I Bell's Theorem: more general interactions with detector?

[Heinera]

I've made a new illustration with how one boat has a propeller that goes CW and the other CCW, and both boats sail off a waterfall making one shoot left (up) vs. right (down).

At the lower next level these two boats get into a new stream, one up and the other down; they now sail towards the other detector ... whatever box you open up first there's always an opposite on the other side.

So? There is no way such a scheme will allow you to violate Bell's inequality. Bell's theorem does not say that outcomes from a local realistic model must be completely uncorrelated. E.g, you can have a hidden variable instructing Alice's result to be up when setting is a and down when setting is a', and Bob's result to be down when setting is b and up when setting is b'. For settings (a,b) or (a',b') results would be perfectly anti-correlated, and for settings (a, b') or (a',b) they would be perfectly correlated. Bell's inequality would still not be violated.

 

[DrChinese]

I've made a new illustration with how one boat has a propeller that goes CW and the other CCW, and both boats sail off a waterfall making one shoot left (up) vs. right (down).

...

I would ask you to remove this example, or provide some suitable reference that supports it. This is not a description of anything related to linear polarization of photons, as I keep saying. It is a hypothetical model you made up and represents your misunderstanding of quantum properties. Personal speculation is not allowed here. Orbital angular momentum is something else entirely and essentially unrelated as to the example.

 

[jknm]

John Murphy here, Gill1109 pointed out this discussion to me and I thank him for that. I put it to you that I do understand Bell's theorem, and that I am not wrong about there being simple assumptions built into the model of measurement, and the logical inferences one can make from the information that is acquired from a quantum interaction. This is demonstrated by Rachel Garden in her paper "Logic, States and Quantum Probabilities" Int. Journal Theoretical Physics, 35, No. 5 1996.

 

[Mentz114]

So in quantum probability $P(a) \ne P(a)P(b) + P(a)P(-b) = P(a)(P(b)+P(-b))$ so $P(b)+P(- b) \ne 1$. ( $-b$ means 'not b').

Now that is weird.

Or as Hamlet said 'to b or not to b, that is the question'.

 

[DrChinese]

So in quantum probability $P(a) \ne P(a)P(b) + P(a)P(-b) = P(a)(P(b)+P(-b))$ so $P(b)+P(- b) \ne 1$. ( $-b$ means 'not b').

Now that is weird.

Or as Hamlet said 'to b or not to b, that is the question'.

I love it!

 

[Nugatory]

Now that is weird.
Or as Hamlet said 'to b or not to b, that is the question'.

And with tongue back out of cheek...
The point here (of course Mentz114 understands this already, but others following the thread may not) is that $b$ and $\neg b$ are the propositions "The spin along the axis not measured is +1/2" and the "spin along the axis not measured is -1/2". Those statements don't have meanings, let alone probabilities of being true that sum to unity, except in a "realistic" (in the sense of counterfactual definiteness) theory. Thus, we're just looking at another way of agreeing with the essential result of Bell's theorem: that no local realistic theory can match all the predictions of QM.

 

[Nugatory]

John Murphy here, Gill1109 pointed out this discussion to me and I thank him for that. I put it to you that I do understand Bell's theorem, and that I am not wrong about there being simple assumptions built into the model of measurement, and the logical inferences one can make from the information that is acquired from a quantum interaction. This is demonstrated by Rachel Garden in her paper "Logic, States and Quantum Probabilities" Int. Journal Theoretical Physics, 35, No. 5 1996.

But none of this has anything to do with the claims that @Michel_vdg attributed to you:
- "The Bell inequality arises because Bell included an ad-hoc assumption taken from quantum interpretations (that the wave-function represents a complete description of particle alone, and that when interacting with a passive instrument, it is like a wave encountering a passive barrier). That assumption is then used to place a constraint on the 'hidden variable' model. Bell constrained the hidden variable model so that the selection of the outcome is solely on the basis of the disposition of orientation variables (for spin/polarization measurement) internal to the particle, relative to the axis of the of the analyzer. The outcome of the interaction supposedly depends on the orientation of internal properties of the particle alone, the analyzer is required to be a passive marker.
- "The answer is stunningly simple, and idea that non-locality is required is a fallacy. This is consistent with the QM prediction that the expectation function for the density of a polarization state of a particle while interacting with a polarization analyzer, is a Cos^2(theta) curve. The spatial orientation of the expectation functions depends on the orientation of the analyzers. When this is modeled by discrete hidden variables mapping onto a suitable analyzer it is a simple task to build simulation exactly matches the statistical predictions of quantum theory."

The first of these is simply incorrect, as the the post by stevendaryl above and the discussion of Bell's $\lambda$ parameter earlier in this thread shows. The second is interesting only if someone can point to a peer-reviewed example of such a simulation. (It's easy to find non-peer-reviewed ones that contains errors that would have been caught by peer review. People who advance these to support their position just make the case that they do not understand the question).

This thread is closed - as always, PM me if you have something to add that would justify reopening.