Bell's Theorem: more general interactions with detector?

[Nugatory]

I guess this quote from Murphy explains it best:

The PhysicsForum rules require that sources be properly cited, and "this quote from Murphy" is not a proper citation. We are going to have to ask you to provide more information about where it came from.

 

[Michel_vdg]

The PhysicsForum rules require that sources be properly cited, and "this quote from Murphy" is not a proper citation. We are going to have to ask you to provide more information about where it came from.

Alright, besides that I guess you do agree with what was said by the author (Wayne Myrvold) that Gill linked to where he said that: 'One should not take for granted that every sort of non-locality involves spooky action at a distance'. Which is for me the most important thing I would like to know, namely if the door is still open to have possibly in the future a complementary theory to QM that doesn't need 'action at a distance', maybe something that is based on a kind of superfluid.

 

[Nugatory]

Which is for me the most important thing I would like to know, namely if the door is still open to have possibly in the future a complementary theory to QM that doesn't need 'action at a distance',

Hmmm... You may have been wrestling with a straw man all along... Bell's theorem says that quantum mechanical predictions cannot be produced by a local realistic hidden variable theory. That's not the same thing as saying that quantum mechanics requires action at a distance, at least as the phrase is usually understood.

maybe something that is based on a kind of superfluid.

That's not discussing physics, that's something between throwing out sciency-sounding words and speculation... Neither activity is allowed under the Physics Forums rules.

 

[Michel_vdg]

Hmmm... You may have been wrestling with a straw man all along... Bell's theorem says that quantum mechanical predictions cannot be produced by a local realistic hidden variable theory. That's not the same thing as saying that quantum mechanics requires action at a distance, at least as the phrase is usually understood.

Ok.

That's not discussing physics, that's something between throwing out sciency-sounding words and speculation... Neither activity is allowed under the Physics Forums rules.

Yes of course that is speculation but it wasn't my intention to talk about something specific, my interest was only to know if there are still some openings to try an idea (superfluid - local). The reason for jumping into this discussion about Bell's theorem was because I ran into an argument with a mathematician and he dismissed the idea because Bell's Theorem should rule it out. I'm pasting here his argumentation:

The "non-locality" I'm talking about is much worse than the pilot wave of the drop.

1. a "classical mechanics" theory is defined as anything with a fixed spacetime background (x,y,z, time) on which fields (like fluids) and particles move. That is, particles have a definite position as a function of time.
2. a "classical" theory also includes things based on general and special relativity (so gravity and electrodynamics).
3. a "local" classical theory means that the instantaneous motion of a particle or point in a field depends only on the history of the field in the point's light-cone. That means that information travels only at the speed of light or slower.
4. Bell's theorem proves that any theory which is both "local" and "classical" will directly contradict observations of quantum mechanics.

So if you have some local classical theory whose goal is to be an underlying theory of the universe, you directly contradict observations of quantum mechanics. So, when you talk about particles in a fluid or things like that, I'm forced to conclude you're not talking about this universe!

Pilot wave theory works because the motion of a particle depends explicitly on the configuration of the entire universe. If communication wasn't instantaneous, but instead was like the water droplet bouncing, then there would be measurable departures from the predictions of quantum mechanics.

So it's not interesting to me precisely because I don't think it's true that one can "model and simulate elementary particles and gravity" using anything resembling what you are suggesting.

 

[Nugatory]

The reason for jumping into this discussion about Bell's theorem was because I ran into an argument with a mathematician and he dismissed the idea because Bell's Theorem should rule it out.

Seems like his argument is pretty compelling to me...

Bell's theorem says that any theory in which the result of a measurement on one particle can be calculated from what we know about the two particles and what we know about the measuring device (settings, what's going on inside it, stuff like the polarizers you were asking about earlier in the thread, ...) but not the setting of the other detector, cannot match the experimentally confirmed results of QM. To agree with QM, you have to include the setting of the other detector in the calculation as well - it doesn't have to be via "spooky action at a distance", but one way or another it has to be included.

Both detectors may be set at the last moment, just microseconds before the measurement is made and long after anything moving at the speed of light can get from one detector to the other, and the two detectors may be separated by an enormous distance... but you still need both settings.

 

[Michel_vdg]

mh, the way you explain it makes me think of the shell-game where the game is rigged by hiding the ball during play and replace it as required, it is all in the quickness of the hands of the trickster and his companionship vs. the slowness of the observer.

 

[morrobay]

I guess this quote from Murphy explains it best:

"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.

Spatial symmetry means that such a model must operate within the Bell limits, which is essentially a straight-line correlation curve from analyzers aligned to counter-aligned/right-angles.

In the case of spin/polarization interactions, if the encounter with the instrument spatially distorts the probability distributions along the axes of the analyzer, then there is no surprise that the correlation between one analyzer and another depends on the relative angle of the analyzers. 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."

Independently of whether this quote is properly cited. In the last paragraph is there any thing that is not a physically valid mechanism for an explanation of of Bell Inequality violations ? Mant times I have suggested a local non realistic model ( not as good as the above) that like the above equates photon/particle/hidden variable interactions with detectors that determine probability distributions.In this case counter factual definiteness would not apply but the perfect (or anti ) correlations when detectors are aligned is consistant with this contextual model.

 

[Michel_vdg]

Independently of whether this quote is properly cited. In the last paragraph is there any thing that is not a physically valid mechanism for an explanation of of Bell Inequality violations ? Many times I have suggested a local non realistic model ( not as good as the above) that like the above equates photon/particle/hidden variable interactions with detectors that determine probability distributions. In this case counter factual definiteness would not apply but the perfect (or anti ) correlations when detectors are aligned is consistant with this contextual model.

Here is a reference in relation that last paragraph:
http://www.pnas.org/content/9/5/158 (672 kb)

The Transfer in Quanta of Radiation Momentum to Matter

1. The reflection by a crystal of X-radiation characteristic of the atoms in the crystal itself, which Dr. G. L. Clark and the writer discovered, does not appear to be explainable in a simple manner by the theory of interference of waves. This note describes an attempt to formulate a theory of the reflection of X-rays by crystals, based on quantum ideas without reference to interference laws.
2. The fundamental hypothesis of the theory now presented is that the momentum of radiation is transferred to and from matter in quanta, and further, that the laws of the conservation of energy and of momentum apply to these transfers.
3.In order to illustrate the meaning of this hypothesis, let us take a particular example, namely, that of the reflection of an X-ray by a crystal.
...
This is Braggs' law of reflection of an X-ray by a crystal.
By similar reasoning, if τ' = 0 and τ differs from 0, we deduce the equation:

τλ' = 2a cos θ,

which represents reflection according to Braggs' law from the y-planes. If both τ and τ' differ from 0, the equation obtained reduces to Braggs' equation representing the reflection from a set of planes other than the principal planes. In the case where the axes of the crystal are not at right angles to each other, we apply the law of the transfer of momenta in quanta to the total component of the radiation momentum in the direction of each axis and we equate this component to τh/a where a is the parameter of the crystal along the axis. This gives us equations which reduce to Braggs' equation for the reflection from each set of planes, as in the orthogonal problem.

 

[Nugatory]

Here is a reference in relation that last paragraph:
http://www.pnas.org/content/9/5/158 (672 kb)

I must confess that I am utterly unable to see the relevance of that article to the hypothetical mechanism of that "Murphy" quote... Which reminds me... You still haven't provided a citation, which makes it impossible to satisfactorily answer Morrobay's question about it.

You will be unable to post any more in this thread until you have sent me a private message saying that you're ready to provide the source.

 

[gill1109]

John Murphy seems to be a guy on internet ... https://plus.google.com/+JohnKNMurphy-nz/posts/CSDwN8vcXDm and commenting on a lecture by Susskind: https://www.youtube.com/all_comments?v=XlLsTaJn9AQ&lc=NxuYxn-ZMbJvQPrU4LxEgWf9YJyuL0ZAGnvRnpxbRO8

He's apparently a Software & Electronic Engineer from Auckland, NZ

He writes "When this is modeled by discrete hidden variables not mapping onto, but interacting with, a suitable analyzer it is a simple task to build simulation exactly matches the statistical predictions of quantum theory." This remark means that he does not understand Bell's theorem. Someone should ask him for this simulation model.

 

[morrobay]

John Murphy seems to be a guy on internet ... https://plus.google.com/+JohnKNMurphy-nz/posts/CSDwN8vcXDm and commenting on a lecture by Susskind: https://www.youtube.com/all_comments?v=XlLsTaJn9AQ&lc=NxuYxn-ZMbJvQPrU4LxEgWf9YJyuL0ZAGnvRnpxbRO8

He's apparently a Software & Electronic Engineer from Auckland, NZ

He writes "When this is modeled by discrete hidden variables not mapping onto, but interacting with, a suitable analyzer it is a simple task to build simulation exactly matches the statistical predictions of quantum theory." This remark means that he does not understand Bell's theorem. Someone should ask him for this simulation model.

So you are implying that Murphy does not understand Bell's theorem because Murphy is saying that the particles/hidden variables do interact with the detector during measurement ? Then that Bell made no assumption that there is any particle/detector interaction during measurement in his derivation. And that assumption in the derivation leads to S_EPR resulting in Bell inequality violations . That may be so .But all Murphy is stating is that there is interaction with photons and detectors as functions of θ and that is the cause and effect for probability distributions and inequality violations. For example : The entangled photons are created | Ψ} = 1/√2 ( | V_A} |V_B } + |H_A.} | H_B } ) And when photons encounter aligned detectors the photon/detector interactions are equivalent and their properties at measurement ( | V }| V} or | H }|H} are conserved and outcome is perfect correlations*. But when the detectors are not aligned then the physics of photon / detector interaction at a and photon interaction at b.are not equal (contextuality) Murphy is stating that this is cause of inequality violations, S_QM * My added interpretation of perfect correlations related to aligned detectors..

 

[gill1109]

So you are implying that Murphy does not understand Bell's theorem because Murphy is saying that the particles/hidden variables do interact with the detector during measurement ? Then that Bell made no assumption that there is any particle/detector interaction during measurement in his derivation. And that assumption in the derivation leads to S_EPR resulting in Bell inequality violations . That may be so .But all Murphy is stating is that there is interaction with photons and detectors as functions of θ and that is the cause and effect for probability distributions and inequality violations. For example : The entangled photons are created | Ψ} = 1/√2 ( | V_A} |V_B } + |H_A.} | H_B } ) And when photons encounter aligned detectors the photon/detector interactions are equivalent and their properties at measurement ( | V }| V} or | H }|H} are conserved and outcome is perfect correlations*. But when the detectors are not aligned then the physics of photon / detector interaction at a and photon interaction at b.are not equal (contextuality) Murphy is stating that this is cause of inequality violations, S_QM * My added interpretation of perfect correlations related to aligned detectors..

I'm indeed saying that Murphy is wrong. He should study Bell (1981) "Bertlmann's socks" which has got a much more thorough analysis and makes weaker assumptions than Bell (1964) and does allow any kind of interaction and any kind of physics going on in the detectors. Murphy also states that it is easy to simulate violations of Bell's theorem using this idea of interactions. He's wrong there too.

 

[stevendaryl]

So you are implying that Murphy does not understand Bell's theorem because Murphy is saying that the particles/hidden variables do interact with the detector during measurement ? Then that Bell made no assumption that there is any particle/detector interaction during measurement in his derivation.

Bell's result, that the predictions of quantum mechanics are not compatible with any local hidden-variables theory, does not require the assumption that there is no interaction between particles and detector. I can understand why people might think that there is such an assumption behind the theorem, because the way that the theorem is often presented seems to implicitly make that assumption. But I think that that's just for clarity of the presentation. Adding more complexity to how hidden variables result in measurement values doesn't change the result.

You can go through the proof all over again where you introduce more state variables representing additional details about detectors, and allow for hidden interactions between the detector hidden variables and the hidden variables of the particle. But it won't make any difference. In the case of EPR, the perfect correlations (or anti-correlations, depending on the precise type of experiment) between the results at the two detectors in the case where the experimenters choose the same detector settings shows that there really isn't any room for a complicated dependency on the microscopic details of the detectors.

 

[DrChinese]

What you said was: "There is no CW or C-CW in a CHSH type Bell test. Period."

My comment was only intended to disprove only that.

You have confused a number of different ideas. These references have nothing to do with what you are talking about, and in no way speak to anything I said. The references - such as the one about "twisted photons" - are obviously outside the scope of your familiarity. They didn't perform CHSH type tests, for one.

Once linearly polarized photons pass a linear polarizer, they do NOT retain some "special" handedness attribute that affects their likelihood of passing subsequent linear polarizers. The "twisting" effect has no bearing on this.

 

[Michel_vdg]

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.

 

[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.