Examining the details of the Bell Inequality.

[dormouse]

Hi,

I was reading Heinz Pagels' description of the nail gun experiment in the chapter about
"Bell's Inequality" from his book, The Cosmic Code: Quantum Physics as the Langauge of
Nature, 1982, pp. 160-176. He describes the record of hits and misses after "turning
polarizer A clockwise by a small angle theta and holding polarizer B as a fixed standard..."
and says, "The record might look like

A:0001011000101011100011110010110010100100...
...==]==]============== ]==== ]==========
B:0011001000101011100011010010010010100100...

where the mismatches are indicated."

My question for everyone is this, how can there ever be a 1-1 pair in the nail gun experiment
when the polarizers are not lined up but fixed and the correlation of the nail orientation is assumed?

It seems to me the only truth table entries can be 1-0, 0-1, or 0-0.

Any thoughts?

dormouse

 

[Doc Al]

My question for everyone is this, how can there ever be a 1-1 pair in the nail gun experiment
when the polarizers are not lined up but fixed and the correlation of the nail orientation is assumed?

It seems to me the only truth table entries can be 1-0, 0-1, or 0-0.

I agree. I think his 'nail gun experiment' is just a poor analogy.

I'll go one further. Even when the 'polarizers' (slits, actually) are lined up, I would expect 0-0 for the vast majority of random firings of the nail gun. Only rarely will the nails happen to align with the slits, giving you a 1-1.

 

[dormouse]

Pagels is attempting to give a real world example to match the ='s case of the Bell's Inequality so a lay person could/might grasp the concepts of the < being broken. I do not think this 1-1 observation destroys the example but it does change how it looks.

What is a caution to me is the fact this writing has gone through two peer reviews: the first for his original book; and the second in an anthology (which is what I am reading) - "The World of Physics, a small library of the Literature of Physics from Antiquity to the Present" Vol II: The Einstein Universe and the Bohr Atom, by Jefferson Hane Weaver, 1987, pp 468-483. While we would like to think peer reviewing will catch things, it does appear that some things can get through. Unfortunately Pagels is no longer with us, having passed in a mountain climbing accident on Pyramid Peak in Colorado on 23 July 1988, so we cannot have him comment on this finding.

In his writing he goes on to describe a photon experiment similar to the nail gun. I am going to quote his work again to get to a point where another question arises:

"If a photon hits the polarizer it has a certain probability of getting through and being detected."

I find this sentence to be quite interesting: probability theory can give us many insights into the behavior of systems but it cannot give us much information about the actual physical components of the system itself. I will give you an example (three actually) as a way of clarification.

1) Heads, Heads, Tails, Heads, Tails, Tails, Heads...
2) Tails, Heads, Heads, Heads, Tails, Heads, Tails...
3) Tails, Tails, Heads, Tails, Tails, Tails, Heads,...

These sequences are produced by two physical systems and one electronic system. Can you tell me which sequence was produced by which system? I think not. Probability theory can give us predictive information concerning these sequences but cannot know all the information - one of the physical systems could possibly produce the following sequence after a million instances:

1) ...(a million times)...Heads, Heads, Tails, -, Tails, Tails, Heads...

A no result occurs, completely unpredictable unless you already know everything about the physical system and the possible outcomes.

OK, to let you know 1) is a coin toss system, the no result happening when the coin lands on its edge and does not fall over; 2) is a 6-sided dice with three sides having Heads written on the facings and three sides having Tails written on the facings; and 3) a computer program which randomly chooses Heads or Tails based on some random number generator.

So what is my point, you cannot say much about the physical system of photons going through a polarizer just using the probability information. If there are some concrete rules that photons follow when going through one, we cannot fathom those rules by looking at the probability behavior. Did Bell make this same argument about the probability behavior of photons through a polarizer?

Dormouse

 

[ThomasT]

So what is my point, you cannot say much about the physical system of photons going through a polarizer just using the probability information. If there are some concrete rules that photons follow when going through one, we cannot fathom those rules by looking at the probability behavior.

Your point is well taken, imho. But I suspect you want to say more. So, let me venture a guess. The logical extension of your point is that violations of BIs don't necessarily reveal anything about the deep reality underlying the instrumental behavior that produces the detection attribute statistics -- a view apparently held by many, if not most, physicists.

Did Bell make this same argument about the probability behavior of photons through a polarizer?

I don't know. As far as I know, Bell's argument doesn't concern the underlying reality, but rather only confirms that modelling entanglement preparations in a certain general form (generally referred to as LHV or LR) is incompatible with standard qm formulations of entanglement preparations. Identifying the salient component(s) of Bell's formulation that determine this incompatibility, and the deep meaning (ie., any correspondence with an underlying reality) that might be attached to this incompatibility, is a matter of some contention, and continued research, discussion and refinement.

Anyway, since your point seems to me to be a sane and rationale one, then I hope you continue studying this stuff, and maybe one day explain it to me in a way that I can understand.

 

[DevilsAvocado]

Gentlemen, please correct me if I’m wrong – but Bell's inequality is not primarily a question about probabilities but correlations.

Probabilities for Alice & Bob are always 50/50 no matter the settings...

 

[Doc Al]

Gentlemen, please correct me if I’m wrong – but Bell's inequality is not primarily a question about probabilities but correlations.

Probabilities for Alice & Bob are always 50/50 no matter the settings...

Exactly right.

 

[DevilsAvocado]

Thanks Doc!

 

[yoda jedi]

"Could it be that what is real about two systems in the singlet state are not the local spin values, but merely the correlations between the two systems? Is quantum mechanics about a world consisting not of objective values of quantities but solely of objective correlations, of which some are revealed in experiment?"

"shows that the global state of a composite quantum system can be completely determined by specifying correlations (joint probability distributions) when sufficient local measurements are performed on each subsystem. It thus suffices to consider only correlations when completely specifying the state of the composite system. But can one also think of these correlations to be objective properties that pertain to the composite quantum system in question? As mentioned already in the case of the anti-correlation of the singlet state, one is tempted to think that this is indeed the case. However, in this letter we will demonstrate that, however tempting, no such interpretation is possible and that these questions (as well as the questions mentioned earlier) can thus not be answered in the positive."

 

[ThomasT]

Gentlemen, please correct me if I’m wrong – but Bell's inequality is not primarily a question about probabilities but correlations.

Probabilities for Alice & Bob are always 50/50 no matter the settings...

Yes, that's a good point to keep in mind, but isn't a Bell type LHV-supplemented expectation value (ie., the normalized rate) of coincidental detection wrt an entanglement preparation a probability expression?

The joint probability statement is of course intimately related to the correlation between the offset of the polarizers and the rate of coincidental detection.

The OP is suggesting, and it isn't new or out of the mainstream, that very little if anything can be inferred about an underlying reality from experiments involving correlations/probabilities in which the basic data are the 1s and 0s of dichotomized detection attributes.

 

[ThomasT]

"Could it be that what is real about two systems in the singlet state are not the local spin values, but merely the correlations between the two systems? Is quantum mechanics about a world consisting not of objective values of quantities but solely of objective correlations, of which some are revealed in experiment?"

"shows that the global state of a composite quantum system can be completely determined by specifying correlations (joint probability distributions) when sufficient local measurements are performed on each subsystem. It thus suffices to consider only correlations when completely specifying the state of the composite system. But can one also think of these correlations to be objective properties that pertain to the composite quantum system in question? As mentioned already in the case of the anti-correlation of the singlet state, one is tempted to think that this is indeed the case. However, in this letter we will demonstrate that, however tempting, no such interpretation is possible and that these questions (as well as the questions mentioned earlier) can thus not be answered in the positive."

Where's this from?

 

[DrChinese]

Where's this from?

Well, we know these are not the words of yoda jedi

 

[Doc Al]

Where's this from?

Looks to be from a paper by Michael Seevinc. See: http://philsci-archive.pitt.edu/3710/1/correlations_seevinck_final_quant-ph.pdf"

 

[yoda jedi]

Where's this from?

from
http://philsci-archive.pitt.edu/3710/1/correlations_seevinck_final_quant-ph.pdf

or

http://arxiv4.library.cornell.edu/PS_cache/quant-ph/pdf/0508/0508175v3.pdf

 

[DrChinese]

Looks to be from a paper by Michael Seevinc. See: http://philsci-archive.pitt.edu/3710/1/correlations_seevinck_final_quant-ph.pdf"

The paper does not say that the correlations are not "real"; more like they cannot offer any explanation which resolves any underlying mysteries.

You could say the correlation is what is real in the same sense you say the conservation property is real. Spin is conserved is essentially like saying the correlation is real. And this is all mostly semantics anyway. So yoda has not provided anything useful.

 

[Doc Al]

The paper does not say that the correlations are not "real"; more like they cannot offer any explanation which resolves any underlying mysteries.

You could say the correlation is what is real in the same sense you say the conservation property is real. Spin is conserved is essentially like saying the correlation is real. And this is all mostly semantics anyway. So yoda has not provided anything useful.

No argument from me.

 

[DevilsAvocado]

So yoda has not provided anything useful.

Thanks DrC for saving me the time...

 

[DevilsAvocado]

Yes, that's a good point to keep in mind, but isn't a Bell type LHV-supplemented expectation value (ie., the normalized rate) of coincidental detection wrt an entanglement preparation a probability expression?

It’s probably my fault (dumb)... but I don’t really understand this question? We spent 1.500 posts over at "that other thread", to reconcile that LHV has "joined the bleedin' choir invisibile"... it’s dead. That’s the only probability. If LHV was alive – where’s the probability for something that is already settled?? Do you mean a "pseudorandom generator", like in computers??

The OP is suggesting, and it isn't new or out of the mainstream, that very little if anything can be inferred about an underlying reality from experiments involving correlations/probabilities in which the basic data are the 1s and 0s of dichotomized detection attributes.

At current state, yes, but what if Anton Zeilinger makes a 100% loophole-free EPRB experiment that also settles if which is correct: non-local and/or non-separable

That wouldn’t say anything about the microscopic world??

 

[ThomasT]

It’s probably my fault (dumb)... but I don’t really understand this question? We spent 1.500 posts over at "that other thread", to reconcile that LHV has "joined the bleedin' choir invisibile"... it’s dead. That’s the only probability. If LHV was alive – where’s the probability for something that is already settled?? Do you mean a "pseudorandom generator", like in computers??

I was just reminding that the joint state correlations are expressed as probabilities. I might have misunderstood your point.

... what if Anton Zeilinger makes a 100% loophole-free EPRB experiment that also settles if which is correct: non-local and/or non-separable?

That wouldn’t say anything about the microscopic world??

FAPP, the experiments are already loophole-free, imho. And, while every successful experimental design twist might extend the limits of inferential conjecture regarding the nature of the quantum underworld, the associated formal considerations regarding LHV supplementation and LR formulation don't reveal anything more about it than can be inferred without them.

All of these formulations are based on assumptions regarding the correspondence between the formalism and the underlying reality. Since there's no direct knowledge of the underlying reality to refer to, then exactly what any of it has to with the underlying reality is an open question.

If Zeilinger makes a 100% loophole-free EPRB experiment, then the behavior of the quantum reality underlying the behavior of the instruments will still be a mystery.

 

[ThomasT]

Thanks for the link(s). In "The quantum world is not built up from correlations",
Seevinck proceeds along a line of reasoning similar to that of Bell and others. In Seevinck's case, he considers what would seem to be a plausible conjecture (similar but not quite the same as one that I was led to regarding nonvarying global relationship as opposed to local hidden variable) about the underlying reality of quantum entanglement correlations, defines what he means by correlations, formalizes his LR assumption ("We now assume local realism for these correlations in the following well-known way. Firstly, the correlations party I finds are determined by some hidden variable ... . The same of course holds for II. Secondly, because of locality the correlations one party will obtain are ... statistically independent of the correlations that the other party will find."), formulates an LR model to represent this ["Here we assume a so-called stochastic hidden variables model where the hidden variables ... determine only the joint probabilities ..., (ie., correlations), and not the values of the quantities themselves."], derives a CHSH type inequality ("This is the Bell inequality in terms of correlations that will be used in the next section. Despite the resemblance between our inequality and the usual CHSH inequality, they are fundamentally different because the latter is in terms of subsystems quantities whereas the former is in terms of correlations and does not assume anything about the values of subsystems quantities, which the usual inequality does."), incorporates his LR model into the QM formalism, and shows that this LR-supplemented model violates the inequality.

He then considers the "ontological robustness" of quantum entanglement: ["The SSC theorem of section 2 tells us that entanglement can be completely characterised by the above quantum correlations that it gives rise to. Therefore the result of the previous section also applies to entanglement. Then, if one considers the quantum state description to be complete, entanglement cannot be viewed as ontologically robust in the sense of being a local objective property pertaining to some composite system. If one would do so nevertheless, one can construct a composite system that contains as a subsystem the entanglement (i.e. the entangled system) in question and which would allow for a violation of the Bell inequality of Eq. (6). This implies (contra the assumption) that the entanglement cannot be regarded in a local realistic way, which we take to be a necessary condition for ontological robustness.]

Which is ok wrt his argument and assumptions, and provided one understands exactly what it means to "consider the quantum state description to be complete". It's regarding this last consideration that it might be conjectured that the quantum description is complete without LR supplementation because the entanglement correlations are a function of a nonvarying (from pair to pair) and persistent (wrt time and distance of separation) global relationship between the paired counter-propagating disturbances -- which, even if locally produced via a common cause, would be at odds with Seevinck's or Bell's or any other LHV representation unless the precise qualitative behavior of the underlying processes was known and accurately modeled, neither of which is, evidently, the case.

Anyway, wrt the OP's point, it seems that Seevinck's paper, as well as all attempts at (clearly understandably realistic and indisputadely local) LR-supplemented formulations of QM has supported it. There just isn't much that can be said, objectively, about what's happening in the quantum underworld from the statistical analysis of experimental accumulations of dichotomized detection attributes.

 

[yoda jedi]

All of these formulations are based on assumptions* regarding the correspondence between the formalism and the underlying reality. Since there's no direct knowledge of the underlying reality to refer to, then exactly what any of it has to with the underlying reality is an open question.
If Zeilinger makes a 100% loophole-free EPRB experiment, then the behavior of the quantum reality underlying the behavior of the instruments will still be a mystery.

a representation of an observer’s knowledge of reality rather than reality itself, e.g. an incomplete description of reality.
ψ-epistemic → ψ-incomplete.



*i.e. asumptions of assumptions.

 

[ThomasT]

a representation of an observer’s knowledge of reality rather than reality itself, e.g. an incomplete description of reality.
ψ-epistemic → ψ-incomplete.
*i.e. asumptions of assumptions.

Yes, but might tend to disagree that an epistemic interpretation is necessarily an incomplete one. More likely, it's ontological interpretations that are flawed, which is consistent with Seevinck's assessment, and Bell's theorem, I think.

By the way, I made a rather significant error in my cursory synopsis of Seevinck's paper. I'll leave it to you to point it out.

 

[yoda jedi]

Regardless Seevinck

Yes, but might tend to disagree that an epistemic interpretation is necessarily an incomplete one.

can delve your position
ψ-epistemic not ψ-incomplete consequently:
ψ-epistemic -> ψ-complete