Exploring Spin Correlation in Bells Test Experiments

[SeventhSigma]

Yeah, so if you have one detector measuring at 0 and the other measuring at 120, you'll see different charges cos^2((120-0)/2) = 25% of the time

 

[edguy99]

Yeah, so if you have one detector measuring at 0 and the other measuring at 120, you'll see different charges cos^2((120-0)/2) = 25% of the time

The sequence of post is maybe a little unclear. We start with our standard electron/positron setup and measure 100% up at one end (the electron) and 100% down at the other end (the positron).

We then turn the positron end by 120 degrees and restart the measurement.

Without touching the electron end, we still see 100% up at the electron end, but we now see 75% up at the positron end.

We then start the experiment at the electron end: The first set of measurements with the 2 detectors matched will result in 75% up at the positron end and 75% down at the electron end.

 

[SeventhSigma]

AFAIK, you can't say "We measure 100% up at one end and 100% down on the other." You will get an even split of up and down at both ends, but they'll always be opposite of one another assuming you're using the same angle. You could have 10 ups followed by 10 downs coming out the left, but then you'd also have the entangled particles coming out the other end to the tune of 10 downs followed by 10 ups.

 

[edguy99]

AFAIK, you can't say "We measure 100% up at one end and 100% down on the other." You will get an even split of up and down at both ends, but they'll always be opposite of one another assuming you're using the same angle. You could have 10 ups followed by 10 downs coming out the left, but then you'd also have the entangled particles coming out the other end to the tune of 10 downs followed by 10 ups.

The original poster has assumed that the 2 particles start out with opposite spin and that the positron is being detected down 100% of the time, hence the electron will be detected up 100% of the time (this defines the 0 measurement angle for both detectors).

 

[SeventhSigma]

I would then say that you can't make this assumption and be consistent with QM. I don't see how you can assume that you're going to get 100% up or 100% down coming out of a particular end unless you use filters (such as the lead blocks in that magnet page example), but this has nothing to say about the nature of the actual particle entanglement with respect to observations.

 

[edguy99]

I would then say that you can't make this assumption and be consistent with QM. I don't see how you can assume that you're going to get 100% up or 100% down coming out of a particular end unless you use filters (such as the lead blocks in that magnet page example), but this has nothing to say about the nature of the actual particle entanglement with respect to observations.

To quote the OP "So if I have both of my detectors at 0 degrees I will measure one spin up and the other spin down."

This is what QM predicts 100% of the time.

 

[SeventhSigma]

Yes -- if you have both detectors set to 0, you'll get opposite spins every single time. But that means you have either up/down or down/up. That doesn't mean you get all up at one detector and all down at the other. You have (afaik) a 50% chance of getting up/down and a 50% chance of getting down/up, but altogether this is 100% chance of getting one up and one down in combination.

 

[DrChinese]

AFAIK, you can't say "We measure 100% up at one end and 100% down on the other." You will get an even split of up and down at both ends, but they'll always be opposite of one another assuming you're using the same angle. You could have 10 ups followed by 10 downs coming out the left, but then you'd also have the entangled particles coming out the other end to the tune of 10 downs followed by 10 ups.

Yup.

 

[edguy99]

Yup.

So you would not agree with this for the OP setup?

At 0° - 100% measured up, 0% down
At 45° - 85% measured up, 15% down
At 90° - 50% measured up, 50% down
At 135° - 15% measured up, 85% down
At 180° - 0% measured up, 100% down
At 225° - 15% measured up, 85% down
At 270° - 50% measured up, 50% down
...
At 360° - 100% measured up, 0% down

and specifically:

At 120° - 25% measured up, 75% down
At 240° - 25% measured up, 75% down

 

[SeventhSigma]

I'd change the wording to "100% measured opposite-spin, 0% measured same-spin"

So:

At 120° - 25% measured opposite-spin, 75% measured same-spin
At 240° - 25% measured opposite-spin, 75% measured same-spin

 

[edguy99]

I'd change the wording to "100% measured opposite-spin, 0% measured same-spin"

So:

At 120° - 25% measured opposite-spin, 75% measured same-spin
At 240° - 25% measured opposite-spin, 75% measured same-spin

For context, please check the earlier posts (#36). We are talking about measurements at one end, not comparison measurments.

 

[DrChinese]

So you would not agree with this for the OP setup?

At 0° - 100% measured up, 0% down
At 45° - 85% measured up, 15% down
At 90° - 50% measured up, 50% down
At 135° - 15% measured up, 85% down
At 180° - 0% measured up, 100% down
At 225° - 15% measured up, 85% down
At 270° - 50% measured up, 50% down
...
At 360° - 100% measured up, 0% down

and specifically:

At 120° - 25% measured up, 75% down
At 240° - 25% measured up, 75% down

That the entangled stats for the subset (half) where you have A=up . Otherwise, you won't have an entangled pair.

 

[SeventhSigma]

For context, please check the earlier posts (#36). We are talking about measurements at one end, not comparison measurments.

Okay, if you're looking only at one end, then you'll see the following:

At x° (any angle) - 50% measured up, 50% down

 

[DrChinese]

For context, please check the earlier posts (#36). We are talking about measurements at one end, not comparison measurments.

Are we talking about entangled electrons? I thought that was the discussion topic, since we are on Bell tests.

 

[edguy99]

That the entangled stats for the subset (half) where you have A=up . Otherwise, you won't have an entangled pair.

The discussion assumes the particles are prepared in such as way so the positron always measures down at 0 degrees and the preparation method is never changed.

 

[SeventhSigma]

You can't control what spin a particle assumes afaik (edit: I have no idea if you actually can do this). It comes out either spin up or spin down with equal probability and you have no way of controlling this. You can control what kinds of spins are allowed to exit a detector, but this doesn't change the fact that the particle assumed that particular spin in the first place.

Even if you could change the spin by forcing it, you'd be breaking the entanglement anyway.

 

[DrChinese]

The discussion assumes the particles are prepared in such as way so the positron always measures down at 0 degrees and the preparation method is never changed.

This is not a spin entangled setup. The only way to get that is to look at the subset where your criteria is met. You cannot otherwise "force" it to be up AND entangled as to spin.

 

[DrChinese]

Entangled state, by definition, is not pure. It is a superposition of pure states.

 

[SeventhSigma]

Entangled state, by definition, is not pure. It is a superposition of pure states.

What does "a superposition of pure states" mean?

 

[DrChinese]

What does "a superposition of pure states" mean?

It can get confusing because of terminology.

Just means a combination of possible pure states: i.e. H + V. H is pure because it is known. There are 2 ways the state is called unknown: when it is in a superposition and when it is mixed. Mixed is actually an ensemble of items in pure states but is usually randomly distributed from a source.

If it is mixed or pure, it cannot be entangled on that same basis (spin for example).

A ensemble of entangled particles will be experimentally indistinguishable from mixed state UNLESS you perform matching on the entangled partner.

 

[edguy99]

You can't control what spin a particle assumes afaik (edit: I have no idea if you actually can do this). It comes out either spin up or spin down with equal probability and you have no way of controlling this. You can control what kinds of spins are allowed to exit a detector, but this doesn't change the fact that the particle assumed that particular spin in the first place.

Even if you could change the spin by forcing it, you'd be breaking the entanglement anyway.

These types of experiments are often conducted with the spin controlled and the measuring devices rotated to see the effects, especially the effects when 2 matching particles are detected. See http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205171v1.pdf" as an example of preparing entangled spin up particles (photons in this case).

 

[DrChinese]

These types of experiments are often conducted with the spin controlled and the measuring devices rotated to see the effects, especially the effects when 2 matching particles are detected. See http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205171v1.pdf" as an example of preparing entangled spin up particles (photons in this case).

Maybe you can quote something. Because it doesn't say that.

 

[edguy99]

Maybe you can quote something. Because it doesn't say that.

"To create the state | EPRi or something close to it, we adjust the parameters which determine the laser polarization. First we adjust l to equalize the coincidence counts N(0◦, 0◦) and N(90◦, 90◦). Next we set l by rotating the quartz plate about a vertical axis to maximize N(45◦, 45◦). When performing these optimizations, we typically collect a few hundred photons per point which requires an acquisition window of a few seconds."

 

[DrChinese]

"To create the state | EPRi or something close to it, we adjust the parameters which determine the laser polarization. First we adjust l to equalize the coincidence counts N(0◦, 0◦) and N(90◦, 90◦). Next we set l by rotating the quartz plate about a vertical axis to maximize N(45◦, 45◦). When performing these optimizations, we typically collect a few hundred photons per point which requires an acquisition window of a few seconds."

Yes, an EPR state is entangled. Notice the discussion of coincidences?

 

[edguy99]

Yes, an EPR state is entangled. Notice the discussion of coincidences?

Yes, they have "fixed" the orientation of the photon stream, and are rotating the two measuring devices to see the effect on the number of coincident (entangled) hits. An entangled hit is essentially when they see both detectors go off at "almost exactly" the same time.

 

[SeventhSigma]

That paragraph just talks about how they calibrated the equipment as far as I can tell -- it's not saying that they're somehow "fixing" the streams to produce certain types of spins that break the entanglements. They adjust the first parameter (the theta-l) so that N(0,0) and N(90,90) produce roughly the same output counts, and then they determine where the proper 45 degree mark is by going between those two thresholds (hence the "maximize N(45,45)" part).

Someone else can correct me if I'm wrong, here.

Nowhere in here is it implying that it's breaking entanglement by "fixing" the spins in any way. The conclusion of that paper is also consistent with what's been put forth in this thread (local realistic variables contradicted, Bell's Inequality violated, etc).

 

[DrChinese]

Yes, they have "fixed" the orientation of the photon stream, and are rotating the two measuring devices to see the effect on the number of coincident (entangled) hits. An entangled hit is essentially when they see both detectors go off at "almost exactly" the same time.

Yes, and we are looking at the subset where Alice's side is all up, which is 50% of the total stream from the PDC crystal.

The point is that the stream going to Bob consists of ones in which Alice is up, and where Alice is down. You must coincidence match to find the desired subset of Alice=up.

 

[DrChinese]

The sequence of post is maybe a little unclear. We start with our standard electron/positron setup and measure 100% up at one end (the electron) and 100% down at the other end (the positron).

We then turn the positron end by 120 degrees and restart the measurement.

Without touching the electron end, we still see 100% up at the electron end, but we now see 75% up at the positron end.

We then start the experiment at the electron end: The first set of measurements with the 2 detectors matched will result in 75% up at the positron end and 75% down at the electron end.

OK, I think I see what you are wanting to do. Let's just refer to this as the subset so it is clear. Then everything you are saying is fine. We will simply ignore the other subgroup for our discussion purposes, knowing that the "true" universe does not have this attribute.

 

[edguy99]

That paragraph just talks about how they calibrated the equipment as far as I can tell -- it's not saying that they're somehow "fixing" the streams to produce certain types of spins that break the entanglements. They adjust the first parameter (the theta-l) so that N(0,0) and N(90,90) produce roughly the same output counts, and then they determine where the proper 45 degree mark is by going between those two thresholds (hence the "maximize N(45,45)" part).

Someone else can correct me if I'm wrong, here.

Nowhere in here is it implying that it's breaking entanglement by "fixing" the spins in any way. The conclusion of that paper is also consistent with what's been put forth in this thread (local realistic variables contradicted, Bell's Inequality violated, etc).

If the photon is modeled as http://en.wikipedia.org/wiki/Polarization_(waves)" , he is setting the properties of the photons to keep the photon properties consistent throughout the experiment. This allows him to continue the experiment where the only change being made is the rotation of the measuring device. My use of the word "fix" means the properties of the particle stream are known and unchanging.

 

[edguy99]

OK, I think I see what you are wanting to do. Let's just refer to this as the subset so it is clear. Then everything you are saying is fine. We will simply ignore the other subgroup for our discussion purposes, knowing that the "true" universe does not have this attribute.

I am not sure I understand if you are agreeing or not (is there a 50% chance of us agreeing?). What probabilities would you assign to the OP question?