Demystifying Spin: A QM Intro to Probability & Geometry

[pivoxa15]

Can someone explain the basics of spin in the most simple terms? I have seen the formalism of it in an intro QM course but don't seem to connect how the matrices apply to reality. IN particular I am lacking a geometric view to the subject.

So if we use the z axis matrix, we will find the wavefunction hence the probability of the electron in the spin up or down state. I have heard of the possibility of being in both spin and spin down state. Is that true? But when a measurement is down, it has to be in either one. I guess that in this way, it is like the other aspects of QM as well.

What happens when we change to the x axis? The electron is still as it is but what has changed? It can only spin up or down wrt the x axis?

 

[pivoxa15]

Spin up and down are eigenstates of a measurement wrt the axis of the direction of the magnetic field. correct?

Since the operator S hat tries to measure the particle's intrinsic angular momentum. The only physical thing that can measure it is a magnetic field. So S hat wrt the x-axis refers to the magnetic field along the x axis. After the electron has passed through this field along whichever axis, intrinsic angular momentum is measured via one of two path the particle takes after encourtering the field. One path is referred to as spin up and the other is spin down.

So it seems like spin up or down is a bit of a misnomer as the electron travels after it splits up by the magnetic field perpendicular to the magnetic field. So it is not along the direction of the magnetic field. ONe could just as well call it spin 1 and spin 2.

 

[RandallB]

In SIMPLE terms the reason they call it up or down is when the electron comes into the testing device the alignment of the spin axis can be at any angle to x, y, z. but when it comes near the magnetic field it is turned flat and horizontal in line with the flat horizontal magnetic field. Once the spin axis is in that new alignment from the reference of the magnet, you can IMAGINE the particle is spinning clockwise or counter-clockwise. Or IMAGINE the front of the particle rotating up or down into the field as it plows though the field. Now like a spinning ball going into water it will drive itself UP or DOWN depending on UP or DOWN spin. (Easy to understand than which way “clockwise” is).

Pretty simple geometric view to IMAGINE really. But if you want to account for, or explain how it does this without actually spinning like the Earth rotates -- -- -- that takes eigenstate operators - - Nothing simple about that and you will need some one else to work on that issue.

 

[pivoxa15]

Now like a spinning ball going into water it will drive itself UP or DOWN depending on UP or DOWN spin. (Easy to understand than which way “clockwise” is).

Interesting, how does this work? I didn't know that.

 

[RandallB]

Interesting, how does this work? I didn't know that.

?? how does what work?? A ball into water should be easy. So is a sphere spining with sharges covering the surface as it rotates going into a magnetic field. the spin give the polar alinement that turns in line with the field and the charges turning around still must react to the field like a ball spinning into water causing it to divert up or down as I said for an electron;
SIMPLE TO IMAGINE
The hard part to remember is if the electron was really spinning to account for the real spin force that is there requires a local speed at the tangent points of the "sphere" would need to be FTL.
So if what your asking is what is it really doing - Beats me that what they call Quantum weirdness and you use QM to explain that - as I said I can't help you there.

 

[pivoxa15]

?? how does what work?? A ball into water should be easy. So is a sphere spining with sharges covering the surface as it rotates going into a magnetic field. the spin give the polar alinement that turns in line with the field and the charges turning around still must react to the field like a ball spinning into water causing it to divert up or down as I said for an electron;

That is not rigorous. I should first understand the how this classical situation work. I don't see why a ball spinning one way will be such that it falls into the water and spinning the other make it bounce out.

 

[RandallB]

That is not rigorous. I should first understand the how this classical situation work. I don't see why a ball spinning one way will be such that it falls into the water and spinning the other make it bounce out.

?? Get you head into the perspective of the experiment. Directions are not based on gravity but the path of the ball hitting a flat surface of water. Up and Down will be perpendicular to both the original path of the ball and a line on the surface that the spin axis is forced to align with. Falling, gravity, bouncing, or coming out of the water has nothing to do with it. When they do real experiments with the magnetic access turned vertically electrons move left or right – they need to define if “left” means Up or Down, it won’t mean bouncing out of the experiment.

 

[pivoxa15]

So let's think of the classic spinning ball into a tub of water. You are saying spinning one way will make the ball turn in one direction. Spinning another will make the ball spin in another direction? In both situtations, the ball will fall into the water but it will fall into the water at different directions, one verging to the left and one to the right, depending on the spin exerted on the ball?

 

[RandallB]

depending on the spin exerted on the ball?

Spin is not exerted on the ball (AKA entity, particle, and electron) the ball already has spin before encountering the water (field).
It’s a thought experiment, at least think it through and start to develop some of your own thoughts. Or get on a diving board and start pitching curve balls straight down.

Think of it as a career choice theoretical physicist or experimental physicist.

Alternative experiment; why do curve balls curve and would they in a vacuum?