Spin Interference: Looking for Thought Experiments with Single Electrons

[msumm]

I'm looking for a simple experiment (even if it's not practicle to implement; just a "thought experiment") that demonstrates spin interference for an electron. Some experiment that can be performed N times, each with a single electron so that after the N trials one will see some type of intereference pattern if the electron spin is not "observed" just before entering the device, otherwise no interference pattern.

Does anyone know of a good example?

 

[michael879]

yea, make a stern-gerlach device that opens into a double slit. The stern-gerlach device splits electrons based on spin, so all electrons with +1/2 spin will go through 1 slit, and the others will go through the other. If the electrons spin isn't observed, it will "go through both slits" and cause an interference pattern.

 

[msumm]

OK,thanks. Now, let's say N pairs of electrons are entangled at some position x=0 so that each electron spin can be determined from it's entangled partner. Half travel off in the +x direction, while the entangled counterparts travel off (same speed) in the -x direction. N of the interference devices you mentioned above are sitting at x=10, and N regular Stern-Gerlach devices sit at x= -10. The regular Stern-Gerlach devices may be turned all on or all off with a switch (so they can either measure the spin or not).

Isn't it true that:

1) When the regular Stern Gerlach devices are turned on, the spin of each electron (and it's entagled counterpart) are known, and therefore the collection of measurements from the N interference devices (at x=10) show no interference pattern.

2) When the regular Stern Gerlach devices are off, the spin of the electrons (and their entangled counterparts) is unknown, and therefore the N measurements from the interference device show an interference pattern.

3) From 1 and 2, someone standing at x=10 can determine (with arbitrarily high probability by increasing N) whether or not the regular Stern Gerlach devices at x=-10 were turned on?

Something must be wrong with with what I've just said, since it would lead to all sorts of contradictions (info about the switch being on or off travels an arbitrary distance faster than c). However, I can't seem to spot the problem.

Any input would be greatly appreciated.

 

[michael879]

wow that's a really cool thought experiment. I was trying to make a point similar to this in another thread but nobody really explained what was wrong with it. My example was very abstract however, unlike this. I don't see anything wrong with that either, but I am sure there is since a lot of smart people have shown that information can't travel faster than c with entanglement.

 

[michael879]

ok well I remembered the reason someone posted on my thread why this wouldn't work. However it didn't really make much sense to me. Basically putting two particles in an entangled state doesn't make each particle act like its in its own super position. Thats what I got out of the response, but that answer isn't satisfying at all to me.

 

[cesiumfrog]

2) When the regular Stern Gerlach devices are off, the spin of the electrons (and their entangled counterparts) is unknown, and therefore the N measurements from the interference device show an interference pattern.

Obviously this is false. (Obvious in the sense you've already noticed, that such an assumption leads to absurd contradictions.) Hence we can conclude that whether the regular measurement device is on or off (noting that either way, whether or not you record that information down, in both cases that information is still available in principle) there is no interference pattern. Several experiments show this conclusion is correct.

So all that remains is to try to satisfy you with a theoretical explanation. I trust you're familiar with the idea of complementarity (e.g., between different spin axes: if you know whether the result of a vertical spin measurement will be up as opposed to than down, then you cannot simultaneously know whether the result of a horizontal spin measurement will be left or right). I've recently been reading a paper (PRA 63 063803) that notes "basic complementarity between coherence and entanglement" in the mathematical theory of QM, which means that strong entanglement washes out the phase coherence that would be necessary for a visible interference pattern (remember: incoherent light sources do not interfere), and any attempt to maintain coherence will break the entanglement.

 

[michael879]

Im not trying to argue with you, because I too figured the problem was with #2, and I know that there is obviously some wrong assumption here. However, the state of two entangled electrons would be given by:
1/sqrt(2) (|0>|0> + |1>|1>)
right?

so doesn't this mean that the particle going through the double slit would be in the state 1/sqrt(2) (|0> + |1>) ?

Obviously what I just said is wrong because if its true you would observe an interference pattern. However I don't understand what's wrong with it.

 

[msumm]

cesiumfrog, I realize the conclusion should be false, what I'm asking is what is wrong with the statements. looks like yall are saying that, due to the entanglement, the electron (that enters the interference device) looses its coherence, even when the other electron is not measured. is there a description of that process somewhere, or a name for it that I could google? is it possible for entagled particles loose their coherence AND violate Bell's inequalities? something doesn't seem right about that. anyway, if i get some time i'll try to think about it a little clearer and do the math to see if I can get an understanding.

 

[cesiumfrog]

is there a description of that process somewhere

Well, you could start with the paper I quoted from (or PRA 62 043816, which they cite). Sorry, but I haven't had time to finish studying these yet myself.