Can you unscramble a scrambled egg?

[Swamp Thing]

Here is a fascinating article about the story of the landmark SG Experiment.

http://www.physicstoday.org/vol-56/iss-12/p53.html

There are some interesting twists to the tale, but I won't spoil them for you.

Some contemporary reactions to the results:-
http://www.physicstoday.org/vol-56/iss-12/captions/p53box1.html

Cheers,
S.T.

 

[Swamp Thing]

Question about SGE

What if we do a S-G experiment with a uniform magnetic field?

Each atom will still have to "decide" to point up or down, only we won't be able to tell them apart at the output of the apparatus because there will be no vertical deflection. Now, is this not a different situation from the input beam? At the input, (if I understand correctly) each atom is essentially "unpolarized" i.e. in a 50-50 superposition of both states. At the output, we have a 50-50 mixture where each individual atom is definitely "up" or "down".

My questions:
(a)is the above reasoning correct

(b) if so, is there an experiment that we can do to distinguish a beam that has been "combed out" by a uniform magnetic field, from a beam that has not passed through any field.

 

[NateTG]

Originally posted by Swamp Thing
What if we do a S-G experiment with a uniform magnetic field?

Each atom will still have to "decide" to point up or down, only we won't be able to tell them apart at the output of the apparatus because there will be no vertical deflection. Now, is this not a different situation from the input beam? At the input, (if I understand correctly) each atom is essentially "unpolarized" i.e. in a 50-50 superposition of both states. At the output, we have a 50-50 mixture where each individual atom is definitely "up" or "down".

My questions:
(a)is the above reasoning correct

(b) if so, is there an experiment that we can do to distinguish a beam that has been "combed out" by a uniform magnetic field, from a beam that has not passed through any field.

I'm not a QM guru, so this won't be very specific:

Let's say we have a beam of electrons that's been polarized s.t. all spins are pointing up at orientation 0. Then if we slap a detector at an angle of θ to 0, then the probability of getting an electron with spin up orientation θ is cos(θ/2)².
The probability for the other orientation from the 'combed pair' is cos((π-θ)/2)²=sin(θ/2)²
So, along any orientation, you would still get a 50-50 distribution of spins since you get .5*(sin²+cos²) probability of spin up.

So the splitting and recombining does not unscramble the electrons. In fact it scrambles them. You can do the following:

Let's say we've got a beam of electrons that is all spin-up in orientation 0. Now, if we split it into beams along orienation π/4, and then recombine it, we will get a beam with a 50-50 orientation split along spin orientation 0.

 

[NateTG]

Oh, there's a nice easy experiment for you to check this.
It takes 3 polarizing filters and a light source.

Take the two polarizing filters, and line them up so their polarization is perpendicular. You should get almost no light coming through.

Now, if you put the third filter between them, you'll get *more* light coming through from before.

Analagous experiments are , I believe, possible with birefringent materials such as calcite, which can act as a beam splitters instead of eliminating a particular polarization.

 

[Doc Al]

Originally posted by NateTG
So the splitting and recombining does not unscramble the electrons. In fact it scrambles them. You can do the following:

Let's say we've got a beam of electrons that is all spin-up in orientation 0. Now, if we split it into beams along orienation π/4, and then recombine it, we will get a beam with a 50-50 orientation split along spin orientation 0.

I'm not exactly sure what you are saying, but you can certainly recombine the exit beams of a SG magnet by putting them through a second (reversed) SG. If you can maintain the coherence of the beams, you will not be able to distinguish the final beam from the original: it will be in its original pure state. That's (part of) what's weird about this stuff.