Non-locality and Counterfactual definiteness

[Daniel K]

I understand that through Bell's theorem both locality and counterfactual definiteness cannot exist within physics. However shouldn't the double slit experiment give physicists a clue that losing counterfactual definiteness is actually the best way of interpreting the problem? The double slit experiment proved that the wave that guides light is in fact probabilistic. How does an advocate of particles having definite preexisting qualities account for this?

 

[Daniel K]

Just realized that it could be explained by pilot wave theory. However is this the only way out?

 

[wle]

You don't need to assume determinism or counterfactual definiteness in order to derive Bell inequalities.

 

[Daniel K]

You don't need to assume determinism in order to derive Bell inequalities.

I'm aware. However if you do, then non-locality is the only way in which you can explain the correlations.
I am asking how do advocates that say particles have definite properties explain the probabilistic manner that the double slit experiment proved

 

[zonde]

I'm aware. However if you do, then non-locality is the only way in which you can explain the correlations.
I am asking how do advocates that say particles have definite properties explain the probabilistic manner that the double slit experiment proved

The point is that FTL is the only way in which you can scientifically explain the correlations.
Definite properties or not is unrelated to the question.

The double slit experiment proved that the wave that guides light is in fact probabilistic.

Experiments do not prove anything. They can confirm or falsify some model or theory.

 

[Demystifier]

Just realized that it could be explained by pilot wave theory. However is this the only way out?

Try http://lanl.arxiv.org/abs/1112.2034
which is a sort of hybrid between pilot wave theory and denial of counterfactual definiteness.

 

[Demystifier]

However if you do, then non-locality is the only way in which you can explain the correlations.

Not necessarily. One logical possibility is superdetermisism, in which the laws of physics are objective, deterministic and local, but (there is always a "but") the initial conditions are fine tuned. Not many physicists find that idea reasonable, but among them there is one Nobel Prize laureate.

 

[DrChinese]

Just realized that it could be explained by pilot wave theory. However is this the only way out?

Not sure why a couple of the other posters passed on this point, but we usually say:

Every interpretation of Quantum Mechanics is an attempt to provide a "way out". MWI, Time Symmetric/Retrocausal, and as you point out, the explicit FTL mechanisms such as Bohmian Mechanics (pilot wave).

 

[billschnieder]

You don't need to assume determinism or counterfactual definiteness in order to derive Bell inequalities.

The Perfect ant-correlation assumption is Counterfactual Definiteness. Without it you don't have Bell's inequalities.

Bell wrote: "if measurement by Alice along axis "a" produces outcome +1, then according to quantum mechanics, measurement by Bob along axis "b" must produce outcome -1 and vice versa"

Counterfactual Definiteness means that a measurement that was not performed had a single definite result, which is the case for the perfect ant-correlation assumption.

 

[stevendaryl]

The Perfect ant-correlation assumption is Counterfactual Definiteness. Without it you don't have Bell's inequalities.

I think that there are two ingredients in the derivation of Bell's inequality: Perfect anti-correlation + local realism. The first is a consequence of QM (in the spin-1/2 EPR experiment), so it shouldn't be considered an assumption of Bell's theorem.

1. QM predicts perfect anti-correlations in the spin-1/2 EPR experiment.
2. Perfect anti-correlation + the assumption of local realism implies counterfactual definiteness.
3. Local realism + counterfactual definiteness implies Bell's inequality.
4. QM predicts the violation of Bell's inequalities.

So putting this altogether:

QM + Local realism is inconsistent (since it predicts both Bell's inequality and the violation of Bell's inequality)​

which is logically equivalent to:

QM implies that local realism is false​

I'm sure there must be an alternative derivation of Bell's inequalities (or some other related inequality) that doesn't assume counterfactual definiteness, but I don't know what it is.

Counterfactual definiteness comes into the derivation when Bell assumes that there are two functions:

$A(\alpha, \lambda)$
$B(\beta, \lambda)$
that return $\pm 1$ as deterministic functions of the detector settings $\alpha$ and $\beta$, and the hidden variable $\lambda$

Local realism by itself doesn't imply the existence of such functions. Instead, what it implies is the existence of two functions:

• $P_A(\alpha, O_A, \lambda)$ : the probability of Alice measuring +1, given her detector setting $\alpha$, other local conditions relevant to the detection [/itex]O_A[/itex] and hidden variable $\lambda$

• $P_B(\beta, O_B, \lambda)$ : the probability of Bob measuring +1, given his detector setting $\beta$, other local conditions relevant to the detection [/itex]O_B[/itex] and hidden variable $\lambda$

The perfect anti-correlation prediction of quantum mechanics implies that $O_A$ and $O_B$ are irrelevant, and implies that these two probabilities must in fact must be 0 or 1. In other words, the outcomes are deterministic functions of $\alpha, \beta$ and $\lambda$ (which is basically counterfactual definiteness).

 

[wle]

The Perfect ant-correlation assumption is Counterfactual Definiteness. Without it you don't have Bell's inequalities.

Bell wrote: "if measurement by Alice along axis "a" produces outcome +1, then according to quantum mechanics, measurement by Bob along axis "b" must produce outcome -1 and vice versa"

Counterfactual Definiteness means that a measurement that was not performed had a single definite result, which is the case for the perfect ant-correlation assumption.

Two sentences later, in Bell's summary of the EPR argument from the same paper:

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.​

So as far as Bell was concerned, nondeterministic local hidden variable models had no chance of working, so there was no point in further considering them.

But this is moot, since exactly the same Bell inequalities hold for nondeterministic LHVs as for deterministic LHVs.

 

[morrobay]

The Perfect ant-correlation assumption is Counterfactual Definiteness. Without it you don't have Bell's inequalities.

Bell wrote: "if measurement by Alice along axis "a" produces outcome +1, then according to quantum mechanics, measurement by Bob along axis "b" must produce outcome -1 and vice versa"

Counterfactual Definiteness means that a measurement that was not performed had a single definite result, which is the case for the perfect ant-correlation assumption.

With this table for perfect anti correlations I see two cases where Alice produces outcome +1 along axis "a" and Bob produces outcome +1 along axis "b" in disagreement with above. So it seems this conflict with the table is part of inequality violations explanation.

Alice......Bob
a b c......a b c
+++...... ---
++-......--+
+-+.....-+-
+--..... -++
-++.....+--
-+-......+-+
--+......++-
---......+++

 

[billschnieder]

if measurement by Alice along axis "a" produces outcome +1, then according to quantum mechanics, measurement by Bob along axis "a" must produce outcome -1 and vice versa.

Even if Bob had measured along "b". According to QM, he would still have obtained the definite value -1, had he measured along "a".

If perfect anti-correlation is a consequence of QM, and perfect anti-correlation is CFD, there is no way for Bell's theorem to reject CFD without rejecting QM. BTW, CFD and realism are equivalent.

In quantum mechanics, counterfactual definiteness (CFD) is the ability to speak meaningfully of the definiteness of the results of measurements that have not been performed (i.e. the ability to assume the existence of objects, and properties of objects, even when they have not been measured). -- Wikipedia

 

[stevendaryl]

If perfect anti-correlation is a consequence of QM, and perfect anti-correlation is CFD, there is no way for Bell's theorem to reject CFD without rejecting QM.

I see it as:

1. QM implies AC (perfect anti-correlations)
2. AC + LR (local realism) implies CFD.
3. LR + CFD implies BI (Bell's inequalities)
4. QM contradicts BI
5. Therefore, QM contradicts LR

BTW, CFD and realism are equivalent.

I think they should be distinguished. In the case of a measurement with two possible results, $\pm 1$, I would say that the model is locally realistic if the probability of getting $+1$ depends only on conditions local to the measurement. CFD is the special case in which the result, $\pm 1$, is a deterministic function of those conditions. So you could have a purely local stochastic model, which would not obey CFD. But such a model couldn't produce perfect anti-correlations among twin pairs unless it also obeyed CFD.

 

[DrChinese]

BTW, CFD and realism are equivalent.

In quantum mechanics, counterfactual definiteness (CFD) is the ability to speak meaningfully of the definiteness of the results of measurements that have not been performed (i.e. the ability to assume the existence of objects, and properties of objects, even when they have not been measured). -- Wikipedia

I actually agree with you on this. Although I know there are those who want to define Realism as different than CFD, they are used interchangeably in the literature and there is no significant difference between them. Essentially, any example of realism is also an example of CFD, and vice versa.

QM does NOT require CFD due to perfect correlations. That is an extra assumption.

 

[stevendaryl]

I actually agree with you on this. Although I know there are those who want to define Realism as different than CFD, they are used interchangeably in the literature and there is no significant difference between them.

I would say that they are used indistinguishable in discussions of QM, because QM predicts perfect correlations in certain situations, and perfect correlations plus realism implies CFD.

 

[RUTA]

I would say that they are used indistinguishable in discussions of QM, because QM predicts perfect correlations in certain situations, and perfect correlations plus realism implies CFD.

Most of my foundations colleagues equate CFD with realism, but there are realistic interpretations without CFD, e.g., http://www.ijqf.org/wps/wp-content/uploads/2015/06/IJQF2015v1n3p2.pdf. In general, a realistic retrocausal interpretation is indifferent to CFD, e.g., https://www.physicsforums.com/insights/retrocausality/.

 

[billschnieder]

Most of my foundations colleagues equate CFD with realism, but there are realistic interpretations without CFD

I think this is not possible, I would be interested to see their definition of "realistic" and "CFD" and what the difference is.

Is it true in RBW, that if Alice measured along "a" and obtained +1, Bob would have obtained "-1" if he measured along "a", even if he actually ends up measuring along "b" instead? But this is exactly the meaning of CFD.

I do not agree with the statement that "perfect correlations plus realism implies CFD". Perfect correlations is CFD, and is Realism already.

 

[stevendaryl]

I do not agree with the statement that "perfect correlations plus realism implies CFD". Perfect correlations is CFD, and is Realism already.

"Realism" is too fuzzy a concept to reason about, but Bell had a pretty precise notion of what a "local realistic theory" was. It was described in his essay "Theory of Local Beables". The fact of perfect correlations does not imply that there is a local realistic theory underlying those observations.

 

[billschnieder]

"Realism" is too fuzzy a concept to reason about, but Bell had a pretty precise notion of what a "local realistic theory" was. It was described in his essay "Theory of Local Beables". The fact of perfect correlations does not imply that there is a local realistic theory underlying those observations.

The moon is there when nobody is looking. Particles have properties even when they are not being measured. Not fuzzy at all, very precise statement.

 

[stevendaryl]

The moon is there when nobody is looking. Particles have properties even when they are not being measured. Not fuzzy at all, very precise statement.

If they are precise statements, how would you go about falsifying them? Or verifying them? Or deducing a consequence from them?

 

[billschnieder]

If they are precise statements, how would you go about falsifying them? Or verifying them? Or deducing a consequence from them?

They are not falsifiable. Still does not mean they are not precise. CFD is not falsifiable either.

 

[RUTA]

I think this is not possible, I would be interested to see their definition of "realistic" and "CFD" and what the difference is.

Is it true in RBW, that if Alice measured along "a" and obtained +1, Bob would have obtained "-1" if he measured along "a", even if he actually ends up measuring along "b" instead? But this is exactly the meaning of CFD.

The view according to retrocausality (experimental outcome is part of the computation as in path integral) is that you have some sort of field or graphical or ... structure in the spacetime region between Source and sink. This field/graph exists in spacetime (as opposed to configuration space), so it can have ontic status in the normal sense. The field/graph relates all elements of the experimental procedure and is unique for different detector settings, so CFD is meaningless even though there is a fact of the matter concerning the ontology in that region of spacetime. So, if Bob doesn't measure "a," then the field/graph structure in the spacetime region of the experimental procedure is different than if he had measured "a." In other words, you're working in a blockworld (spacetime) perspective with a particular outcome (again, as with path integral) rather than a dynamical, time-evolved perspective in configuration space (as with Schrodinger's equation).

 

[zonde]

The moon is there when nobody is looking. Particles have properties even when they are not being measured. Not fuzzy at all, very precise statement.

Realism is well established concept in philosophy. If you want to use a term with your own definition just pick another word.

 

[Demystifier]

They are not falsifiable. Still does not mean they are not precise.

In the same spirit, I would add that logical consistency (which has to do with precision) is even more important than observation (which has to do with falsifiability). For instance, what would you say if somebody told you that they observed a cat which is both dead and not dead? I would say: "You didn't!" before looking at the details of their experiment.

 

[billschnieder]

The view according to retrocausality (experimental outcome is part of the computation as in path integral) is that you have some sort of field or graphical or ... structure in the spacetime region between Source and sink. This field/graph exists in spacetime (as opposed to configuration space), so it can have ontic status in the normal sense. The field/graph relates all elements of the experimental procedure and is unique for different detector settings, so CFD is meaningless even though there is a fact of the matter concerning the ontology in that region of spacetime. So, if Bob doesn't measure "a," then the field/graph structure in the spacetime region of the experimental procedure is different than if he had measured "a." In other words, you're working in a blockworld (spacetime) perspective with a particular outcome (again, as with path integral) rather than a dynamical, time-evolved perspective in configuration space (as with Schrodinger's equation).

That theory is inconsistent. Can it make valid predictions before Bob measured anything? Are those predictions still valid if Bob measured something else? Then you can't avoid CFD. CFD is a logical necessity of any theory that makes valid predictions for experiments that might not be performed irrespective of ontology.

 

[stevendaryl]

They are not falsifiable. Still does not mean they are not precise.

The point is that they aren't statements that you can reason about, one way or the other.

CFD is not falsifiable either.

No, it's not. CFD is a property of a model, or theory. Given a theory, you can mathematically check whether it satisfies CFD, or not.

 

[stevendaryl]

CFD is a logical necessity of any theory that makes valid predictions for experiments that might not be performed.

I would say that's the definition of CFD. If retrocausal models don't obey CFD, then they don't give definite answers to questions about experiments not performed.

 

[Ralph Dratman]

The point is that FTL is the only way in which you can scientifically explain the correlations.
Definite properties or not is unrelated to the question.

If you believe FTL is involved, how do you explain the impossibility of using these correlations to communicate information?

 

[zonde]

If you believe FTL is involved, how do you explain the impossibility of using these correlations to communicate information?

I don't.
No-communication theorem that says one can't use QM measurements for FTL (or any) communication. This no-go theorem states that performing/not-performing measurement at Alice's side does not change possible result at Bob's side (if I can trust Wikipedia). But the locality condition that allows derivation of Bell type inequality is that measurement angle at Alice's side does not affect possible result at Bob's side.
So it would be more convincing if it can be shown in similar proof that changing measurement angle at Alice's side does not affect possible result at Bob's side.

 

[Demystifier]

If you believe FTL is involved, how do you explain the impossibility of using these correlations to communicate information?

To communicate information, FTL is not enough. What one needs is controllable FTL.

Let me be more specific. Presumably, FTL happens at the level of hidden variables, i.e. variables which, at least with current technology, cannot be directly observed. (Something like atoms before the 20th century.) Since they cannot be observed, it should be clear that they cannot be controlled. And without a control, they cannot be used for any communication, either faster or slower than light.

Very roughly, this is like asking the following question. If there are eagles flying faster than pigeons, then why can't we use them to send messages with a speed faster than the speed of pigeons? That's because eagles (unlike pigeons) cannot be controlled.

 

[RUTA]

That theory is inconsistent. Can it make valid predictions before Bob measured anything? Are those predictions still valid if Bob measured something else? Then you can't avoid CFD. CFD is a logical necessity of any theory that makes valid predictions for experiments that might not be performed irrespective of ontology.

You supply the specific detector settings and outcomes when computing a probability amplitude using path integral. If you want the amplitude for a different experimental configuration and outcome, you have to do an different computation.

 

[billschnieder]

You supply the specific detector settings and outcomes when computing a probability amplitude using path integral. If you want the amplitude for a different experimental configuration and outcome, you have to do an different computation.

And you can do all those possible calculations and obtain definite predictions, even if only one of them is actualized in an experiment. The rest will be Counterfactual definite. You haven't avoided CFD.

 

[RUTA]

And you can do all those possible calculations and obtain definite predictions, even if only one of them is actualized in an experiment. The rest will be Counterfactual definite. You haven't avoided CFD.

You're not seeing the picture. Imagine a field in the spacetime region between Source emission, detector settings (polarizer or SG magnet orientations, for example) and the detector outcomes for a particular trial in the Mermin device. With CFD that field would contain R and G for each setting for each side (Alice and Bob) no matter what the actual settings are. You can imagine three stripes, for example, on each side with each stripe being R or G corresponding to each possible detector setting. That's CFD or what Mermin calls "instruction sets." Now a realistic no-CFD field would have only one color R or G on each side for the actual outcome corresponding to the actual settings of Alice and Bob.

 

[DrChinese]

And you can do all those possible calculations and obtain definite predictions, even if only one of them is actualized in an experiment. The rest will be Counterfactual definite. You haven't avoided CFD.

In this setup, you have avoided it (as RUTA points out). Like Bohmian mechanics, there is no counterfactual case to consider in a retrocausal/blockworld configuration. All of the settings are readily available; and the Bell premise - that a measurement here does not affect an outcome there - is false (rejected).