Another Gedanken Experiment

[Little Bang]

The cathode of a CRT is made from metal, probably a tungsten filament. If you heat the filament to what ever the threshold temperature is it starts emitting electrons. Then you use an electric field to accelerate the electrons toward the anode. The electrons in the filament have an orientation (static attributes) with respect to the lattice structure of the atoms that make up the filament. When the electrons leave the filament, they have no orientation (we can’t tell electron number two from number two hundred). If left in this manner the entire phosphor screen beyond the anode will glow. The electrons take all possible paths.

 

If we wish to turn the electrons into an electron beam, and I’m guessing at this, we probably use four perpendicular electric fields to pinch the electrons into a beam. At this point the only attributes here are still static. The next step as in Stern-Gerlack we send the beam of electrons between the poles of a magnet. Now to the crux of my question, as the electrons approach the magnetic field at what point does the spin attribute wave function collapse into spin-up or spin-down? Is there some attribute about an electron that makes it decide to become a spin-up or spin-down electron?

[infamous]

Is there some attribute about an electron that makes it decide to become a spin-up or spin-down electron?

There is in my mind only two answers to this question. Either the electrons balance their spins one opposed to the other so that the final result is 50% up, and 50% down, or, they bring with them a memory of their former state. I can't give you a definitive answer. One thing is certain however, and that is the electron understands a few things about it's environment and can adjust it's state of spin to find a balance.

[Little Bang]

Ok, supose we do this, we make the cathode from a single hydrogen atom and we induce it to emit it's one electron. Now this electron's only relationship, as far as we know, is to the proton that just gave it up. As this electron approaches the magnetic field where, when, and how does it know to be spin-up or spin-down?

[infamous]

Ok, supose we do this, we make the cathode from a single hydrogen atom and we induce it to emit it's one electron. Now this electron's only relationship, as far as we know, is to the proton that just gave it up. As this electron approaches the magnetic field where, when, and how does it know to be spin-up or spin-down?

My guess would be, conditions within the hydrogen atom imprinted a memory upon the electron before it left.

[Little Bang]

Are you saying that each proton has a preference for either a spin-up or spin-down? That is possible, maybe that is an attribute of protons and electrons that at present we are unaware.

[infamous]

Are you saying that each proton has a preference for either a spin-up or spin-down? That is possible, maybe that is an attribute of protons and electrons that at present we are unaware.

Check your E-mail Little Bang, I've sent you a message.

[UncleAl]

The electrons in the filament have an orientation (static attributes) with respect to the lattice structure of the atoms that make up the filament.

That's a bunch of hooie. The anode is coiled coils of tungsten filament covered with mixed alkali metal oxides for enhanced emittance. The HOMO electron density in a solid conductor's band structure looks like jellium. You are confused with a field emission micrscope.

 

The electrons take all possible paths.

No, they don't. You wouldn't see a picture if they could - and the shadow screen wouldn't fix that. The electrons in a large CRT need relativistic correction. They are well-defined particles on the scale of phosphor dots.

 

The next step as in Stern-Gerlack we send the beam of electrons between the poles of a magnet.

Gerlach. You don't know what you are talking about.

 

http://www.if.ufrgs.br/~betz/quantum/SGtext.htm

http://rugth30.phys.rug.nl/quantummechanics/stern.htm

http://hyperphysics.phy-astr.gsu.edu/hbase/spin.html

[Little Bang]

Unc, did I at any time claim that I am an expert on anything, no, and apparently you don't know what the word gedanken means, And the only joke around here is your antagonistic bad disposition.

[Qfwfq]

Uncle Al, that's not the way to help someone who asked a question.

[Qfwfq]

Spin is a quite complicated topic of QM.

 

Essentially, if a collection of electrons is at a given temperature and in a magnetic field the average numbers with spin up an spin down will be according to the Boltzmann distribution. At a very low temperature few will be against the field and most will be with it, just like a compass needle settles to point north. Because of thermal agitation they won't be always all the "right" way.

 

If there is no magnetic field, what way is up and what way is down?

 

With the thermal agitation but no magnetic field, directions are equivalent and the distribution will be uniform.

 

Once the single electron is emitted, a magnetic field is what can act as a probe to determine one of the two possibilities, given the direction of the field.

[infamous]

 

Once the single electron is emitted, a magnetic field is what can act as a probe to determine one of the two possibilities, given the direction of the field.

Is there a symmetry manifest here, that is to say, because 50% will be spin up and, 50% will be spin down? And another question which has come to mind is, what if there is an uneven number of electrons present at the beginning of the experiment? Does the odd electron have a preference for either up or down spin? And if so, do we understand why?

[Little Bang]

I know that QM is probably the most successful branch of science that humans have ever developed. But I don't understand why the scientific community seems to shy away from the measurement problem. It's almost as though they are afriad to tinker with it for fear that it might come tumbling down.

 

In the case of a single electron approaching the magnetic field there are only two possiblities, or a combination of the two. One, the electron knows that it is either spin-up or spin-down. Two the observer decides that it is either spin-up or spin-down. If the electron knows, then it has an attribute that QM doesn't know anything about. If the observer decides, then the observer has an attribute that QM doesn't want to admit to.

[Qfwfq]

Is there a symmetry manifest here, that is to say, because 50% will be spin up and, 50% will be spin down?

Yes and no.

 

If you mean symmetry in the sense of Nöther's theorem, it isn't a symmetry itself, it's a statistical distribution. However, the fact that it will be 50-50 is due to a symmetry argument; there is no priviledged direction or verse.

 

And another question which has come to mind is, what if there is an uneven number of electrons present at the beginning of the experiment? Does the odd electron have a preference for either up or down spin? And if so, do we understand why?

Which of the 2n + 1 electrons is the odd one?

 

The average will be n + 1/2. Measurement for a given, specific sample of 2n + 1 might even give n + d up and n + 1 - d down.

[Qfwfq]

But I don't understand why the scientific community seems to shy away from the measurement problem. It's almost as though they are afriad to tinker with it for fear that it might come tumbling down.

Many people do tinker with it.

 

In the case of a single electron approaching the magnetic field there are only two possiblities, or a combination of the two. One, the electron knows that it is either spin-up or spin-down. Two the observer decides that it is either spin-up or spin-down. If the electron knows, then it has an attribute that QM doesn't know anything about. If the observer decides, then the observer has an attribute that QM doesn't want to admit to.

Look up hidden variable theories.

 

Since the early 20th century people have tried all kinds of ideas. Some people draw mystical conclusions. What is certain, there are limitations on what can be known about an object.

[Little Bang]

You may be right Q, but it is very difficult for me to believe that phenomena exist that we are incapable of findind a reason for their existence. The two possibilities that I mention in my example are better than no reason at all.

[infamous]

You may be right Q, but it is very difficult for me to believe that phenomena exist that we are incapable of findind a reason for their existence. The two possibilities that I mention in my example are better than no reason at all.

You make an interesting point Little Bang. For either example you give, consciousness at some level must influence the result. Either the electron has a memory of it's former state or, the observer can by observation influence the outcome. Am I going wrong somewhere with these thoughts or are we still missing some important facts regarding these experiments.

[nkt]

Surely someone will have actually measured the spin polarisations of a bunch of randomly emitted electrons? I would think 50% and random.

 

As for the idea about a single emitting atom, and the distribution resulting, I strongly suspect it will be 50% and random.

 

Look at the way that an electron goes round an atom. It's a random path, but time averaging gives you a statistical clustering that shows where it is likely to be. The electrons that actually come off the tip are pumped in by the electrical supply, and so could be of any spin. After a fraction of a second, there will have been milions of interactions with the electrons already in orbit, and this would probably have an effect on the spins.

 

As a final point, you would need to measure the spins before they left the tip, then again afterwards, to see if they had taken a bias, changed, or not changed, or else the results would be meaningless.