I Bell's Theorem: Understanding Bell's Nonlocality and How it Applies to Photons

[jk22]

Looking at experimental results it seems that measuring Bell's nonlocality in semiconductors, ie very close (see Ansmann) lead to a smaller value than the correlation for more further configuration for example Aspect or Hensen.

Is there any study about this tendency that seems highly counterintuitive physically ?

 

[DrChinese]

Looking at experimental results it seems that measuring Bell's nonlocality in semiconductors, ie very close (see Ansmann) lead to a smaller value than the correlation for more further configuration for example Aspect or Hensen.

Is there any study about this tendency that seems highly counterintuitive physically ?

I see Ansmann for 3 articles, not sure which you are referring to. Any of these?

http://arxiv.org:443/find/nlin/1/au:+Ansmann_G/0/1/0/all/0/1

 

[jk22]

The link for Ansmann et al. is : http://www.nature.com/nature/journal/v461/n7263/full/nature08363.html

There is another experiment with efficient detection by Wineland et al. where apparently the particles are quite near too giving a value for the signal 2.25.
http://www.nature.com/nature/journal/v409/n6822/abs/409791a0.html

Whereas Aspect obtained 2.67 for photons meters apart if i remember well.

Or maybe is it that photons have a higher correlation ?

Then the Hensen et al. Experiment closing all loopholes obtained 2.46 with electrons.

Could it be that a theory that were in agreement with experiment were between quantum theory (2.82) and Lhv (2) ?

 

[DrChinese]

The raw value is not as important as its relationship to the local realistic limit. I don't really understand your point, as the Ansmann paper features violation of that limit by 244 standard deviations. Each experiment features different practical limitations and trade-offs. There is no known correlation between distance and results as the title of the thread seems to touch on.

You ask "Could it be that a theory that were in agreement with experiment were between quantum theory (2.82) and Lhv (2) ?"

Yes, that is certainly a "possibility" that a new nonlocal theory - in disagreement with quantum theory - could better explain the results of this experiment and others. However, there is currently no candidate theory of that kind to discuss which has not already been shown to have other, more serious problems. So you would need to come up with one first.

On the other hand, the experimental values are fairly easily explained as relating to imperfections and/or inefficiencies in the setup itself. And improvements in technology have regularly led to closer and closer agreement with the quantum predictions. So there really isn't a whole lot of concern at this time. That could change, of course.

 

[zonde]

The link for Ansmann et al. is : http://www.nature.com/nature/journal/v461/n7263/full/nature08363.html

There is another experiment with efficient detection by Wineland et al. where apparently the particles are quite near too giving a value for the signal 2.25.
http://www.nature.com/nature/journal/v409/n6822/abs/409791a0.html

Whereas Aspect obtained 2.67 for photons meters apart if i remember well.

Or maybe is it that photons have a higher correlation ?

Then the Hensen et al. Experiment closing all loopholes obtained 2.46 with electrons.

In Ansmann et al and Wineland et al experiments there are problems with making entangled state, keeping entangled quantum systems from changing their state and then measuring them with high accuracy. These problems are easier to overcome with photon entanglement (for photons there are other problems).
And it is sort of obvious that the most reliable setup was used for loophole free test (Hensen et al experiment) where these technical problems can be reduced most efficiently.

Could it be that a theory that were in agreement with experiment were between quantum theory (2.82) and Lhv (2) ?

From descriptions of experiments reduced Bell 'signal' approximately agrees with independently measured imperfections of setups. So there does not seem to be clear evidence for some additional factors.

 

[jk22]

(For photons there are other problems)

Speaking of that i worked a bit around it. If we consider that photon are spin 1 bosons is the singlet states $$\frac {1}{\sqrt{3}}(|+->-|00>+|-+>) $$ ? (With the table of clebsch gordan coefficients from wikipedia)

If so i thought the correlation function should be $$-\frac {2}{3}cos (\theta) $$

This leads to a very minor violation if we say it is when the quantum covariance is stronger than the classical linear covariance.

Is this one issue with photons ?

 

[vanhees71]

Again and again I can only warn to bother about photons before learning non-relativistic quantum theory and then quantum field theory. A photon cannot be described like a massive particle. It has "spin 1" but that has a different meaning for massless quantum fields. There are only two helicity eigenstates with eigenvalues $\pm 1$, which are the two polarization states (right- and left-circular polarized if you take the helicity eigenbasis). You can also take linearly polarized states as a basis say $H$ and $V$ for horizontally and vertically polarized photons (in the plane perpendicular to the momentum of the photon). In this basis the two-photon "singlet state" is given by
$$\frac{1}{\sqrt{2}} (|HV \rangle-|VH \rangle).$$