkowski space (which in principle, a mathematician in 1905 might have done, well before the Stern-Gerlach experiment), then the spinor representations of the Lorentz symmetry are still interesting.

 

[Char. Limit]

No, charge is a separate property. Neutrons have no charge and half spin. So do neutrinos. Photons have no charge and integer spin.

What I mean is that if a charged object is spinning, it exerts a magnetic field, right? So an electron with angular momentum would have a magnetic moment, because it is charged.

Does a neutron have a magnetic moment?

 

[watcher]

I don't understand electron spin. What is it? Does spin have units? Does it do anything like electric charge or gravitation does? What does it represent? Any help for a "wikipedia physicist" (as I call myself) would really help. Just keep in mind: I haven't taken a class in QM.

according to milo wolff. in an all wave model, electron spin is as a spherical rotation...

http://www.youtube.com/watch?v=uKrM...2E390874&playnext=1&playnext_from=PL&index=42


Spherical Rotation

Rotation of the inward quantum wave at the center to become an outward wave is an absolute requirement to form a particle structure. Rotation in space has conditions. Any mechanism that rotates (to creates the quantum "spin") must not destroy the continuity of the space. The curvilinear coordinates of the space near the particle must participate in the motion of the particle. Fortunately, nature has provided a way - known as spherical rotation - a unique property of 3-D space. In mathematical terms this mechanism, according to the group theory of 3-D space, is described by stating that the allowed motions must be represented by the SU(2) group algebra which concerns simply-connected geometries.

Spherical rotation is an astonishing property of 3-D space. It permits an object structured of space to rotate about any axis without rupturing the coordinates of space. After two turns, space regains its original configuration. This property allows the electron to retain spherical symmetry while imparting a quantized "spin" along an arbitrary axis as the inward waves converge to the center, rotate with a phase shift to become the outward wave, and continually repeat the cycle.

The required phase shift is a 180o rotation that changes inward wave amplitudes to become those of the outward wave. There are only two possible directions of rotation, CW or CCW. One choice is an electron with spin of +h/4pi, and the other is the positron with spin of -h/4pi.

It is an awesome thought that if 3-D space did not have this geometric property of spherical rotation, particles and matter as we know them could not exist.

 

[ytuab]

according to milo wolff. in an all wave model, electron spin is as a spherical rotation...

http://www.youtube.com/watch?v=uKrM...2E390874&playnext=1&playnext_from=PL&index=42

Spherical Rotation

Rotation of the inward quantum wave at the center to become an outward wave is an absolute requirement to form a particle structure. Rotation in space has conditions. Any mechanism that rotates (to creates the quantum "spin") must not destroy the continuity of the space. The curvilinear coordinates of the space near the particle must participate in the motion of the particle. Fortunately, nature has provided a way - known as spherical rotation -
After two turns, space regains its original configuration. This property allows the electron to retain spherical symmetry while imparting a quantized "spin" along an arbitrary axis as the inward waves converge to the center, rotate with a phase shift to become the outward wave, and continually repeat the cycle.

The required phase shift is a 180o rotation that changes inward wave amplitudes to become those of the outward wave.
It is an awesome thought that if 3-D space did not have this geometric property of spherical rotation, particles and matter as we know them could not exist.

I think it is quite natural for us to dream of a real particle and a real spinning of the electron. (These are inseparable.)
Your statement is very interesting, but I'm afraid it is imposibble to treat the spin as a real spinning in the quantum mechanics(QM).

You said the electron spin is "a spherical rotation". But how fast is the electron rotating(spinning) ?

Foundations of Quantum Physics by Charles E.Burkhardt (in page 264)
------------------------------
They imagined that the electron is a spherical shell having total charge e uniformly smeared over its surface, reminiscent of the model used to derive the classical radius of the electron in Section 1.2.5.
This spinning sphere creates a magnetic moment identical with that of a bar magnet.
Is this model consistent with the classical radius of the electron? No-- as can be seen by
equating the angular momentum of the spinning sphere to 1/2 hbar. Solving for the speed of a point on the sphere leads to a speed that is roughly 100 times the speed of light.
--------------------------------

So If the spinning speed does not exceed the speed of light, the electron must be 100 times bigger than the classical radius size(2.8 x 10^-15 m) or an proton (10^-15 m).

But of course, by the scattering experiment or the fact of the electron capture, the electron size must be much smaller than that. (In any state and any process, the electron always has spin 1/2, doesn't it?)

And in your model, after two turn, suddenly the electron field seems to regain its original configuration by returning the fully-twisted field to the untwisted original field artificially. This does not seem to be changing continuously like e^{i\phi/2} . Is this contradictry to the experimental results of rotating the spinning neutron in this thread ?

Do I misunderstand something?

I think if we can consider an electron as a real particle with real spinning in QM, we could have already done this a long time ago (in 1920's ~1930's). If you use some "new instruments" which could not be made at that time, this is a different matter.

 

[Fredrik]

according to milo wolff. in an all wave model, electron spin is as a spherical rotation...
...
Spherical rotation is an astonishing property of 3-D space. It permits an object structured of space to rotate about any axis without rupturing the coordinates of space. After two turns, space regains its original configuration. This property allows the electron to retain spherical symmetry while imparting a quantized "spin" along an arbitrary axis as the inward waves converge to the center, rotate with a phase shift to become the outward wave, and continually repeat the cycle.

You should be more careful about what sources you're referring to at Physics Forums. This Milo Wolff doesn't seem to be an actual physicist, and more importantly, he doesn't seem to publish in peer reviewed journals. Also, the things you said about electron spin and rotations are very misleading.

 

[Naty1]

Nobody knows EXACTLY whan quantum mechanical spin is, anymore than we know exactly what "charge" is...both do have real world macroscopic effects we can observe/measure. In general spin is a degree of freedom of a particle. The polarization of light is a physical manifestation of quantum mechanical spin.

Roger Penrose notes:

Photons are indeed particles that possesses spin, but being massless, their spin behaves in a way that is a little different from the more usual spin of a massive particle (electron or proton) as necessarily spinning about its direction of motion.

From his book, THE ROAD TO REALITY, where he also goes into a lot of math related to spin ...too much of which is over my head...

 

[watcher]

I think it is quite natural for us to dream of a real particle and a real spinning of the electron. (These are inseparable.)
Your statement is very interesting, but I'm afraid it is imposibble to treat the spin as a real spinning in the quantum mechanics(QM).

what do you mean by real? you probably meant non-classical spin.

You said the electron spin is "a spherical rotation". But how fast is the electron rotating(spinning) ?

sorry if my post mislead you. let me try again.
space is what rotates in a spherical way. spin is the result of phase shift ( from up spin to down spin, vv) due to the meeting of the so called advanced and retarded emf waves (feynman),
the electron is the particle effect at the center of these waves or the amplitude of these quantum waves.

I think if we can consider an electron as a real particle with real spinning in QM, we could have already done this a long time ago (in 1920's ~1930's). If you use some "new instruments" which could not be made at that time, this is a different matter.

yes i think it is misleading to think of electron spin as a classical spin, that is a spinning spherical particle. but i thought i mentioned that the model i am referring is an all wave model as proposed by Schrödinger. whereas the particle does not spin but space spins and in turn "create" a particle ...

During this period Schrödinger turned from mainstream quantum mechanics' definition of wave-particle duality and promoted the wave idea alone causing much controversy. - wiki


The particle can only appear as a limited region in space in which the field strength or the energy density are particularly high. (Albert Einstein, Metaphysics of Relativity, 1950)

.

 

[watcher]

You should be more careful about what sources you're referring to at Physics Forums. This Milo Wolff doesn't seem to be an actual physicist, and more importantly, he doesn't seem to publish in peer reviewed journals. Also, the things you said about electron spin and rotations are very misleading.

fredrick and folks,

i don't like to appear like i am pitching for milo but his biography is in the internet, judge for yourselves if his "not so mainstream science idea of all wave model of matter" is not worthy of physics forum.

perhaps my reply to ytuab clarify some of the confusion.

 

[Fredrik]

i don't like to appear like i am pitching for milo but his biography is in the internet, judge for yourselves if his "not so mainstream science idea of all wave model of matter" is not worthy of physics forum.

I sympathize with this to some degree, but the policy here at PF is to only discuss things that have already been judged, by well-known and respected science journals. So this is actually against the forum rules. The James Randi Educational Foundation has a good forum for those who want to discuss material that isn't allowed here.

 

[watcher]

I sympathize with this to some degree, but the policy here at PF is to only discuss things that have already been judged, by well-known and respected science journals. So this is actually against the forum rules. The James Randi Educational Foundation has a good forum for those who want to discuss material that isn't allowed here.

understood

 

[ytuab]

sorry if my post mislead you. let me try again.
space is what rotates in a spherical way. spin is the result of phase shift ( from up spin to down spin, vv) due to the meeting of the so called advanced and retarded emf waves (feynman),
the electron is the particle effect at the center of these waves or the amplitude of these quantum waves.

During this period Schrödinger turned from mainstream quantum mechanics' definition of wave-particle duality and promoted the wave idea alone causing much controversy. - wiki

The particle can only appear as a limited region in space in which the field strength or the energy density are particularly high. (Albert Einstein, Metaphysics of Relativity, 1950)

I have seen some comments in which the spin is caused by the waves around the electron.
But it is difficult, I think.

The electron also has the charge.
To create the spin magnetic moment of the electron (for example, in hydrogen) the charge of one electron of the hydrogen must be spreading over the very large space, if it actually rotates. (due to spin g-factor = 2)

Of course, the EM fields can not cause this spin magnetic moment because the EM fields has spin 1 (not 1/2).

If the charge of one electron is so spreading over, when the electron was captured by the nucleus, suddenly all this charge was taken into the nucleus?

 

[passingthru]

A study of particle physics reveals that electrons have internal structure, if I understand it correctly, and that's a big if, three quarks. I don't know anything about how the quarks are coupled inside the electron. The classical concept of angular momentum of a rotating bead is the simplest way of visualizing it, with more and more sophisticated explanations growing out of continued research and very hard work. A study of quantum mechanics in an introductory course suggests that mass particles are more like standing waves in an organ pipe, than the hard little spheres we are used to picturing in our minds. Spin that, and it might be kind of like spinning a water balloon. I don't know for sure, but I really appreciate all the thought that has gone into all these explanations. Thank you for helping.

 

[Vanadium 50]

I think you are misunderstanding something. There are no quarks inside an electron, and to the extent of our ability to measure, an electron seems to have no substructure.

 

[DrChinese]

A study of particle physics reveals that electrons have internal structure, if I understand it correctly, and that's a big if, three quarks.

As Vanadium50 says: You are referring to the proton, rather than the electron.

 

[planck42]

In Dr. Stephen Hawking's famous book A Brief History of Time, he defines spin as the reciprocal of the number of revolutions of an image necessary for that image to look identical to itself e.g. keyboards have a "spin" of 1, a clean sheet of paper has a "spin" of 2, etc. The intent of the book was merely to encourage interest in physics, and not to explain advanced concepts to significant depth, so it is possible that Dr. Hawking butchered the details intentionally.

 

[Galap]

OK, I think I might be getting a (very) basic idea now. One thing confuses me though: how can electron "spin" be synonymous with charge, if an electron has one possible value for charge, and two for "spin"?

Also, in the equation for the post above, what are those strange | and > symbols?

One good way of thinking of spin up and spin down particles is to think of them as mirror images of each other. a +1/2 spin electron will be itentical to a -1/2 spin electron, except it is a 'mirror image' of sorts.

 

[haael]

I have a question: what is the relationship between "standard" spin (say, electron has spin 1/2, photon has 1) and tensor-like approach, where electron is a spinor and photon is a vector? Why do spinors yield 1/2 and vectors give 1?

Also, how spin number translates into vector direction? Photons, as vectors, point into some direction, right? I thought that spin states -1, 0, 1 are "base vectors", but the numbers don't quite match.

 

[conway]

Also, how spin number translates into vector direction? Photons, as vectors, point into some direction, right? I thought that spin states -1, 0, 1 are "base vectors", but the numbers don't quite match.

The three spin states are all along the z axis, but you can transform the basis so you get them along the x,y, and z axes. Maybe the best way to see this is to think about the way you see p orbitals (spin 1) of hydrogen drawn in textbooks. The chemists tend to use the vector representation with three dumbbells oriented along the three axes. The physicists use the z-axes symmetry with two swirling clouds and one dumbbell.

Notice that the swirling clouds have a complex phase and maybe you can see that if you add together the physicists +1 and -1 states you get the chemists "vector state" along the x or y-axis (depending if you add or subtract).

CRANK ALERT: I am a crank.

 

[haael]

Notice that the swirling clouds have a complex phase and maybe you can see that if you add together the physicists +1 and -1 states you get the chemists "vector state" along the x or y-axis (depending if you add or subtract).

OK, thanks, but what about spin 2 tensors? There are 9 numbers that build up a tensor, but only 5 spin states.

BTW, happy Easter :).

 

[conway]

The nine tensors correspond in my picture to the nine d-orbitals: a single spin-zero (with two spherical nodes), three spin-one (with a single spherical node), and five spin-two elements. You've seen the weird pictures of the electron clouds in chemistry textbooks. The peculiar thing is that these are usually shown with an implied z-axis symmetry, including the funny vertical dumbbell with the ring around the outside. I don't know if I will succede in describing in words how this lines up to the vector picture I talked about for spin-one, but I can try.

First of all, let me ask if you will agree with my picture for the p-orbitals. Let me first ignore the "physicist's" orbitals with their swirlling complex amplitudes, and concentrate on the "chemist's" orbitals, the three dumbbells aligned along the x,y, and z axis. I am going to ask you to consider what happens if we add a small component of p orbitals in any combination to the ground state, e.g:

0.955{|s&gt;} + 0.2{|p_x&gt;} + 0.2{|p_y&gt;} + 0.1|p_z&gt;

I wonder if you will agree that the effect of this superposition in, say, the hydrogen atom, is essentially to displace the ground state a small distance in the direction (2,2,1)? So basically, to a good approximation, the whole cloud just moves a little bit in that direction?

(The cloud can do more things if you allow complex values for the coefficients, but I am just thinking about the real-valued cases for now.)