Description of Electron spin

[Wolframthejam]

Homework Statement

Can someone tell me if the spin on an electron can change orientation as it flits around in our universe? Is the spin confined to specific orientations. or can it the axis shift around in a continuum? For entangled particles, is the spin locked into a specific orientation for each particle, or can it shift around? Thanks!

Homework Equations

The Attempt at a Solution

 

[Mindscrape]

The spin isn't in an orientation until you collapse the wavefunction by measuring it. The axis is arbitrary, physicists usually pick spin to be "along z," but that's really just saying you pick the local coordinates as such. Even with entangled particles, the spin is still just a wavefunction, though the two wavefunctions are linked together.

 

[Wolframthejam]

Thanks!

If a beam of electrons is subjected to a magnetic field, will they individually diverge in many directions on account of their undefined spin orientations that are collapsed by "measuring" with the magnetic field? Are these divergencies a continuum of angles?

Also, consider two missing electrons in the outermost s shell of an atom that has been ionized. When two electrons return to the s shell to restore the atom's neutral charge, they will have opposite spins. How are two electrons "selected" to fill the s shell from a number of electrons with undefined spins? Will any two electrons do- the interaction with the +2 ionized atom will cause the two electrons to assume spins that are opposite?

Finally, do you believe that atoms could be stable if electron spins were not paired up- i.e. is spin a necessary property in the way electrons interact with the nucleus while orbiting to keep atoms stable?

 

[Mindscrape]

Just putting a magnetic field in doesn't collapse the wavefunction. The classic experiment that actually detected spin was similar to what you mentioned, the Stern-Gerlach experiment.

The electrons have to follow the selections rules. I don't understand your second question.

Many atoms don't have paired up spins, and are stable. However, the Pauli exclusion principle says that 2 electron spins in the same state (same n and l) cannot occupy the same spins (they are fermions after all), so they "pair" for up and down.

If you do research on Stern-Gerlach, selection rules, and Pauli exclusion principle you'll find more elaborate answers that are appropriate to your level (I have no idea what level of explanation you're looking for).

 

[Wolframthejam]

Thanks again for the quick response. I'm writing a book and in one chapter I want to convey the concept of electron spin within the context of quantum considerations in a qualitative way- no math. I did the research you recommended. I know you physics guys tend to be perfectionists, so I just wanted to briefly point out that two electron spins within the same n and l level actually do have the same spins if the ml levels are not filled. According to a chemistry textbook, the p, d, l and further orbitals are first populated with parallel spins until each ml level has one electron, then the anti-parallel spins are paired up in each ml level. Experiments have shown that this results in the lowest energy state for each given configuration. Why would the fact that electrons are fermions predicate the spin-up, spin down pairing as you mentioned?

Let me elaborate on the atom question. Consider Magnesium with two electrons in the outer 3s shell with opposite spins. Imagine these electrons are removed and jettisoned to the far corners of the universe. The resulting Magnesium 2+ ion now restores its neutral charge by picking up two other electrons. Can you explain the process by which the two electrons wind up being exactly opposite spins? Why would one electron not have, say, spin that has an axis that is 165 degrees off from the other one? Does the atom collapse the wave function of each electron and somehow force opposite spin? Or does the electron know how to collapse just right?

What would happen if the spin of one electron is determined by collapsing its wavefunction and then shot into an ion trap containing the 2+ Magnesium ion. Then the spin of another electron is determined to be non-opposite to the first electron and then also shot into the ion trap. Would the Magnesium atom re-orient the spins as needed and incorporate both electrons into its outer shell?

Consider a filled p shell of any atom with 3 pairs of electrons. Is the axis of spin in one pair of electrons exactly the same as in the other two pairs? Or could one pair of electrons have an axis of spin that might be off by 70 degrees from another pair- the only criteria is that each pair has opposite spin?

Thanks for conveying your insight.

 

[Mindscrape]

I'll try to answer as much as I can, as accurately as I can (but I'm starting to stretch my knowledge going into physical chemistry territory -- someone may very well come in and knowledge slap me). Your chemistry book is, in general, correct that the p, d, l orbitals fill with arbitrary spins until all the spins are filled, and then the other "anti-parallel" spins come in. The only reason I say in general is because there may be a couple exceptions, I can't remember either way, to this rule. You see, it all has to do with what configuration gives the lowest ground state energy. This order of filling is this way so that the ground state energy is the lowest. The bit about fermions comes into play because once all the p,l,d,etc. shells are filled with spin states, it is still more favorable to continue filling the ml levels than to add another n level (sorry for mixing quantum numbers, but didn't want s to get confused with spin). However, as a fact of nature, fermions (which electrons fall into the category of) do not share the same energy states. As such, the additional electrons filling the atomic "orbitals" have to pair in an opposite spin.

Something to get at your second question is that the spins of electrons aren't physical spins as you may be thinking of them. Electrons are point charges, so you have to be careful you think of giving them a direction. Really, the electrons are just filling intrinsic states, and the multiplicity of spin for an electron is 1/2, which means it can either be +1/2 or -1/2 state.

For your 3rd question, what's to say the magnesium ion takes the electron you shot into the trap? Furthermore, are you continuously monitoring the spin of the electron you shoot in? If not, the electron can go back to following its eigenvalues, its probability.

Maybe someone more expert than I can fill in the gaps.

 

[Wolframthejam]

OK. I think I get it. Here's the way I'll probably state it in my book:
It is better to visualize the fundamental particles as waves- that's the reason why Schroedinger's equation is called a wave function. When the wave function collapses, it becomes a particle. Particles have arbitrary spins when they are in the wave state. The axis of spin can be in any direction. A measurement of spin will yield a component of spin that is either up or down with respect to the axis of the measuring device. It is unknown how the spin of an electron winds up being oriented correctly in atoms. Isolated particles whose wave function collapses will soon return to their wave state and become more and more spread out in space per Schroedinger's wave function. However, when electrons attach to atoms, their wave function is much more compact and stays that way. Interesting that these building blocks of reality assume more precise form when atoms are assembled, but I speculate that they still require some measure of indistinctness (electron cloud) for the atom to remain stable.

Thanks for your help- let me know if I need to fix up anything I wrote above.

 

[Mindscrape]

-The Schrodinger equation really is a diffusion equation, not a wave equation. One time derivative makes a big difference between wave phenomena and diffusion phenomena. Of couse, we can get "wave" solutions to the Schrodinger equation, i.e. infinite well, but the form follows diffusion. You even talk about how a collapsed wave diffuses after its measurement.
-A particle is always a particle. When you collapse the wave function the particle simply collapses to one of its probable states. It's not like it suddenly goes from not being a particle to being a particle. It's always been a particle, it's just a particle with a measurable value, of many possible measurable values, when the wavefunction collapse.
Aside: Young's double slit experiment demonstrating particle-wave duality is not an accurate story in my opinion. There's always been a question about light being a wave. In fact, Newton kind of set us back because he was so much in favor of light being a particle that the wave ideas were put on hold until Fresnel re-ignited the wave concept.

 

[Wolframthejam]

Thanks! Can particles with no spin become entangled? Are there any experimental results confirming this?