# Bells' Inequality Spin Violations

Gold Member

## Main Question or Discussion Point

When entangled photons are generated from a cascade of a Calciums' 6s level
this inequality : n[y+z-] + n[x-y+] ≥ n[x-z-] is derived for what is equivalent to spin in photons.
When the detectors at A and B are parallel the perfect anti correlations are due to conservation
laws of angular momentum - a total spin of zero.
When the inequality is dis proven with non parallel detector settings what happened to
the conservation law ?
Regarding Bells' inequality with electrons: When a sample is measured for 45° , 1/2 are found
to be spin up. When a sample is measured for 90° , 1/2 are spin down. But when the sample that
was measured for spin up at 45° is measured at 90° , only 15% are spin up.
How can the possibility that the magnetic field in the detector alters electron spin be distinguished from QM forbidding knowledge of mutually non commuting observables when the inequality is
dis proven ?

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This paper:www.arxiv.org/pdf/quant-ph/0407041 Correlation Function, Bells inequality and
fundamental conservation laws. Bells inequality and a theory that satisfies the fundamental conservation law violates the inequality.
Therefore - a theory of correlations satisfying Einstein locality, reality in the Einstein - Bell sense
and the validity of the fundamental conservation laws cannot be constructed.

When entangled photons are generated from a cascade of a Calciums' 6s level
this inequality : n[y+z-] + n[x-y+] ≥ n[x-z-] is derived for what is equivalent to spin in photons.
When the detectors at A and B are parallel the perfect anti correlations are due to conservation
laws of angular momentum - a total spin of zero.
When the inequality is dis proven with non parallel detector settings what happened to
the conservation law ?
Regarding Bells' inequality with electrons: When a sample is measured for 45° , 1/2 are found
to be spin up. When a sample is measured for 90° , 1/2 are spin down. But when the sample that
was measured for spin up at 45° is measured at 90° , only 15% are spin up.

How can the possibility that the magnetic field in the detector alters electron spin be distinguished from QM forbidding knowledge of mutually non commuting observables when the inequality is
dis proven ? [..]

This paper:www.arxiv.org/pdf/quant-ph/0407041 Correlation Function, Bells inequality and
fundamental conservation laws. Bells inequality and a theory that satisfies the fundamental conservation law violates the inequality. [..]
Very interesting paper!

If I understand you correctly, you ask why it is assumed that although the detector clearly interacts with the electron when it passes through, it can only act on (and not interact with) the electron spin. Indeed, that article (which was apparently reviewed) seems to ignore that in my eyes necessary option completely - it handles the measurement interaction as a "projection"!

Can anyone clarify that issue?

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stevendaryl
Staff Emeritus
Very interesting paper!

If I understand you correctly, you ask why it is assumed that although the detector clearly interacts with the electron when it passes through, it can only act on (and not interact with) the electron spin. Indeed, that article (which was apparently reviewed) seems to ignore that in my eyes necessary option completely - it handles the measurement interaction as a "projection"!

Can anyone clarify that issue?
I think you're right. One could imagine that there is angular momentum transferred between the particle and the detector. In that case, looking at the spin of the particles alone would not be sufficient to account for all the angular momentum. So there would be no reason for particle spins to add up to zero after interacting with the detector. So I agree that the correlation doesn't follow from angular momentum conservation alone.

stevendaryl
Staff Emeritus
I think you're right. One could imagine that there is angular momentum transferred between the particle and the detector. In that case, looking at the spin of the particles alone would not be sufficient to account for all the angular momentum. So there would be no reason for particle spins to add up to zero after interacting with the detector. So I agree that the correlation doesn't follow from angular momentum conservation alone.
Actually, now I'm not sure. The interaction with the detector would mean that you don't have conservation of momentum for just the particles, but maybe when you take AVERAGES, the effect of the detectors should average to zero?

Actually, now I'm not sure. The interaction with the detector would mean that you don't have conservation of momentum for just the particles, but maybe when you take AVERAGES, the effect of the detectors should average to zero?
Maybe it should, according to classical theory. But that's I think another issue than the one that the paper addresses: Unnikrishnan claims in the summary that 'any theory of correlations of such discrete variables satisfying the fundamental conservation law of angular momentum violates the Bell’s inequalities'.
And more clearly in the body text:
'a physical system with discrete observable values can show correlations different from what
is predicted by quantum mechanics only by violating a fundamental conservation law!'.

In view of Morrobay's pertinent question, I don't see how that follows from that paper.