What causes the electron spin collapse

[USeptim]

I have read about the Stern-Gerlach experiment in Wikipedia, this experiment proved that electron spin could only take two discrete values.

The experiment consist in sending neutral charged atoms through a inhomogeneous magnetic field so it would change the particle’s direction a quantity that would depend on the direction of the spin in relation with the magnetic field’s direction.

Before the experiment, it was thought that the magnetic field would scatter the particles in different directions in a continuous way, while the result was that the particles were only scattered in two “opposite” directions.

It also says that the experiment was done in a concatenated way changing the direction that was measured and found the [now] well known result that when you measure the spin in one direction you lose all knowledge about the particle’s spin in other previous direction.

My question is know: if the particles initially have random spin directions. What causes them to collapse in the new direction? I suspect that it’s the magnetic because although the particle must be detected in some “box”, the box where it ends it’s a consequence of the effect of the magnetic field over a well-defined spin so it must have collapsed before…

I have searched quite for the internet but I have found no evidence.

 

[UltrafastPED]

See http://en.wikipedia.org/wiki/Stern–Gerlach_experiment

There is an animation at the top, to the right.

 

[Rena Cray]

"I have read about the Stern-Gerlach experiment in Wikipedia, this experiment proved that electron spin could only take two discrete values."

Do you think this is proved, or some other conclusion can be reached? I'm most interested in your reaction to my question.

 

[Drakkith]

"I have read about the Stern-Gerlach experiment in Wikipedia, this experiment proved that electron spin could only take two discrete values."

Do you think this is proved, or some other conclusion can be reached? I'm most interested in your reaction to my question.

There is no "proof" except in math. The best we can do is say the conclusion that an electron can only take 1 of 2 discreet values has been verified time after time, and never once been invalidated by any experiment.

 

[USeptim]

See http://en.wikipedia.org/wiki/Stern–Gerlach_experiment

There is an animation at the top, to the right.

I had already seen the animation showing how quantum and classical particles behave. But muy qüestion is not that but to know when the spin wave function changes (collapses) so that it takes the value ±1/2 in the z axis.

If the spin is initially in an arbitrary direction, it can be projected to the z axis using the \sigma_{z} operator. This projection will imply a probability to take the +1/2 or -1/2 value but my qüestion is: WHAT process makes the initial spin to collapse in the new direction.

After the collapse, of course \sigma_{z} ψ= (1,0) or (0,1).

 

[UltrafastPED]

but to know when the spin wave function changes (collapses) so that it takes the value ±1/2 in the z axis.

This question shows that you have studied quantum mechanics, yes?

So in that case you should know that there is no answer to your question. All we know is that when we interrogate the detector we find definite states.

Your OP hypothesized that it was a magnetic effect; I pointed you to the animation to show you that this was definitely excluded.

If you want to explore this non-answer in more detail I suggest Feynman's Lectures on Physics, the opening chapters of book III.

This document has the table of contents and the opening lecture:
http://physics.ucsd.edu/~dcstone/teaching/2013sum2-phys2d/docs/feynmanLecturesOnPhysicsVol3Chap1-QuantumBehavior.pdf

 

[USeptim]

This question shows that you have studied quantum mechanics, yes?

So in that case you should know that there is no answer to your question. All we know is that when we interrogate the detector we find definite states.

Your OP hypothesized that it was a magnetic effect; I pointed you to the animation to show you that this was definitely excluded.

If you want to explore this non-answer in more detail I suggest Feynman's Lectures on Physics, the opening chapters of book III.

This document has the table of contents and the opening lecture:
http://physics.ucsd.edu/~dcstone/teaching/2013sum2-phys2d/docs/feynmanLecturesOnPhysicsVol3Chap1-QuantumBehavior.pdf

Thanks UltrafastPED! I have had a look to your document and I see the connection between the double slit experiment and the Stern-Gerlach experiment.

As long as the atoms or electrons are not detected, they may be passing through both ways (the one for +1/2 spin and the other for -1/2). Therefore, the magnetic field is not what collapses them!

 

[Ravi Mohan]

As long as the atoms or electrons are not detected, they may be passing through both ways (the one for +1/2 spin and the other for -1/2). Therefore, the magnetic field is not what collapses them!

After studying opening chapters, do read chapter 5. There, the Stern-Gerlach experiment is dissected in detail.
[EDIT]
Magnetic interaction does indeed collapse the state.

 

[vanhees71]

Well, the collapsing of the state is a hypothesis in some flavors of the Copenhagen interpretation of quantum mechanics. In my opinion it makes more trouble than anything else. The good thing is that it's not needed to apply quantum theory to real-world applications. You can as well use the minimal statistical interpretation, which causes much less physics head aches than collapse assumptions but some people don't like it for some philosophical implications, but here we are doing physics.

What the inhomogeneous magnetic field does is to provide an entanglement between the position of the particles and their spin state. You can make this entanglement as close to 100% as you like.

Then the preparation of a state with definite spin is simply done by absorbing all particles that do not have the wanted spin state by just bumping the unwanted particles, which are assumed to be well-enough separated in space, which can be done (in principle) at any accuracy you want.

Thus the "collapse of the wave function", if you want to call it like this, is simply filtering out the state you want. That's all. I'd not call it "collapse of the wave function" but a preparation procedure on neutral atoms through a Stern-Gerlach apparatus :-).

 

[ZapperZ]

I had already seen the animation showing how quantum and classical particles behave. But muy qüestion is not that but to know when the spin wave function changes (collapses) so that it takes the value ±1/2 in the z axis.

If the spin is initially in an arbitrary direction, it can be projected to the z axis using the \sigma_{z} operator. This projection will imply a probability to take the +1/2 or -1/2 value but my qüestion is: WHAT process makes the initial spin to collapse in the new direction.

After the collapse, of course \sigma_{z} ψ= (1,0) or (0,1).

But each of the spin quantum number has its own magnetic moment. When an external magnetic field is applied, depending on the energy of the system, there is a torque applied to each moment, resulting in the spin magnetic moment will either be aligned parallel or antiparallel to the external field. This is essentially what happens in NMR/MRI.

Zz.

 

[vanhees71]

I forgot to mention the following nice paper, giving a fully quantum-theoretical description of the SG experiment:


http://link.aps.org/doi/10.1103/PhysRevA.71.052106
http://arxiv.org/pdf/quant-ph/0409206

 

[USeptim]

After studying opening chapters, do read chapter 5. There, the Stern-Gerlach experiment is dissected in detail.
[EDIT]
Magnetic interaction does indeed collapse the state.

Thanks Ravi, in chapter 5.4 it's very well explained:

You can pass a beam of particles by three concatenated "Stern-Gerlach" device, the first with the magnetic field in Y direction and only one slit opened (for example "+"), then a field in X direction but both (or three, for 1-spin particles) slits opened, and finally another device again with the magnetic field pointing in the Z direction and only the "+" slit opened.

The result is that all the particles that passed the first device will pass the third one because the second device, having all the slits opened, has not "collapsed" the particles!

 

[UltrafastPED]

You can do something similar with light and three linear polarizers ...

 

[Ravi Mohan]

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The result is that all the particles that passed the first device will pass the third one because the second device, having all the slits opened, has not "collapsed" the particles!

This is because Feynman uses modified Stern-Gerlach apparatus (which is not being referred in original post). I would advise you to read it again and then analyse the original apparatus associating proper bras and kets.