Do I understand Bell's Inequality Test correctly?

[MichaelPower17]

Hi,
I've been looking at Bells inequality test.

To see if I understand it correctly I'd like to state it in my own words.

Could you please let me know of I have it right?
Thanks
Michael

We have 4 measurements, A,B,C,D
Each measurement is True or False

A is 0 degrees
B is 45 degrees
C is 25.5 degrees
D is 67.5 degrees

By splitting a photon into two smaller entwined photons we can take two of the four possible measurements on a single photon.

Question: Are the observed counts in each category determined by a hidden variable present in the photon to begin with or do the results preclude the action of a hidden variable?

Einstein said yes you had two left gloves to begin with so the results are predetermined by a hidden variable present in the photon.Bohr said you have two spinning coins that only land when observed and results are not dictated by a hidden variable.

Bell invented his inequality test based on a stastical analysis of the results.
The four measurements can be represented visually as three intersecting circles in a venn diagram.
The results for all the two intersections is known.
If the results are determined by a hidden variable it follows that the centre of the diagram ( with three inrersections) must not be greater than anyone of the areas with two intersecting sections.
That is 'the more intersections, the less results'.

Results however show that the three intesection section has more results than any of the two intersecting sections meaning that final state was not predeteined but decided at the end.

Stated another way, the results of the four measurements exhibits the following pattern,
100%, 85%, 50%, 15%
Whereas the hidden variable theory could only be supported by the linear pattern of
100%, 75%,, 50%, 25%,

This is Bells inequality. The effect can also be seen by passing light through three intersecting polarised light disks, each angled at the above angles.
The centre intersection is brighter than the surrounding two intersecting sections!

This is a problem for Einsteins General relativity as the entwined photons must instantionusly communicate the agreed final state thus exceeding the speed of light!

 

[DrChinese]

Hi,
I've been looking at Bells inequality test.

To see if I understand it correctly I'd like to state it in my own words.

Could you please let me know of I have it right?
Thanks
Michael

We have 4 measurements, A,B,C,D
Each measurement is True or False

A is 0 degrees
B is 45 degrees
C is 25.5 degrees
D is 67.5 degrees

By splitting a photon into two smaller entwined photons we can take two of the four possible measurements on a single photon.

Question: Are the observed counts in each category determined by a hidden variable present in the photon to begin with or do the results preclude the action of a hidden variable?

Einstein said yes you had two left gloves to begin with so the results are predetermined by a hidden variable present in the photon.Bohr said you have two spinning coins that only land when observed and results are not dictated by a hidden variable.

Bell invented his inequality test based on a stastical analysis of the results.
The four measurements can be represented visually as three intersecting circles in a venn diagram.
The results for all the two intersections is known.
If the results are determined by a hidden variable it follows that the centre of the diagram ( with three inrersections) must not be greater than anyone of the areas with two intersecting sections.
That is 'the more intersections, the less results'.

Results however show that the three intesection section has more results than any of the two intersecting sections meaning that final state was not predeteined but decided at the end. ...

A few items to pass along:

1. The usual term is "entangled" rather than "entwined", but I understand your meaning.

2. Entangled photons are most often created by "splitting" 1 photon into 2 using a process called "down conversion". The quantum result is a system of 2 entangled photons. Technically they cannot be considered 2 individual photons because they are not "separable" even though they seem "separated". (Yes, the language can be confusing.)

3. The analogy you describe with the intersecting filters (Venn diagrams) is not a quantum analogy. You get similar results with classical setups. I would steer clear of this way of viewing things.

4. Bell's result used 3 angles rather than 4. The one you have with 4 is called the CHSH inequality, and is a convenient way for experimentalists to run Bell tests.

What Bell did was assume that Einstein (actually EPR) was correct about hidden variables (HV) predetermining the outcomes of all possible measurements. He then showed that their HV approach could not be consistent with the statistical predictions of QM. Yes, you are correct that Venn diagrams can be drawn that appear to demonstrate the statistical idea. But the actual issue is what is called subjective realism, which is the same thing as observer dependence (also known as contextuality - again, the terms can be quite confusing). Einstein believed in objective realism, i.e. observer independence where the quantum outcome is not dependent on how the observer chooses to make a measurement.

So if there are HVs which predetermine the outcomes, Bell asks: what are their values? Turns out that even by hand picking them, you cannot reproduce the QM predicted results at most angle settings.