Bell Non Locality, Quantum Non Locality, Weak Locality, CDP

[stevendaryl]

1:-- I do not understand your claim that "It's just a fact about local realistic theories, which [were] the most complete physical theories prior to quantum mechanics were."

I began with a complete specification of "Bell's Locality Hypothesis":

$P(A_iB_i|αa_ib_iλ_i)=P(A_i|αa_iλ_i)P(B_i|αb_iλ_i);$ [?]

I now understand you to be saying that: "[?] is a fact about local realistic theories, which [were] the most complete physical theories prior to quantum mechanics were."

Does [?] account for the probability of the joint occurrence of a good Apple crop (A) and a good Banana crop (B) from widely separated farms (in a given region) when the growing conditions are correlated by the common rainfall over that region?

Yes, as I said, it applies to every non-quantum theory. I gave you an extensive explanation.

 

[stevendaryl]

2:-- Are you implying that entanglement (the pairwise correlation of particle pairs) via the conservation of total angular momentum in EPRB and Aspect (2004) is not a sufficient and explanatory common cause?

Classically, conservation of momentum would be explained in terms of a "hidden variable", namely momentum itself. You have two particles created by (say) the decay of a more massive particle. Later, after the two particles have separated to a sizable distance, two experimenters perform measurements on the momenta of each of the particles.

So let $P_1(\vec{p_1})$ be the probability distribution for measurements of the momentum of the first particle. Let $P_2(\vec{p_2})$ be the probability distribution for measurement of momentum of the second particle. Let $P(\vec{p_1}, \vec{p_2})$ be the probability distribution for the two momenta.

What we find is that $P(\vec{p_1}, \vec{p_2}) = 0$ unless $\vec{p_2} = -\vec{p_1}$. So obviously, if $P_1(\vec{p_1}) \neq 0$ and $P_2(\vec{p_2}) \neq 0$, then

$P(\vec{p_1}, \vec{p_2}) \neq P_1(\vec{p_1}) P_2(\vec{p_2})$.

Now, look at it from the point of view of a hidden variable $\vec{\lambda}$:

Assume that at the moment of creation, one particle has momentum $\vec{\lambda}$ and the other particle has momentum $- \vec{\lambda}$. So we can take $\vec{\lambda}$ as the hidden variable.

$P(\vec{p_1} | \vec{\lambda}) = 0$ unless $\vec{p_1} = \vec{\lambda}$
$P(\vec{p_2} | \vec{\lambda}) = 0$ unless $\vec{p_2} = - \vec{\lambda}$

So in terms of $\lambda$, we have:

$P(\vec{p_1}, \vec{p_2} | \vec{\lambda}) = P_1(\vec{p_1} | \vec{\lambda}) P_2(\vec{p_2} | \vec{\lambda})$.

So classically, conservation of momentum is explained in a locally realistic way, and Bell's factorizability condition holds. Quantum-mechanically, if the momenta are entangled, then the correlation is not explained in a locally realistic way, and the factorizability condition does not hold.

 

[stevendaryl]

Does [?] account for the probability of the joint occurrence of a good Apple crop (A) and a good Banana crop (B) from widely separated farms (in a given region) when the growing conditions are correlated by the common rainfall over that region?

I believe that if you actually knew all the causal influences on apple and banana crops, then Bell's factorizability condition would hold. Conversely, I believe that if the factorizability condition doesn't hold, that means that there is some common causal influence that you haven't taken into account. This has been said many many times, but you keep asking the question again (in some variation). So what exactly are you looking for?

Something to keep in mind:

1. Pre-quantum physics was deterministic.
2. Every deterministic theory is factorizable in Bell's sense.

You can actually go further, and allow some nondeterminism, as long as the nondeterminism is local randomness. For example, suppose you have a world that is deterministic (with causal influences limited by the speed of light) except for coin flips, and a coin flip gives a completely unpredictable 50/50 chance of getting heads or tails. As long as coin flips of different coins are independent, then Bell's factorizability condition will hold.

 

[PeterDonis]

Does [?] describe the prediction for drawing (without replacement) an Ace (A) and a King (B) from a standard deck of 52 playing cards?

No, because there are no independent measurement settings $a$ and $b$ in this scenario; the first draw affects the "settings" of the second draw, because one card is now missing from the deck when the second draw is made.

I do not understand your claim that: "[?] does correctly describe the predictions of every theory we have except QM."

Set up a scenario where the measurements, whose settings are described by $a$ and $b$, are spacelike separated, and stipulate that $a$ and $b$ are independent. Include all information that is in the past light cones of both measurement events in $\lambda$. Then every theory we have except QM predicts that [?] will hold for the correlations between measurement results.

Technically, the spacelike separated condition is not necessary, as long as you can ensure that the settings $a$ and $b$ are independent, and properly distinguish those independent settings from the information $\lambda$ that is common to both measurements. But your repeated attempts to construct scenarios in this thread have illustrated how hard it is in practice to do that properly for measurements that are not spacelike separated.

 

[rubi]

I consider your last sentence to verge on being abusive. It's a tautology to say that there is a theory that makes the same predictions as quantum mechanics--quantum is an example. The issue is what kind of theory quantum mechanics is.

It is perfectly clear what kind of theory quantum mechanics is, because there are axiomatic formulations, in which it is an undeniable fact that only measurable things have a correspondence in the theory. Denying this is a personal belief and completely unscientific. We have clear terms for people who think that their personal beliefs can replace scientific knowledge. One can't expect to be entitled an opinion on scientific questions if one refuses to accept scientific standards.

Would it be ok to say that:
we must be able to repeat the experiment and the prediction must be correct in 100% of the cases except those cases where there is power outage at Bob's laboratory?

Power outages are the same situation. Even if were possible to check the predictions in situations of unaligned angles (reminder: it isn't), we still couldn't be sure if they were still true in the case of power outages. Of course, for practical purposes this doesn't matter. The difference is that the power outage situation is sufficiently classical and it so happens that there is enough decoherence going on and the system behaves like one would classically expect. But of course, it is theoretically possible (but practically impossible) to shield macroscopic objects from decohering and then of course, the state of the power could also be entangled with the system.

 

[PeterDonis]

Even if were possible to check the predictions in situations of unaligned angles (reminder: it isn't)

Can you clarify what you mean by this? We can certainly run experiments with unaligned angles at the two measurements, and collect data on the correlations between the results, and compare those with the predictions from theory on the correlations.

 

[stevendaryl]

It is perfectly clear what kind of theory quantum mechanics is, because there are axiomatic formulations, in which it is an undeniable fact that only measurable things have a correspondence in the theory. Denying this is a personal belief and completely unscientific.

Well, I disagree.

 

[rubi]

Can you clarify what you mean by this? We can certainly run experiments with unaligned angles at the two measurements, and collect data on the correlations between the results, and compare those with the predictions from theory on the correlations.

I was referring to my earlier posts in this thread. What I'm saying is that it is impossible in principle to measure the spin of a particle along two different angles $\alpha$ and $\alpha'$ simultaneously. No experimenter can design an experiment that can accomplish this. You can't calculate correlations between such angles, because they never co-occur. The correlations in Bell tests are of a different kind. They correlate things that can be measured simultaneously (a single spin of Alice commutes with a single spin of Bob) an do indeed co-occur.

Well, I disagree.

Then I have to refer you to the peer-reviewed literature on CH for instance, where it is stated unamiguously. If you disagree, scientific standards would require you to respond to the literature and undergo a peer-review process.

 

[stevendaryl]

Then I have to refer you to the peer-reviewed literature on CH for instance, where it is stated unamiguously. If you disagree, scientific standards would require you to respond to the literature and undergo a peer-review process.

If there were anything like a consensus that consistent histories is the correct interpretation of quantum mechanics, there would not be any discussions such as this. I think your pretending that there is a consensus when there is none is just bullying.

 

[rubi]

If there were anything like a consensus that consistent histories is the correct interpretation of quantum mechanics, there would not be any discussions such as this. I think your pretending that there is a consensus when there is none is just bullying.

I'm not saying that there is consensus that it is the correct interpretation. I'm saying that it is one working example of a theory, where only measurable things are represented within the theory. One example is enough to debunk zonde's claims.

(By the way, CH is just Copenhagen, formulated in a conceptually clear and axiomatic way. It's not like it was non-standard. Everyone is using it already without knowing.)

 

[stevendaryl]

If there were anything like a consensus that consistent histories is the correct interpretation of quantum mechanics, there would not be any discussions such as this. I think your pretending that there is a consensus when there is none is just bullying.

Reluctantly, I am planning to take advantage of the "ignore" option here.

 

[Strilanc]

I think you mean that outside of QM there are no examples of violations of the locality condition, correct? QM violates it, but we don't know of any other theory that does.

That's incorrect. There are many thought-experiment models that violate the Bell inequalities without allowing for communication. For example, "non-local boxes".

A specific classic example is the "Popescu-Rohrlich Box", which is a thought-experiment where you have a magic pair of boxes that wins CHSH games more than quantum mechanics can. Yet having such a pair of boxes still doesn't allow for FTL communication. There are many many other variants of this idea. If we managed to find a PR-box in the real world, that would prove there was major flaws in quantum mechanics.

 

[stevendaryl]

That's incorrect. There are many thought-experiment models that violate the Bell inequalities without allowing for communication. For example, "non-local boxes".

I think @PeterDonis meant that there are no examples consistent with pre-quantum physics.

 

[Strilanc]

I think @PeterDonis meant that there are no examples consistent with pre-quantum physics.

That's correct. iI you limit yourself to classical physics with a finite speed of propagation for forces, then you don't have these effects.

 

[PeterDonis]

What I'm saying is that it is impossible in principle to measure the spin of a particle along two different angles $\alpha$ and $\alpha'$ simultaneously.

Ah, ok, got it.

 

[rubi]

There are some situations, where the factorization condition can also be violated classically. For example, if you perform post-selection on some data set. Assume Alice and Bob throw dies and the corresponding data sets are $(A_i)_i$ and $(B_i)_i$. Then you can post-select only those events where $A_i = B_i$ and you will get perfect correlations even though the factorization condition will be violated. There are also some other ways to violate the condition. Classically, all of them can be fixed by coming up with more general conditions, but it already shows that the factorization condition is a heuristic rather than a law of nature.

 

[zonde]

I will try to make my point using older statement in this thread:

The question is: Can the EPR argument be applied to the situation when Alice and Bob measure different angles? And the answer is undeniably no, it can't, because in such a situation, Alice would have to make a prediction that cannot even in principle be tested experimentally.

This statement is of course correct but it is missing the point.
So I would ask different question: Can the EPR argument be applied to the model that is Einstein's local and not superdeterministic?
And the answer is yes, using following reasoning:
1) For a model that is not superdeterministic measurement angles are external parameters and it has to produce predictions for any measurement angle.
2) If model is Einstein's local it has to produce predictions independently for Alice and Bob (when Alice's and Bob's measurements are spacelike separated).
Putting 1) and 2) together the model has to produce two sets of independent predictions for Alice and Bob that can be compared and for the cases where Bob's and Alice's measurement angles are the same we can apply EPR argument.

So the next question would be - can we compare (correlate) predictions of model where Alice's and Bob's measurement angles are different? And the answer to this question seems to be that they better be comparable as we do that a lot in real entanglement experiments.

 

[rubi]

This statement is of course correct but it is missing the point.

No, it doesn't miss the point. You don't want to acknowledge the fact that unmeasurable quantities don't need to exist and that models needn't model unmeasurable quantities. And there are examples that prove that you are wrong.

For a model that is not superdeterministic measurement angles are external parameters and it has to produce predictions for any measurement angle.

That's just false. You have just stated your personal belief without any argument. You have hidden variables in mind and think that your intuitions about them also hold for non-hidden variable models. But there is just no way to argue that unmeasurable quantities must exist.

What you and Denis are trying to argue is: There must be predictions for any angle and thus we can use the EPR argument to conclude that there must be predictions for any angle. It's circular reasoning and cannot be saved. Either you postulate it as an axiom, as you just did. Then it can be denied (for instance by QM). Or you try to use the EPR argument, but then you must admit that your reasoning is circular and therefore unacceptable.

So the next question would be - can we compare (correlate) predictions of model where Alice's and Bob's measurement angles are different? And the answer to this question seems to be that they better be comparable as we do that a lot in real entanglement experiments.

We don't correlate quantities that never co-occur, such Bob's spins along different angles. It doesn't even make sense to speak about correlations of things don't co-occur. QM beautifully prevents us from doing this by having the corresponding operators not commute. The correlations between Alice and Bob can of course also be calculated in QM, but that's irrelevant for your argument, since correlations for different angles are not perfect and thus can't be used to predict anything with certainty, contrary to what the EPR argument would require.

 

[zonde]

You don't want to acknowledge the fact that unmeasurable quantities don't need to exist and that models needn't model unmeasurable quantities.

I acknowledge that unmeasurable quantities don't need to exist and that models needn't model unmeasurable quantities.

For a model that is not superdeterministic measurement angles are external parameters and it has to produce predictions for any measurement angle.

That's just false.

Which part is false?
Is this part false? - "For a model that is not superdeterministic measurement angles are external parameters"
Or the other part?
Argument for the other part (if the first part is ok) is as follows:
As measurement angles are external parameters, experimentalist can choose whichever angle he wants and test prediction for that angle. Predictions have to be made before test is performed.
As experimentalist's choice lies outside the model, predictions have to be made independently from that choice and before the measurement.
For me it seems enough to claim that the model should be capable of producing predictions for any measurement angle.

 

[rubi]

Is this part false? - "For a model that is not superdeterministic measurement angles are external parameters"

Yes, this part is false. QT is capable of modeling measurement angles within the model and it is definitely not superdeterministic. No fine-tuning is required.

Or the other part?
Argument for the other part (if the first part is ok) is as follows:
As measurement angles are external parameters, experimentalist can choose whichever angle he wants and test prediction for that angle. Predictions have to be made before test is performed.
As experimentalist's choice lies outside the model, predictions have to be made independently from that choice and before the measurement.
For me it seems enough to claim that the model should be capable of producing predictions for any measurement angle.

This is false as well. An experimenter can predict whatever he or she wants. This does not imply that there must be something corresponding to that prediction. If I predict that there is a pink unicorn behind you, it is not necessarily true. If Alice predicts that the spin of Bob's particle along the angle $\alpha$ is so and so, even though his detector is aligned along a different angle $\beta\neq\alpha$, this doesn't imply that Bob's particle has a spin along the angle $\alpha$. And given that it is impossible in principle to test such a prediction, there is no reason to expect that the prediction would be correct. And we understand the issue very well. QT is contextual and that means that properties that don't commute with all observables emerge from the experimental setup rather than existing independent of the setup.

 

[zonde]

Yes, this part is false. QT is capable of modeling measurement angles within the model and it is definitely not superdeterministic. No fine-tuning is required.

Well, but you can model only one measurement angle at the same time, and which particular angle you are modeling you take from outside the model as external parameter.
Maybe this will be more clear - "For a model that is not superdeterministic choice of measurement angle is external parameter"

This is false as well. An experimenter can predict whatever he or she wants. This does not imply that there must be something corresponding to that prediction. If I predict that there is a pink unicorn behind you, it is not necessarily true.

"Pink unicorn behind you" is hypothesis not prediction. Prediction would be statement about what I would observe if I turn around.

If Alice predicts that the spin of Bob's particle along the angle $\alpha$ is so and so, even though his detector is aligned along a different angle $\beta\neq\alpha$, this doesn't imply that Bob's particle has a spin along the angle $\alpha$.

Predictions are conditional. If you do such and such you will observe this. What you are talking about is hypothesis not prediction.