Can we violate Bell inequalities by giving up CFD?

[Derek Potter]

What do you mean by that? If you have poor visibility you don't have 100% correlation at certain angles. You have 100% correlation modulus visibility at these angles.

To suppress the [+ -] and [- +] cases, which are half of the total, the [+ +] and [- -] rates would have to be doubled. Otherwise the experimenters would notice that the coincidence rate was being depressed. I believe that single detector rates can now exceed 80% so the coincidence detection rate should be more than 50% making it a bit hard for the Conspiracy Fairies to double it for the desired outcomes. So they must resort to making the detectors register wrongly - a [+ -] as a [+ +] for instance. They would still need to collude superluminally (edit - or alter the recorded data - who cares?).

 

[atyy]

What do you mean by that? If you have poor visibility you don't have 100% correlation at certain angles. You have 100% correlation modulus visibility at these angles.

Let's say they can get the EPR result of 100% correlation at certain angles.

But at other angles the prediction of QM is violated, so there is no Bell inequality violation.

Perhaps we could still model that using QM - maybe we just got the Hamiltonian is wrong - rather amazingly at such a low energy.

 

[Derek Potter]

Let's say they can get the EPR result of 100% correlation at certain angles.
But at other angles the prediction of QM is violated, so there is no Bell inequality violation.
Perhaps we could still model that using QM - maybe we just got the Hamiltonian is wrong - rather amazingly at such a low energy.

And if we could it would be a cute model of something that does not exist.

 

[Ilja]

"without CFD" is what the question asks: "Can we violate Bell inequalities by giving up CFD?"
I don't know what you mean by CFD being "derived". Where is it derived? What is it derived from?

In Bell's proof it is derived, in the very beginning, using the EPR argument.

That means, it is derived from:
1.) The EPR criterion: I we can, without in any way disturbing a system, predict with certainty the result of an experiment, then there exists an element of reality which defines this measurement result.
2.) The experimental fact about the 100% anticorrelation in this particular experiment if Alice and Bob measure in the same direction,
3.) Einstein causality, which makes sure that nothing measured by Bob can influence the system measured by Alice, and reverse.
and this derivation works only for this particular experiment - for other experiments, it is far away from clear if one can derive such a thing. So, there is no CFD assumption to be given up.

 

[atyy]

And if we could it would be a cute model of something that does not exist.

We should all definitely say QM will never be falsified, since historically that's the surest way to get something falsified.

OK, to be fair to Thomson, he only really got aeroplanes wrong. He actually was pretty prescient about relativity and quantum mechanics.

For an argument against QM, here is http://arxiv.org/abs/hep-th/0106109. It's a sophisticated form of the argument that the only widely agreed on interpretation of QM is Copenhagen, which needs a classical observer who presumably has a lab in classical spacetime, contrary to quantum gravity where spacetime is quantum.

 

[zonde]

To suppress the [+ -] and [- +] cases, which are half of the total, the [+ +] and [- -] rates would have to be doubled. Otherwise the experimenters would notice that the coincidence rate was being depressed. I believe that single detector rates can now exceed 80% so the coincidence detection rate should be more than 50% making it a bit hard for the Conspiracy Fairies to double it for the desired outcomes. So they must resort to making the detectors register wrongly - a [+ -] as a [+ +] for instance. They would still need to collude superluminally (edit - or alter the recorded data - who cares?).

To violate BI you need around 75% efficiency. That is about the efficiency experimenters get in experiments that close fair sampling loophole (but efficiency is marginally enough to violate BI in these experiments).
But considering present experimental results, for loophole free experiment to fail nature would have to exploit both loopholes - fair sampling loophole and communication loophole (or I would rather say feedback loophole to sound less "conspiracy").

Otherwise the experimenters would notice that the coincidence rate was being depressed.

Coincidence rate is not depressed if you have poor visibility. You just have "wrong" pairs of detections.
And in real experiments there are plenty of reasons why visibility can go down. To notice that at one moment visibility starts to correlate with efficiency might be nearly impossible if you don't have clear protocol at what things you have to look and what things you have to notice.

Anyways hypothetical falsification of prediction can not relay on things like "experimenters would notice".

 

[Derek Potter]

In Bell's proof it is derived, in the very beginning, using the EPR argument.
That means, it is derived from:
1.) The EPR criterion: I we can, without in any way disturbing a system, predict with certainty the result of an experiment, then there exists an element of reality which defines this measurement result.
2.) The experimental fact about the 100% anticorrelation in this particular experiment if Alice and Bob measure in the same direction,
3.) Einstein causality, which makes sure that nothing measured by Bob can influence the system measured by Alice, and reverse.
and this derivation works only for this particular experiment - for other experiments, it is far away from clear if one can derive such a thing. So, there is no CFD assumption to be given up.

In that case I don't understand why you need to ask: "What means "without CFD" if the CFD is derived?" Given that CFD is a corollary of the EPR criterion, "without CFD" simply means "without assuming the EPR criterion".

 

[Derek Potter]

To violate BI you need around 75% efficiency. That is about the efficiency experimenters get in experiments that close fair sampling loophole (but efficiency is marginally enough to violate BI in these experiments).
But considering present experimental results, for loophole free experiment to fail nature would have to exploit both loopholes - fair sampling loophole and communication loophole (or I would rather say feedback loophole to sound less "conspiracy").

Coincidence rate is not depressed if you have poor visibility. You just have "wrong" pairs of detections.
And in real experiments there are plenty of reasons why visibility can go down. To notice that at one moment visibility starts to correlate with efficiency might be nearly impossible if you don't have clear protocol at what things you have to look and what things you have to notice.

Anyways hypothetical falsification of prediction can not relay on things like "experimenters would notice".

Most of that is precisely what I said but I have no idea why you say we can't rely on experimenters to notice the very things they know have to be checked.

 

[zonde]

In that case I don't understand why you need to ask: "What means "without CFD" if the CFD is derived?" Given that CFD is a corollary of the EPR criterion, "without CFD" simply means "without assuming the EPR criterion".

When I asked I had no idea that we can view CFD as derived. And to be honest I'm still not sure that CFD, in a particular sense that say individual photons have a property - polarization, unequivocally follows from EPR argument about elements of reality in conjunction with QM prediction about perfect correlations.

 

[zonde]

Most of that is precisely what I said but I have no idea why you say we can't rely on experimenters to notice the very things they know have to be checked.

What exactly are they going to write in a paper about experimental results? "We failed to perform the experiment but there is something fishy about how it failed."
That is job of theoreticians to point out how to know when the experiment is successful but it fails to confirm prediction, no?

 

[Derek Potter]

When I asked I had no idea that we can view CFD as derived. And to be honest I'm still not sure that CFD, in a particular sense that say individual photons have a property - polarization, unequivocally follows from EPR argument about elements of reality in conjunction with QM prediction about perfect correlations.

It doesn't. The state of the entangled pair is an element of EPR reality, the individual photons do not have states.

 

[Derek Potter]

What exactly are they going to write in a paper about experimental results? "We failed to perform the experiment but there is something fishy about how it failed."

In what sense is discovering a rate suppression that was specifically looked for a failure?

That is job of theoreticians to point out how to know when the experiment is successful but it fails to confirm prediction, no?

I am not a Trade Unionist, but I understand the job of theoreticians is to split hairs rather than design experimental protocols.

 

[andrewkirk]

In Bell's proof [CFD] is derived, in the very beginning, using the EPR argument.

That means, it is derived from:
1.) The EPR criterion: I we can, without in any way disturbing a system, predict with certainty the result of an experiment, then there exists an element of reality which defines this measurement result.
2.) The experimental fact about the 100% anticorrelation in this particular experiment if Alice and Bob measure in the same direction,
3.) Einstein causality, which makes sure that nothing measured by Bob can influence the system measured by Alice, and reverse.
and this derivation works only for this particular experiment - for other experiments, it is far away from clear if one can derive such a thing. So, there is no CFD assumption to be given up.

This is not a derivation. Try writing it out as a formal logical deduction and you will see that it has fatal gaps.

I agree that Bell hypothesises your (3), which he calls 'hypothesis [2]'. He also hypothesises your (2), in the 4th and 5th lines of the first paragraph under heading 'II. Formulation'. Note however that that is not an 'experimental fact' but a hypothesis (see Popper again - it is impossible to experimentally prove that there will always be a 100% anticorrelation). Bell accurately describes this as 'according to quantum mechanics', not an 'experimental fact'.

I don't know where you get your (1) from though. What Bell wrote is 'Since we can predict in advance the result of measuring any chosen component of $\vec{\sigma}_2$, by previously measuring the same component of $\vec{\sigma}_1$, it follows that the result of any such measurement must actually be predetermined'. There is no mention of 'reality' in that part of his paper. Further, one way that the result of the second measurement could be predetermined is if it was predetermined at the time of entanglement, or earlier, what measurements, and at what spacetime locations, would be performed on the two particles, as well as their results. In that case CFD is rejected because it is impossible that any other measurements could be performed instead.

 

[Ilja]

In that case I don't understand why you need to ask: "What means "without CFD" if the CFD is derived?" Given that CFD is a corollary of the EPR criterion, "without CFD" simply means "without assuming the EPR criterion".

If one means "giving up the EPR criterion" one should say so.

First of all, because the derivation of CFD from the EPR argument has a much better candidate for rejection than the EPR criterion, namely the assumption (3) that the "measurement" made by Bob does not influence the system of Alice.

If one says, instead, "giving up CFD", one creates a very false impression of what is given up. Because CFD is a very strong assumption, and it is easy to have theories completely compatible with common sense and completely realistic which don't have CFD: all one needs is to reinterpret the "measurement" as an "interaction". The idea that unperformed interactions should have predetermined results is nonsensical. To give up such a strong and unnecessary assumption would be, therefore, a natural solution for the "problem" which is created by the (misleading) presentation of Bell's theorem as "CFD + Einstein causality => contradiction with QM", which seems to preserve Einstein causality. In fact, it does't, given that we have this first part "EPRC + Einstein causality + QM => CFD".

To give up the EPR criterion is, instead, much harder. It is essentially equivalent to Reichenbach's common cause: On starts with a correlation, in this case one "with certainty", between the prediction and the measurement result, then excludes one direct causal explanation directly by "without in any way disturbing the system", the other one implicitly by naming this a prediction, thus, assuming a temporal order, and what remains is the common cause - the element of reality - which has to predict the result, because everything else would not be sufficient as an explanation for a 100% correlation.

 

[zonde]

In what sense is discovering a rate suppression that was specifically looked for a failure?

What rate do you have on mind? If you mean that there is rate suppression for coincidences then no that was not what I was talking about. Poor visibility means poor quality of entanglement (decoherence, polarization drift). Coincidence rate at the same time can be very good.

 

[Ilja]

This is not a derivation. Try writing it out as a formal logical deduction and you will see that it has fatal gaps.

Not more gaps than usual and acceptable in an informal forum posting with verbal formulation.

I agree that Bell hypothesises your (3), which he calls 'hypothesis [2]'. He also hypothesises your (2), in the 4th and 5th lines of the first paragraph under heading 'II. Formulation'. Note however that that is not an 'experimental fact' but a hypothesis (see Popper again - it is impossible to experimentally prove that there will always be a 100% anticorrelation). Bell accurately describes this as 'according to quantum mechanics', not an 'experimental fact'.

Minor differences, which are relevant for experimenters and experimental-loophole-hopers, but not for the issue which I want to emphasize - the important difference between CFD and the EPR-CR.

I don't know where you get your (1) from though. ... There is no mention of 'reality' in that part of his paper.

From my poor memory about the EPR argument. The argument itself is mentioned in the title of Bell's paper as well as in the text by "With the example advocated by Bohm and Aharonov, the EPR argument is the following." The exact quote of the EPR Criterion of Reality from Einstein, Podolsky, Rosen, Can quantum-mechanical description of physical reality be considered complete, Phys.Rev. 47, p.777 (1935), is the following:

If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.

Further, one way that the result of the second measurement could be predetermined is if it was predetermined at the time of entanglement, or earlier, what measurements, and at what spacetime locations, would be performed on the two particles, as well as their results. In that case CFD is rejected because it is impossible that any other measurements could be performed instead.

Yes, the superdeterminism loophole. You have forgotten to mention the Matrix loophole - that reality is, in one formulation I like, "only a boring advanture game, but the graphics are cool". Above loopholes could be easily considered as variants of giving up causality, because in above worlds causality would be meaningless. Anyway, they would be interesting only for people who would not give up relativity even if a working FTL phone would be presented to them.

 

[harrylin]

[..] The idea that unperformed interactions should have predetermined results is nonsensical. [..]

That "nonsensical idea" is exactly what Bell argues to be logically necessary - and at first sight his reasoning looks sound to me and most others.
He argues as follows:

"We are assuming that particles
have properties which dictate their ability to pass certain tests - whether or
not these tests are in fact made. To account for the perfect anticorrelation
when identical tests (parallel Stern-Gerlach magnets) are applied to the two members
of a pair, we have to admit that the pairing is a generalized à la
Bertlmann - when one has the ability to pass a certain test, the other has not."
- Bertlmans's socks, Bell

I think that for those angles the reasoning is indisputable and I'm curious if you can point out an error in that reasoning.

For me a somewhat tricky part (which he claims to be "trivial") is the expanded reasoning that follows for other angles.

 

[Derek Potter]

If one means "giving up the EPR criterion" one should say so.

Yes and if you mean "one particular case" then one should say so. The derivation you have kindly unpacked for me ("EPRC + Einstein causality + QM => CFD") only derives CFD in one special case, not "QM". A special case where BI is not even violated. As zonde's question is about BI violation you cannot claim that CFD is derived. (edit i.e. for zonde's purposes.)

 

[Ilja]

That "nonsensical idea" is exactly what Bell argues to be logically necessary - and at first sight his reasoning looks sound to me and most others.
He argues as follows:
"...To account for the perfect anticorrelation when identical tests (parallel Stern-Gerlach magnets) are applied to the two members of a pair, we have to admit that ..."
I think that for those angles the reasoning is indisputable and I'm curious if you can point out an error in that reasoning.

(emphasis and ... mine)
I don't even want to do this, because I agree with this reasoning.

My point is that assuming CFD, as a general principle, does not make such arguments, but simply assumes that all unperformed measuerements have outcomes - this is, last but not least, what is implicitly presupposed if one names something a measurement - that means, something existing is measured. But this naive presupposition would disappear if one remains "measurement" into "interaction". If I interact with paper using a pencil, the resulting picture will not be the measurement of some property of the paper, and nobody would suspect that this picture existing as part of the paper before I started my interaction.

Instead, Bell does not make such a presupposition. He proves that, in this particular situation, it follows from the perfect anticorrelation (and, of course, Einstein causality).

 

[Ilja]

Yes and if you mean "one particular case" then one should say so. The derivation you have kindly unpacked for me ("EPRC + Einstein causality + QM => CFD") only derives CFD in one special case, not "QM". A special case where BI is not even violated. As zonde's question is about BI violation you cannot claim that CFD is derived.

Why do you think that BI is not violated in this special case?

The question is, of course, what exactly is the "special case" here. It is defined by the preparation of that special superpositional state - which makes it special - but for all possible measurements of spin components by Alice and Bob. Because for every particular such spin measurement, we can apply the EPR reasoning and conclude that for this particular outcome CFD holds.

And this is already enough CFD to prove the BI.

 

[Derek Potter]

If I interact with paper using a pencil, the resulting picture will not be the measurement of some property of the paper, and nobody would suspect that this picture existing as part of the paper before I started my interaction.

‘In every block of marble I see a statue as plain as though it stood before me, shaped and perfect in attitude and action. I have only to hew away the rough walls that imprison the lovely apparition to reveal it to the other eyes as mine see it.’—Michelangelo

 

[Derek Potter]

Why do you think that BI is not violated in this special case?

This is a bit elementary:
- 2 <= E(a, b) − E(a, b′) + E(a′, b) + E(a′, b′) <= +2 (CHSH)
a = b and a '= b' (the special case)
Therefore E(a, b') = E(a', b); the expression evaluates to 2 (or -2) and BI is not violated.

 

[Ilja]

?
- 2 <= E(a, b) − E(a, b′) + E(a′, b) + E(a′, b′) <= +2
a = b and a '= b'; therefore E(a, b') = E(a', b) and BI is not violated.

And why do you restrict this to a=b or a'=b'?

You obviously should distinguish the reasoning which proves that CFD holds for this type of experiment for above parts and all a, b from the measurements.

The EPR criterion requires only an ability. It is "If ... we can ..." not "if we actually do". After applying it, we have concluded - as a general fact about the particular Einstein-causal theory, not about a particular experiment - that for all directions of possible spin measurements by Alice or Bob CFD holds. Always, that means, even if we measure E(a,b) for a =/= b.

 

[zonde]

Let's say they can get the EPR result of 100% correlation at certain angles.

But at other angles the prediction of QM is violated, so there is no Bell inequality violation.

Perhaps we could still model that using QM - maybe we just got the Hamiltonian is wrong - rather amazingly at such a low energy.

This is of course hypothetical but I would consider more likely that new interpretation (or rather theory in this case) of QM can be constructed that does not violate BI if prediction about 100% correlation is taken as false. That's because CFD assumption in this case surely can be relaxed and without CFD fair sampling assumption is unjustified.

 

[Derek Potter]

And why do you restrict this to a=b or a'=b'?

because that is what you asked about.

You obviously should distinguish the reasoning which proves that CFD holds for this type of experiment for above parts and all a, b from the measurements.
The EPR criterion requires only an ability. It is "If ... we can ..." not "if we actually do". After applying it, we have concluded - as a general fact about the particular Einstein-causal theory, not about a particular experiment - that for all directions of possible spin measurements by Alice or Bob CFD holds. Always, that means, even if we measure E(a,b) for a =/= b.

We have concluded no such thing for the simple reason that the argument relies on 100% correlation. However we can certainly construct a different argument which replaces the 100% correlation with a cos-squared law. The EPRC then refers to the predictability of this correlation, which means that the correlation is a property of the system. On which bombshell I would ask you to define CFD in such a way as to tell us unambiguously whether this property means CFD holds or not.

 

[stevendaryl]

We have concluded no such thing for the simple reason that the argument relies on 100% correlation. However we can certainly construct a different argument which replaces the 100% correlation with a cos-squared law. The EPRC then refers to the predictability of this correlation, which means that the correlation is a property of the system. On which bombshell I would ask you to define CFD in such a way as to tell us unambiguously whether this property means CFD holds or not.

If Bob's experiment has adjustable setting \Theta, then let's say that Bob's experiment satisfies CFD for setting \theta_1 if the question: "What would Bob's result have been if he had chosen setting \theta_1?" has a definite answer, even in the case where Bob didn't choose angle \theta_1. This is a property of theories; it's not just a philosophical question. The theory either does or does not imply CFD.

In this case, the theory is a combination of QM, plus the assumption that definite outcomes occur (no many-worlds), plus the assumption of free-will (that is, Alice and Bob's detector settings are freely chosen parameters, and are not forced by the experimental set-up--no superdeterminism), plus the assumption of Einstein causality (nothing Alice does can instantly change the physical situation for Bob, who is far away).

The argument for CFD given these assumptions is something like:

1. Suppose that in Alice's coordinate system, her measurement takes place before Bob's.
2. Suppose that Alice chooses detector setting \theta_1 and gets result A_1. (For simplicity, let's assume that the result is binary--she either detects a particle at that filter angle, in which case A_1 = 1 or doesn't, in which case A_1 = 0)
   
3. Immediately after Alice's measurement , she knows something definite about Bob's future measurement result: Namely, "if he chooses detector setting \theta_1, he will get result B_1". (Depending on the details of the twin-pair setup, either B_1 = A_1 or B_1 = \neg A_1)
   
4. So she concludes that the implication \theta_1 \rightarrow B_1 is a physical property of Bob's experimental situation.
5. If she also assumes that her measurement has no effect on Bob's situation (since it is far away), then she concludes that the implication \theta_1 \rightarrow B_1 was a physical property of Bob's experimental situation even before her measurement.
6. So even if Bob doesn't choose detector setting \theta_1, Bob's situation satisfies CFD for that angle: If he chose that angle, his result would definitely be B_1

That's what CFD means; regardless of what setting Bob actually chooses, there is a definite answer to the question: "What would Bob's result have been if he had chosen setting \theta_1?"

So, after Alice's measurement, she knows that Bob's situation satisfies CFD for angle \theta_1. Now, she can do hypothetical reasoning on her own choice, as follows:

1. For any angle \theta, if Alice chooses detector setting \theta, then she knows that Bob's situation satisfies CFD for angle \theta.
2. If her choices have no effect on Bob, and after her choice, Bob has CFD for angle \theta, then he must have had CFD for angle \theta before she made her choice.
3. Since \theta is arbitrary, then Bob must have CFD for every angle \theta

 

[atyy]

I usually avoid using the term CFD, because I don't really understand what it means, so as you can see in my answers in this thread, I've always redefined the term.

But what is the actual definition of CFD and who defined it? The only one I know is Peres's famous definition of the negation of CFD being that "unperformed experiments have no results" - but I can't imagine he was serious, just one his jokes.

 

[zonde]

I usually avoid using the term CFD, because I don't really understand what it means, so as you can see in my answers in this thread, I've always redefined the term.

But what is the actual definition of CFD and who defined it? The only one I know is Peres's famous definition of the negation of CFD being that "unperformed experiments have no results" - but I can't imagine he was serious, just one his jokes.

I would like to turn your question on it's head. We need to give a name for this idea:

regardless of what setting Bob actually chooses, there is a definite answer to the question: "What would Bob's result have been if he had chosen setting $\theta_1$?"

Is it ok to name it CFD? If it's not the best choice what would be your choice?

 

[zonde]

I would like to say that I consider my question in OP answered thanks to Ilja, stevendaryl's nice summary of the argument and those who maintained skeptical opposition.

 

[Derek Potter]

[QUOTE="stevendaryl, post: 5155634, member: 372855
That's what CFD means; regardless of what setting Bob actually chooses, there is a definite answer to the question: "What would Bob's result have been if he had chosen setting \theta_1?"
[/QUOTE]
Thanks, Steve, that's pretty clear. So, given Einstein causality, CFD (as you define it and this seems to satisfy zonde) is unavoidable. i.e. A viable theory that gives up CFD must necessarily give up Einstein causality.