Is there any hope at all for Locality?

[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