Is there any hope at all for Locality?

[bhobba]

For locality with probability and statistics see:www.arxiv.org/pdf/quant-ph/0007005v2.pdf

Yes indeed it does seem that entanglement with its strange correlations is the key thing that separates standard probability theory from QM:
http://arxiv.org/pdf/0911.0695v1.pdf

Thanks
Bill

 

[meBigGuy]

I'd like to move forward to refine, my definition of observer. I still say that an observer is anything that interacts with an observed (or symmetrical observer) within space/time. A particle collides with another, or, a photon is absorbed. Consciousness, awareness, note-taking, detection, are all superfluous to observation in a QM sense. I think you can just say that energy must change (exchange?). I specify within space-time because a photon exists on it's long trek to my eye. (Feynman talked about that).

The Albert's-socks discussion makes a significant point about the existence of "that which is not observed", and that point is key to entanglement. The difference between "preparing the dresser" and "arranging the socks", if you will.

 

[bhobba]

I'd like to move forward to refine, my definition of observer. I still say that an observer is anything that interacts with an observed (or symmetrical observer) within space/time.

You can define it as anything you like, but the usual definition of an observation is its an interaction that leaves a mark here in the macro world. An observer is anything capable of doing it. QM is a theory about the outcomes of observations as defined the way I did it. It is not a theory about the way you defined it because QM does not tell us anything until it is actually observed, by which is meant a mark is left.

I think it would be useful for you to learn about QM from a modern textbook such as Ballentine - QM - A Modern Development where it is developed from 2 axioms - one of which is based on the definition I gave previously.

Thanks
Bill

 

[harrylin]

[..] The correlations in Bell's theorem imply that Alice measuring spin along a certain axis has an instantaneous effect on the probability distribution of the results of Bob's measurement. So retreating into the indeterminacy of the Copenhagen interpretation does not appear to have allowed us to preserve locality since an instantaneous effect has occurred across a spacelike interval.[..]

No instantaneous physical effect at a distance has to occur at all for an instantaneous effect on the probability distribution somewhere else (according to us here), as Bell also clarified in the introduction of his "Bertlmann's socks" paper.
As you likely realize, the issue is much trickier than that.

 

[stevendaryl]

For locality with probability and statistics see:www.arxiv.org/pdf/quant-ph/0007005v2.pdf

What the authors are saying here doesn't seem correct to me. Bell's "vital assumption" is that for the EPR twin-pair experiment, the result of the measurement at one detector does not depend on the settings of the distant detector. The authors say that Bell's inequality does not depend on this assumption, but that seems completely wrong.

Let's define two functions

F^{(1)}_a(\lambda, m_1, m_2)
F^{(2)}_a(\lambda, m_1, m_2)

[edit:]
(where m_1 is the detector settings at the first detector, and m_2 is the detector settings at the other detector) as follows:

F^{(1)}_a(\lambda, m_1, m_2) = +1 if 0 \leq \lambda < \frac{1}{2}.
= -1 if \frac{1}{2} \leq \lambda \leq 1.

F^{(2)}_a(\lambda, m_1, m_2) = +1 if 0 \leq \lambda < \frac{1}{2} sin^2(\frac{\theta}{2}).
= -1 if \frac{1}{2} sin^2(\frac{\theta}{2})\leq \lambda \leq 1.

where \theta is the angle between the two detector orientations. That's a perfectly deterministic (although non-local) "hidden variable" theory that reproduces exactly the predictions of QM and violates Bell's inequality.

 

[meBigGuy]

"You can define it as anything you like, but the usual definition of an observation is its an interaction that leaves a mark here in the macro world." "QM does not tell us anything until it is actually observed, by which is meant a mark is left"

Are you saying that QM tells us nothing about an electron that has not yet been measured?

Again, I want to better understand the nuances of "preparing the dresser" and "arranging the socks". The socks exist, but have not been observed *yet*. QM tells us nothing about them?

 

[harrylin]

What the authors are saying here doesn't seem correct to me. Bell's "vital assumption" is that for the EPR twin-pair experiment, the result of the measurement at one detector does not depend on the settings of the distant detector. The authors say that Bell's inequality does not depend on this assumption, but that seems completely wrong.

Let's define two functions

F^{(1)}_a(\lambda, m_1, m_2)
F^{(2)}_a(\lambda, m_1, m_2)

[edit:]
(where m_1 is the detector settings at the first detector, and m_2 is the detector settings at the other detector) as follows:

F^{(1)}_a(\lambda, m_1, m_2) = +1 if 0 \leq \lambda < \frac{1}{2}.
= -1 if \frac{1}{2} \leq \lambda \leq 1.

F^{(2)}_a(\lambda, m_1, m_2) = +1 if 0 \leq \lambda < \frac{1}{2} sin^2(\frac{\theta}{2}).
= -1 if \frac{1}{2} sin^2(\frac{\theta}{2})\leq \lambda \leq 1.

where \theta is the angle between the two detector orientations. That's a perfectly deterministic (although non-local) "hidden variable" theory that reproduces exactly the predictions of QM and violates Bell's inequality.

Likely you mean the inverse of the second function, but that's a detail. If I see it correctly, the probabilities are not the same for your two functions. While you refer to the same λ, the effective hidden parameter functions are different because they are different functions of that λ.The authors say that what Bell's inequality depends on, is that the random variables are defined on the same probability space.

BTW, it seems to me that on p.14 the first time that they use "predetermined", they mean "pre-existing" or "fixed". They explain it better further on.

 

[bhobba]

Are you saying that QM tells us nothing about an electron that has not yet been measured?

Exactly. Other than probabilities of what you would get if you were to measure it - nothing.

I will say it again. QM is a theory about the results of interactions with other systems where those systems leave a mark here in the common sense macro world. What properties it has otherwise it is silent about.

Now a question for you. You do understand that all a state tells you is the possible outcomes of an observable and their probabilities?

This sock thing you keep on talking about is simply a thought experiment illustrating the correlations of entangled systems. This is that some systems are such that if you measure the state of one part of the system you know automatically the state of another part of the system and the result you would get if you were to measure it, even if that other part is on the other side of the universe. This is one of the weird aspects of entanglement. It changes nothing about what a system state tells us, which is about the results of observations.

Here is a way of looking at QM at a foundational level that may make it clearer. Suppose you have a system and some observational apparatus that has n possible outcomes and you associate a number with each of the outcomes. This is represented by a vector of size n with n numbers yi. To bring this out write it as Ʃyi |bi>. Now we have a problem. The |bi> are freely chosen so nature can not depend on them. We need a way to represent it that does not depend on that. The way QM gets around it is to replace the |bi> by |bi><bi| giving Ʃyi |bi><bi|. This is defined as the observable of the observational apparatus. It says to each such apparatus there is a Hermitian operator whose eigenvalues are the possible outcomes of the observation. This is the first axiom of QM. The second axiom says the expected outcome of such an observation is Tr(PR) where R is the observable of the observation and P is a positive operator of unit trace called the state of the system. This can be proven by what is known as Gleason's Theorem if we assume something called non contextuality that you can read up on if you wish. So while the second axiom is not implied by the first it is strongly suggested by it - depending on exactly what you think of non-contextuality.

It is an interesting fact that all of QM is contained in those two axioms. To get the detail see Ballentine's book. The point here though is right at its foundations it is a theory about one and only one thing - the outcome of observations as indicated by observational apparatus.

Thanks
Bill

 

[stevendaryl]

Likely you mean the inverse of the second function, but that's a detail. If I see it correctly, the probabilities are not the same for your two functions. While you refer to the same λ, the effective hidden parameter functions are different because they are different functions of that λ.The authors say that what Bell's inequality depends on, is that the random variables are defined on the same probability space.

BTW, it seems to me that on p.14 the first time that they use "predetermined", they mean "pre-existing" or "fixed". They explain it better further on.

What I described is a single hidden variable, \lambda, that is shared by the two experimenters. It's the same probability space. But Alice's result is a different function of \lambda than Bob's result. That must be the case, because if Alice and Bob both measure the spin in the same direction, one of them will get spin-up, and the other will get spin-down. They can't possibly have the same dependence on \lambda if they get opposite results for the same \lambda.

 

[stevendaryl]

What the authors are saying here doesn't seem correct to me. Bell's "vital assumption" is that for the EPR twin-pair experiment, the result of the measurement at one detector does not depend on the settings of the distant detector. The authors say that Bell's inequality does not depend on this assumption, but that seems completely wrong.

Let's define two functions

F^{(1)}_a(\lambda, m_1, m_2)
F^{(2)}_a(\lambda, m_1, m_2)

[edit:]
(where m_1 is the detector settings at the first detector, and m_2 is the detector settings at the other detector) as follows:

F^{(1)}_a(\lambda, m_1, m_2) = +1 if 0 \leq \lambda &lt; \frac{1}{2}.
= -1 if \frac{1}{2} \leq \lambda \leq 1.

F^{(2)}_a(\lambda, m_1, m_2) = +1 if 0 \leq \lambda &lt; \frac{1}{2} sin^2(\frac{\theta}{2}).
= -1 if \frac{1}{2} sin^2(\frac{\theta}{2})\leq \lambda \leq 1.

where \theta is the angle between the two detector orientations. That's a perfectly deterministic (although non-local) "hidden variable" theory that reproduces exactly the predictions of QM and violates Bell's inequality.

[edit: I made a mistake in defining the two functions. Here's what I should have written:]

F^{(1)}_a(\lambda, m_1, m_2) = +1 if 0 \leq \lambda &lt; \frac{1}{2}.
= -1 if \frac{1}{2} \leq \lambda \leq 1.

F^{(2)}_a(\lambda, m_1, m_2) = +1 if 0 \leq \lambda &lt; \frac{1}{2} sin^2(\frac{\theta}{2}).
= -1 if \frac{1}{2} sin^2(\frac{\theta}{2})\leq \lambda \leq \frac{1}{2} (1 + sin^2(\frac{\theta}{2})).
= +1 if \frac{1}{2} (1 + sin^2(\frac{\theta}{2})) \leq \lambda \leq 1

This gives
P(A) = P(B) = \frac{1}{2}
P(A \wedge B) = P(\neg A \wedge \neg B) = \frac{1}{2}sin^2(\theta)

 

[stevendaryl]

Likely you mean the inverse of the second function, but that's a detail.

Yes, I made a mistake in defining the two functions.

 

[harrylin]

What I described is a single hidden variable, \lambda, that is shared by the two experimenters. It's the same probability space. But Alice's result is a different function of \lambda than Bob's result. That must be the case, because if Alice and Bob both measure the spin in the same direction, one of them will get spin-up, and the other will get spin-down. They can't possibly have the same dependence on \lambda if they get opposite results for the same \lambda.

Indeed the results cannot have the exact same dependence; but that's not the point. Maybe I misunderstand what is meant with single probability space? I don't think that a single probability space just means a common variable. And it seems that according to them it means that the probabilities are complementary, at least in the context of Bell's theorem.

Compare Bell (in Bertlmann's socks):
'we have to consider then some probability distribution ρ(λ) over these complementary variables, and it is for the averaged probability (..) that we have quantum mechanical predictions.'

 

[stevendaryl]

Indeed the results cannot have the exact same dependence; but that's not the point. Maybe I misunderstand what is meant with single probability space? I don't think that a single probability space just means a common variable. And it seems that according to them it means that the probabilities are complementary, at least in the context of Bell's theorem.

You have a single variable, \lambda. You have a single probability distribution, P(\lambda). I don't know what else you want.

Compare Bell (in Bertlmann's socks):
'we have to consider then some probability distribution ρ(λ) over these complementary variables, and it is for the averaged probability (..) that we have quantum mechanical predictions.'

I think he's just saying what I was saying. You have the quantum mechanical prediction:

P(A \wedge B | \alpha \wedge \beta) = \frac{1}{2} sin^2(\frac{\theta}{2})

where \theta is the angle between the two detector orientations \alpha and \beta

To explain this in terms of local variables is to have a probability distribution P(\lambda) and conditional probabilities P_A(\lambda, \alpha) and P_B(\lambda, \beta) so that

P(A \wedge B | \alpha \wedge \beta) = \sum_\lambda P(\lambda) P_A(\lambda, \alpha) P_B(\lambda, \beta)

 

[meBigGuy]

Exactly. Other than probabilities of what you would get if you were to measure it - nothing.

Actually, that is a lot since that says it exists. I'm trying to get at the root of the non-existance of things that don't interact. The unmeasured electron is interacting (exerting a force, charge, etc) in a probablistic way. QM's probabilities tells us a lot about it, even though it has not yet been measured.

This sock thing you keep on talking about is simply a thought experiment illustrating the correlations of entangled systems.

Right. And the point it makes about existence is significant and I'm having trouble communicating it. Things exist that have not yet been measured. Things do not exist that we cannot know anything about.

These spooky effects force us to answer the question 'does something exist if we can not know anything about it?' with a resounding 'no'. What can not be observed does not exist. This is not a crazy philosophical thought, but a hard experimental fact.

So the difference between "What can not be observed" and "What has not been measured" is a big deal, and thought-experiment-wise is expressed in the difference between "preparing the dresser" and "arranging the socks".

So, how does that tie in with "Is there any hope for Locality". I suppose it doesn't. Observation of A is also observation of B. They just exist. You can't consider the alternatives or what might have been.

 

[harrylin]

You have a single variable, \lambda. You have a single probability distribution, P(\lambda). I don't know what else you want.

You mean what they seem to want; which is, I think, a single probability distribution for both photons like that of balls in a box.

I think he's just saying what I was saying. You have the quantum mechanical prediction:

P(A \wedge B | \alpha \wedge \beta) = \frac{1}{2} sin^2(\frac{\theta}{2})

where \theta is the angle between the two detector orientations \alpha and \beta

To explain this in terms of local variables is to have a probability distribution P(\lambda) and conditional probabilities P_A(\lambda, \alpha) and P_B(\lambda, \beta) so that

P(A \wedge B | \alpha \wedge \beta) = \sum_\lambda P(\lambda) P_A(\lambda, \alpha) P_B(\lambda, \beta)

Are you sure that your example has a probability distribution of "complementary variables" such as what Bell referred to?

If your example has indeed that (his eq.11):

P(A,B¦a,b,λ) = P₁(A¦a,λ) P₂(B¦b,λ)

then it should not break his inequality.

That is what Bell referred to with 'we have to consider then some probability distribution ρ(λ) over these complementary variables'

 

[bhobba]

Actually, that is a lot since that says it exists.

Why do you say that? I think most people would say for something to exist it should exist independent of observation. If all you can do is predict the probabilities of outcomes if you were to observe it it has a pretty strange sort of existence. QM is a theory about RELATIONS - the relation of quantum systems to other quantum systems we call observers. It has no existence independent of that. If you have a universe with a single electron in it you would know nothing, zero, zilch about it because it needs to interact with an observer.

The trouble with this stuff is it boils down to how you interpret words which is really the game of philosophy - not physics.

Right. And the point it makes about existence is significant and I'm having trouble communicating it. Things exist that have not yet been measured.

That's not what entangled correlations do at all. It says measurement is non local ie when you measure stuff here you are effectively measuring it over there. When you do a measurement a system changes state. For entangled systems that state can have spatial extent - that's it - that's all. The modern theory of measurement is that measurement is a kind of entanglement. So when you measure an entangled system the system doing the measuring becomes entangled and effectively part of a system that can be extended beyond where you are measuring. It doesn't mean things exist that have not been measured.

I really think you would benefit from watching Lenoard Susskind's lectures on it:
http://theoreticalminimum.com/courses/quantum-entanglement/2006/fall

Thanks
Bill

 

[stevendaryl]

You mean what they seem to want; which is, I think, a single probability distribution for both photons like that of balls in a box.

Are you sure that your example has a probability distribution of "complementary variables" such as what Bell referred to?

If your example has indeed that (his eq.11):

P(A,B¦a,b,λ) = P₁(A¦a,λ) P₂(B¦b,λ)

I'm saying the same thing.

then it should not break his inequality.

What should not break his inequality? I didn't claim that there was a probability distribution of that form that violated Bell's inequality. There provably is not one. What I said was that if you allow the conditional probability of B to depend on a, you can break the inequality:

[edit: it did say "depend on b"]

P(A,B | a,b,\lambda) = P_1(A | a,λ) P_2(B | a, b,\lambda)

 

[harrylin]

I'm saying the same thing.
[..] I didn't claim that there was a probability distribution of that form that violated Bell's inequality. There provably is not one. What I said was that if you allow the conditional probability of B to depend on b, you can break the inequality:

P(A,B | a,b,\lambda) = P_1(A | a,λ) P_2(B | a, b,\lambda)

Once more, it appears to me that you state the same - just looking at it from another angle - as what is said in the part that you think to be wrong, in #55.

 

[stevendaryl]

Once more, it appears to me that you state the same - just looking at it from another angle - as what is said in the part that you think to be wrong, in #55.

Somehow we're not understanding each other. My claim (and I think it's the same as Bell's) is that

1. Any joint probability distribution of the form:P(A, B | \alpha, \beta) = \sum_\lambda P(\lambda) P(A | \alpha, \lambda) P(B| \beta, \lambda)
   will obey Bell's inequality.
2. A probability distribution of the form: P(A, B | \alpha, \beta) = \sum_\lambda P(\lambda) P(A | \alpha, \lambda) P(B| \alpha, \beta, \lambda)
   can violate Bell's inequality.

So what I'm saying is wrong is that a probability distribution of the form 1 can violate Bell's inequality--it can't. I'm also saying that it's wrong to say that a probability distribution of the form 2 will STILL obey Bell's inequality.

I've seen people who claim Bell is wrong because 1 above is false, and I've seen people who claim that Bell is wrong (or at least, irrelevant) because 2 above is false.

 

[harrylin]

Somehow we're not understanding each other. My claim (and I think it's the same as Bell's) is that

1. Any joint probability distribution of the form:P(A, B | \alpha, \beta) = \sum_\lambda P(\lambda) P(A | \alpha, \lambda) P(B| \beta, \lambda)
   will obey Bell's inequality.
2. A probability distribution of the form: P(A, B | \alpha, \beta) = \sum_\lambda P(\lambda) P(A | \alpha, \lambda) P(B| \alpha, \beta, \lambda)
   can violate Bell's inequality.

It appears to me that it is just that point that is stressed in the section following the section that you think to be wrong. Their disagreement with Bell is about which kind of physical models can match which distributions. I don't know if they are right but I'm pretty sure that they agree with the point that you try to make.

Once more, I interpret their assertion that a requirement for the inequality to hold is "that the random variables are defined on the same probability space" as referring to the equation that Bell referred to with similar phrasing. That happens to be your first equation here above, which you also assert to be required for the inequality to hold.

I'm sorry, I don't know how to say clearer that when one person says 1+1=2 and another says that instead 2-1=1, that they say the same thing...

 

[stevendaryl]

It appears to me that it is just that point that is stressed in the section following the section that you think to be wrong. Their disagreement with Bell is about which kind of physical models can match which distributions. I don't know if they are right but I'm pretty sure that they agree with the point that you try to make.

Once more, I interpret their assertion that a requirement for the inequality to hold is "that the random variables are defined on the same probability space" as referring to the equation that Bell referred to with similar phrasing. That happens to be your first equation here above, which you also assert to be required for the inequality to hold.

I'm sorry, I don't know how to say clearer that when one person says 1+1=2 and another says that instead 2-1=1, that they say the same thing...

That's perfectly clear, it's just completely wrong. They are not saying the same thing. The authors say:

Summing up: Theorem (1) proves that Bell’s inequality is satisfied if one takes as hypothesis the negation of his “vital assumption”. From this we conclude that Bell’s “vital assumption” not only is not “vital” but in fact has nothing to do with Bell’s inequality.

I'm saying exactly the opposite of that, that Bell's "vital assumption" is necessary to prove Bell's inequality.

I don't know why you think we are saying the same thing, when we are saying exactly the opposite.

 

[harrylin]

That's perfectly clear, it's just completely wrong. They are not saying the same thing. [..]
I'm saying exactly the opposite of that, that Bell's "vital assumption" is necessary to prove Bell's inequality.

I don't know why you think we are saying the same thing, when we are saying exactly the opposite.

[correction:] Indeed, here you seem to be saying that probability due to "locality" is vital, which is the opposite of what they say, and which they claim to have proven (and your counter example misses it*).
It may well be that what they mean with "the same probability space" differs from the separation of variables; I haven't yet thought about that, sorry!
I replied to your post #55 because that was (and still is) pretty clear to me.

*PS one last try. As I understand it:
- they claim that "locality" is not essential for not breaking (or breaking) the inequality; what matters is the "same probability space".
- in #55 you claim that they are wrong because it is possible to break the inequality without the "locality" condition.
However, that is compatible with what they say (except for the "they are wrong" part).

 

[stevendaryl]

Yes, sure, here you seem to be saying that probability due to "locality" is vital, which is the opposite of what they say, and which they claim to have proven (and your counter example misses it). However it looks to me that one post back you said exactly what they said on a slightly different point - indeed, they emphasize the difference!

Well, it seems to me that the paper has nothing new to say about Bell's inequality. Their example is supposed to show that it is possible for a non-local interaction to still obey Bell's inequality. I don't think that was ever in dispute. Nobody ever said that "Every nonlocal interaction violates Bell's inequality", what they've said is "Every local interaction satisfies Bell's inequality". Yes, the authors claim that the latter is false, also, but they don't prove that in this paper.

 

[harrylin]

Well, it seems to me that the paper has nothing new to say about Bell's inequality.

Note that I'm not sure anymore if your later post agreed with what they say; however that is irrelevant for my explanation why your counter example isn't one.

 

[stevendaryl]

Note that I'm not sure anymore if your later post agreed with what they say; however that is irrelevant for my explanation why your counter example isn't one.

Papers about Bell's inequality seem to universally be bad. They make big claims, and then when you spend the trouble to figure out exactly what they are claiming, it turns out either to be wrong, or beside the point. That's my experience, anyway.

 

[DrChinese]

True, such authors basically say: "Everybody else is wrong". And then forget to present a convincing argument as to why. I have an entire folder of links, incomprehensible arguments with no regard to the obvious questions that arise immediately.

 

[harrylin]

Papers about Bell's inequality seem to universally be bad. They make big claims, and then when you spend the trouble to figure out exactly what they are claiming, it turns out either to be wrong, or beside the point. That's my experience, anyway.

Most papers and commentaries that I have seen on this topic were not very satisfying to me either... However the last two papers which I only discovered two hours ago (one linking to the other) may change that; I'm continuing to read up on this topic.

 

[audioloop]

I don't see how it means that. As I said, it's self-consistent to ignore events of probability zero, but the conclusion that probability zero MEANS that it won't happen isn't justified.

something like, how can an event occur and the same time a probability of not occur ?
(an inverse case)are probabilities incompatible with determinism ?

.

 

[RUTA]

Then what you call 'objective reality' is not fully objective. I have not seen to date a fully objective reality in agreement with the postulates of qm, except maybe the bohemian interpretation. An objective reality that is completely macroscopically causal cannot arise out of indeterminism or multiple possibilities(the MWI). If macroscopic causality is emergent or simply apparent, then objective reality isn't really objective. I am seeking a definition of the adjective 'objective' that both people on the street and Nobel prize winners would collectively agree to and people engaged in fundamental physics are much more flexible about reality than the general population.

I'm not sure what you mean by "objective reality," so here are the slides from our talk at Foundations 2013 in Munich last month. I'm assuming audioloop meant Relational Blockworld when he wrote "RBW." If not, ignore this post with my apologies.

http://users.etown.edu/s/stuckeym/Foundations2013.pdf

We're still working on the corresponding paper (will go into an IOP collection on QG this fall) and expect to have it posted this week. The conference website will then link to it. The version currently posted on the conference website was submitted months ago and does not reflect the progress made since.

 

[stevendaryl]

something like, how can an event occur and the same time a probability of not occur ?
(an inverse case)


are probabilities incompatible with determinism ?

.

Sure. But for a deterministic theory, probabilities always reflect ignorance of initial conditions.

 

[audioloop]

I'm not sure what you mean by "objective reality," so here are the slides from our talk at Foundations 2013 in Munich last month. I'm assuming audioloop meant Relational Blockworld when he wrote "RBW." If not, ignore this post with my apologies.

http://users.etown.edu/s/stuckeym/Foundations2013.pdf

We're still working on the corresponding paper (will go into an IOP collection on QG this fall) and expect to have it posted this week. The conference website will then link to it. The version currently posted on the conference website was submitted months ago and does not reflect the progress made since.

right, i did.


.

 

[audioloop]

Sure. But for a deterministic theory, probabilities always reflect ignorance of initial conditions.

and the case that where probabilities are compatible with determinism ?



.

 

[stevendaryl]

and the case that where probabilities are compatible with determinism ?

.

Probabilities are compatible with determinism if they arise through ignorance of the initial conditions. That's the case in classical statistical mechanics.

 

[mfb]

Sure. But for a deterministic theory, probabilities always reflect ignorance of initial conditions.

Or ignorance of the full system ("I see outcome X, but outcome Y is seen as well in another branch"), as in MWI.

 

[audioloop]

I'm not sure what you mean by "objective reality," so here are the slides from our talk at Foundations 2013 in Munich last month. I'm assuming audioloop meant Relational Blockworld when he wrote "RBW." If not, ignore this post with my apologies.

http://users.etown.edu/s/stuckeym/Foundations2013.pdf

We're still working on the corresponding paper (will go into an IOP collection on QG this fall) and expect to have it posted this week. The conference website will then link to it. The version currently posted on the conference website was submitted months ago and does not reflect the progress made since.

then, in RBW there are no probabilities per se.
that make some logic, because it is thought that classical mechanics is a full deterministic theory and is not, same thing for quantum mechanics that is full probabilistic theory and is not, in the case of classical mechanics there are examples of departures of determinism, The Norton Dome* among others examples. In quantum mechanics supposedly non-deterministic theory , the Schrödinger (126 birthday today ) equation which is of deterministic nature and so on. then and consequently IMO probabilities are case sensitive or context dependant, is argued that that objective probabilities are incompatible (unlike of subjective probalities i.e. ignorance) with determinism but what can be done cos classical mechanics heve departures of the full determinism postulated or assumed, an event is determined to occur, but some probability is assigned to it not occurring !
objective probability rest on chance and subjective probabilty rest on ignorance.

RBW erases objective and subjective probabilities at once and ends the problem.*Causation as Folk Science, J. Norton.

 

[RUTA]

then, in RBW there are no probabilities per se.

I don't want to hijack this thread for RBW, so let me say briefly that we are underwriting quantum physics, not replacing it. Quantum physics is correct as a "higher-level" theory in our view. For example, all the work done on the Standard Model was essential and important, just not fundamental. But, we should leave this point now and stick to the theme of the thread.

 

[harrylin]

A little more on this:

[..] Aspect et al showed, subject to various minor loopholes on which most people seem to place not much reliance, that experimentally observed correlations follow the QM predictions rather than those predicted by a hidden variable theory that preserves locality.

Despite the apparent generality, Bell's mathematics does not take all possible options in account. Thus, it is now widely recognized that not necessarily all possible "local reality" models will disagree with those observations. Consequently, Bell's theorem can be seen as a strong (and tough) requirement for such models.

[..] I find myself unable to imagine what sort of a theory (extension of QM) or interpretation could remain consistent with the Bell results while still preserving locality.

I would be grateful for any light that contributors are able to shed on my fog of puzzlement.

I came to this forum for that very same reason, and only very slowly is the fog clearing* for me. It appears to me that models that reject the metaphysics as suggested by QM (although never offically imposed) will have the best chance of succeeding. As usual, if a question has no reasonable answer, it's good to verify if the question could be pointing in the wrong direction. I'm now reading (and verifying) a few journal papers of about a decade ago that I find very interesting, as they point to a way out of this conundrum about "local realism" that I had not seen elaborated before. Those will be input for a separate discussion thread, perhaps by the end of the month (I can hardly wait but I first would like to understand how the simulation that I just got running on my computer does the trick).

*PS see https://www.physicsforums.com/showthread.php?t=589134 for an example of how simplification of facts ("idealisation") can be misleading; I learned a lot from that discussion!

 

[DrChinese]

Despite the apparent generality, Bell's mathematics does not take all possible options in account. Thus, it is now widely recognized that not necessarily all possible "local reality" models will disagree with those observations. Consequently, Bell's theorem can be seen as a strong (and tough) requirement for such models.

There are NO existing local realistic models that are not ruled out by Bell. Recent attempts have all been refuted. I realize that you believe such a model is possible (despite Bell) but there are none currently on the table to discuss. Last ones I saw were the Stochastic Mechanics series. Since then, about all we have seen are purported disproofs of Bell, which appear regularly and none of which are accepted. Christian's falls into that group, for example.

Keep in mind that the de Raedt et al simulation is in no way a model of quantum mechanics. And Hans does not purport it to be such, as best I recall.

 

[harrylin]

There are NO existing local realistic models that are not ruled out by Bell. Recent attempts have all been refuted. [..] de Raedt et al simulation [..]

I responded to the OP's question if all such models are a priori ruled out by the existing experimental evidence.
Anyway, if in the coming weeks I can't find an error in the program (which is not by DeRaedt) then I will be very much interested to see the refutation.

 

[bhobba]

There are NO existing local realistic models that are not ruled out by Bell.

Scratching head. I can't see how ANY local realistic theory can be compatible with Bell.

What am I missing?

Thanks
Bill

 

[harrylin]

Scratching head. I can't see how ANY local realistic theory can be compatible with Bell.

What am I missing?

Thanks
Bill

Bell started from idealized assumptions that may never be realizable in the real world and there are different understandings of what "local realistic" supposedly means. According to some experts in the field, not necessarily all possible "non-spooky" ideas that could match reasonable experimental agreement with QM are covered by Bell's derivation. There have been derivations by others (such as Hellman) based on more realistic assumptions; I have no idea how solid those are. Thus, pragmatic and careful commentators use such terms as "Bell locality" in order to clearly delineate what has been established in theory.

 

[bhobba]

I have no idea how solid those are. Thus, pragmatic and careful commentators use such terms as "Bell locality" in order to clearly delineate what has been established in theory.

I think I would need to see the detail before understanding how its possible. I have been through Bell from reading his papers and from textbooks and for me it seems pretty airtight.

Thanks
Bill

 

[harrylin]

I think I would need to see the detail before understanding how its possible. I have been through Bell from reading his papers and from textbooks and for me it seems pretty airtight.

Thanks
Bill

The derivation by Hellman that I mentioned, supposedly proves Bell's theorem for imperfect correlations (but still adhering to Bell's assumptions about "local realism" I suppose; Bell addressed what he understood EPR to mean with that). My opinion on this is still swayed in opposite directions by papers on each side of the debate.

 

[sugeet]

I consider it this way, I am sorry for digressing from the above discussion.
Its the play of the mathematical Fourier transformation. Position and momentum, energy-time and all the other conjugate variable pairs are related by the mathematical Fourier transform. This mathematical relationship, handicaps us and thus non-locality. Localizing a particle in the position space will cause its conjugate variable to have infinite uncertainty, possibly if someone could see the mathematics more, it may help!

It is just an opinion, waiting for criticisms and insight!

 

[stevendaryl]

Scratching head. I can't see how ANY local realistic theory can be compatible with Bell.

What am I missing?

Thanks
Bill

Well, the most straight-forward proof that the spin-1/2, twin-pair EPR experiment is incompatible with a local realistic model unrealistically assumes that

1. Every pair of particles is detected.
2. No "stray" particles (not from a twin pair) are detected.
3. The two experimenters correctly associate corresponding detections.

With those assumptions, it's easy to demonstrate that there can't be a local, realistic model accounting for the predictions of QM.

But a real experiment might (and likely will) violate all three of these assumptions. Taking into account the possibility of errors makes the analysis a lot more complicated. At that point, it's beyond me whether the analysis was done correctly or not, so I have to take it on faith. But then if a paper claims that actual experiments have failed to account for possibility X, I don't have any way of judging that.

 

[bohm2]

But I can't see how even accepting that (ie accepting non-realism or non-counterfactual definiteness) allows us to still believe in locality in the face of the Bell theorem and the subsequent experiments.

Yes, some physicists (e.g. Norsen, Gisin, etc.) have argued that Bell's theory implies non-locality regardless of other issues (i.e. non-realism, hidden variables, determinism, etc.):

One can divide reasons for disagreement (with Bell’s own interpretation of the significance of his theorem) into two classes. First, there are those who assert that the derivation of a Bell Inequality relies not just on the premise of locality, but on some additional premises as well. The usual suspects here include Realism, Hidden Variables, Determinism, and Counter-Factual-Definiteness. (Note that the items on this list are highly overlapping, and often commentators use them interchangeably.) The idea is then that, since it is only the conjunction of locality with some other premise which is in conflict with experiment, and since locality is so strongly motivated by SR, we should reject the other premise. Hence the widespread reports that Bell’s theorem finally refutes the hidden variables program, the principle of determinism, the philosophical notion of realism, etc...

Since all the crucial aspects of Bell’s formulation of locality are thus meaningful only relative to some candidate theory, it is perhaps puzzling how Bell thought we could say anything about the locally causal character of Nature. Wouldn’t the locality condition only allow us to assess the local character of candidate theories? How then did Bell think we could end up saying something interesting about Nature?...That is precisely the beauty of Bell’s theorem, which shows that no theory respecting the locality condition (no matter what other properties it may or may not have – e.g., hidden variables or only the non-hidden sort, deterministic or stochastic, particles or fields or both or neither, etc.) can agree with the empirically-verified QM predictions for certain types of experiment. That is (and leaving aside the various experimental loopholes), no locally causal theory in Bell’s sense can agree with experiment, can be empirically viable, can be true. Which means the true theory (whatever it might be) necessarily violates Bell’s locality condition. Nature is not locally causal.

Local Causality and Completeness: Bell vs. Jarrett
http://arxiv.org/pdf/0808.2178v1.pdf

Of course, others argue that it is still possible to have a local and realistic model if one is willing to not deny the possibility of retrocausality:

Similarly, the signicance of Bell's work in the 1960s would have seemed quite different. Bell's work shows that if there's no retrocausality, then QM is nonlocal, in apparent tension with special relativity. Bell knew of the retrocausal loophole, of course, but was disinclined to explore it. (He once said that when he tried to think about backward causation he "lapsed quickly into fatalism".

Dispelling the Quantum Spooks-a Clue that Einstein Missed?
http://arxiv.org/pdf/1307.7744.pdf

 

[PhotonCurve]

As I understand it, EPR proposed their entanglement thought experiment as a means of demonstrating that Quantum Mechanics was incomplete, and hence that the Copenhagen interpretation (which says that the wave function is a complete description of the state of a system) was wrong. They postulated the existence of hidden variables as a way of 'completing' the theory. Here 'hidden' just means 'not in any way reflected in the wave function'.

Bell proved that any extension of QM that uses hidden variables will predict correlations for measurements of entangled particles that differ from what QM predicts, if the principle of locality is to be maintained.

Aspect et al showed, subject to various minor loopholes on which most people seem to place not much reliance, that experimentally observed correlations follow the QM predictions rather than those predicted by a hidden variable theory that preserves locality.

From this we inductively conclude that there is no valid hidden variable theory that preserves locality.

Various presentations of this topic suggest that the tests of Bell's theorem have shown that we cannot maintain both locality and something else, where that something else is variously described as realism, counterfactual definiteness, or other similarly vague-seeming terms. This seems consistent with EPR's and Bell's original ideas, which were to challenge or defend the Copenhagen interpretation that a particle does not have a definite position and momentum unless it is in an eigenstate of one of the two operators.

But I can't see how even accepting that (ie accepting non-realism or non-counterfactual definiteness) allows us to still believe in locality in the face of the Bell theorem and the subsequent experiments. The correlations in Bell's theorem imply that Alice measuring spin along a certain axis has an instantaneous effect on the probability distribution of the results of Bob's measurement. So retreating into the indeterminacy of the Copenhagen interpretation does not appear to have allowed us to preserve locality since an instantaneous effect has occurred across a spacelike interval.

I realize that this is a hand-wave rather than a mathematical proof, but I find myself unable to imagine what sort of a theory (extension of QM) or interpretation could remain consistent with the Bell results while still preserving locality.

I would be grateful for any light that contributors are able to shed on my fog of puzzlement.

I like to think physicists are sometimes a bit biased... the universe is not only non-local, it is also a local phenomenon. We are living proof of it.

 

[DrChinese]

Yes, some physicists (e.g. Norsen, Gisin, etc.) have argued that Bell's theory implies non-locality regardless of other issues (i.e. non-realism, hidden variables, determinism, etc.):

Local Causality and Completeness: Bell vs. Jarrett
http://arxiv.org/pdf/0808.2178v1.pdf

Of course, others argue that it is still possible to have a local and realistic model if one is willing to not deny the possibility of retrocausality:

Dispelling the Quantum Spooks-a Clue that Einstein Missed?
http://arxiv.org/pdf/1307.7744.pdf

I call retrocausal interpretations "non-realistic" because they are contextual/observer dependent. To me, a realistic interpretation means that counterfactual observations are possible. However, not everyone defines things the same as I. Bohmians (I guess you are one) call their interpretation "realistic" even though it is as realistic (or unrealistic) as the retrocausal ones (since it is also contextual/observer dependent).

 

[DrChinese]

Anyway, if in the coming weeks I can't find an error in the program (which is not by DeRaedt) then I will be very much interested to see the refutation.

Their model is not a theory. It is a computer simulation. When I ran it (a particular version), it worked successfully as Kristel indicated it would. I have never completed my analysis of the program, it's one of my long-standing to-do's. However, the version I ran exploited the fair sampling loophole - which has been long closed.

So my point is: there are no existing local realistic theories on the table to disprove. I am confident because of Bell that none is forthcoming either.

 

[bohm2]

I call retrocausal interpretations "non-realistic" because they are contextual/observer dependent. To me, a realistic interpretation means that counterfactual observations are possible. However, not everyone defines things the same as I. Bohmians (I guess you are one) call their interpretation "realistic" even though it is as realistic (or unrealistic) as the retrocausal ones (since it is also contextual/observer dependent).

Yes, I recall you mentioning this before. As an aside, in order to maintain Lorentz invariance there are Bohmian models that are also retrocausal:

A version of Bohm’s model incorporating retrocausality is presented, the aim being to explain the nonlocality of Bell’s theorem while maintaining Lorentz invariance in the underlying ontology...The aim of this paper is to construct a version of Bohm’s model that also includes the existence of backwards-in-time influences in addition to the usual forwards causation. The motivation for this extension is to remove the need in the existing model for a preferred reference frame. As is well known, Bohm’s explanation for the nonlocality of Bell’s theorem necessarily involves instantaneous changes being produced at space-like separations, in conflict with the “spirit” of special relativity even though these changes are not directly observable. While this mechanism is quite adequate from a purely empirical perspective, the overwhelming experimental success of special relativity (together with the theory’s natural attractiveness), makes one reluctant to abandon it even at a “hidden” level. There are, of course, trade-offs to be made in formulating an alternative model and it is ultimately a matter of taste as to which is preferred. However, constructing an explicit example of a causally symmetric formalism allows the pros and cons of each version to be compared and highlights the consequences of imposing such symmetry. In particular, in addition to providing a natural explanation for Bell nonlocality, the new model allows us to define and work with a mathematical description in 3-dimensional space, rather than configuration space, even in the correlated many particle case.

Causally Symmetric Bohm Model
http://arxiv.org/ftp/quant-ph/papers/0601/0601095.pdf