I What is the physical significance of Bell's math?

[Zafa Pi]

I'm talking about IS Bell's notion.

IS??

Yes, that's what a classical physicist would say, and it's what Bell proved is not true.

Indeed, but you must leave your stand alone post for that.

I said, "If, for example, two electrons are produced there with opposite up and down, then Bob's, as an element of reality, will either be up or down. I can measure Bob's to find out, and we will know what each will get in regions 1 & 2. It's just like looking in the shoe box to see which shoe Bob will get. Hence there is no non-local phenomena going on." and you relied:

You know that that's not true of EPR, though. Bob is free to change his detector settings after the particles have left Region 5. Alice is free to change her detector settings after the particles have left Region 5. But regardless of when they choose their detector settings, if Alice measures spin-up along axis ⃗aa→\vec{a} Alice finds out something about Bob's measurement that was not available in Region 5: that Bob did not (or will not) measure spin-up along axis ⃗aa→\vec{a}

You're right I do know, but not because of your post #74. However once I make a measurement on Bob's particle the particles are no longer entangled and unless A and B measure once again at α or α+180º they can't know one another's results. This is a minor detail, the major issue is:

I said non-locality cannot be proved and you replied:

I'm just saying that I think you're wrong. If nonlocality is defined in Bell's terms, then QM is either nonlocal, or one of the weird acausal interpretations (superdeterminism, back-in-time causality) must be true.

I don't care about superdeterminism, (except that it's forcing me to say what I say). Your definition of non-locality in #74 is synonymous with the existence of entangled particles (shoes won't do). Thus according to you and Bell (and I imagine many others) in refuting Bell's Inequality employing entanglement non-locality is required as a tautology. BORING!

With the definition I provided in #54 (which is not unique to me, and must be close to the one Nugatory uses) there is an interesting issue. Do the correlations that are manifest in measuring entangled pairs require FTL phenomena. It appears that issue hasn't been resolved as yet. Also as a matter of taste I find the definition I gave more intuitive. This goes in spades for the 99% who don't know entanglement from a hot rock.

 

[Boing3000]

Thus according to you and Bell (and I imagine many others) in refuting Bell's Inequality employing entanglement non-locality is required as a tautology. BORING!

Well, if you excuse my horrible grammar, the way I would layout this sentence is: In choosing one side of Bell's inequality entanglement requires a non-local phenomenology.
Now I have no idea why you found that boring. It can at least avoid you to loose your time with hidden local state, or spooky-action-at-distance.

 

[stevendaryl]

I don't care about superdeterminism, (except that it's forcing me to say what I say). Your definition of non-locality in #74 is synonymous with the existence of entangled particles (shoes won't do).

No, it's not. It's provable that in certain circumstances, entanglement implies nonlocality in Bell's sense. But they aren't synonymous.

Do the correlations that are manifest in measuring entangled pairs require FTL phenomena.

I would say no. I don't consider FTL and nonlocality to be synonymous.

 

[Zafa Pi]

I claimed your definition of non-locality was synonymous with the existence of entangled particles.

No, it's not.

The reason for my claim is your statement in post #74, "If Alice's result in Region 1 reveals information about Bob's result in Region 2, and that information is unavailable in Regions 4 & 5, then that means that the information is nonlocal in the sense of Bell."

How would that information be unavailable? Not as you point out with a pair of shoes, or even a pair consisting of a positron and electron. Other than an entangled pair do you have an other example? If not (and I see nothing that would indicate otherwise) then nonlocal in the sense of Bell is synonymous with an entangled pair.

When I asked, "Do the correlations that are manifest in measuring entangled pairs require FTL phenomena?

I would say no. I don't consider FTL and nonlocality to be synonymous.

I wouldn't say no or yes to my question, I don't know. However, the definition I provided in post #54 seems to imply that FTL and non locality are synonymous.
I don't see a problem with that. Other than you having a different definition of non locality, do you see a problem? Perhaps there is and I don't see it.

 

[N88]

No, it's not. It's provable that in certain circumstances, entanglement implies nonlocality in Bell's sense. But they aren't synonymous.

What are those circumstances, please? And what is "nonlocality" (BNL = Bell non-locality) in Bell's sense?

I would say no. I don't consider FTL and nonlocality to be synonymous.

IF FTL and BNL are not synonymous, then where is the problem with BNL? I mean this: EPR believed in local causality, and Bell (1964; 2nd sentence) specifically links locality and causality to EPR. So EPR believed in non-FTL causality; as do I.

Perhaps I'm missing some subtlety in Bell's definition of BNL? But (attempting to be very clear): if FTL and NL are not synonymous, Bell's beef with EPR boils down to their error in not clearly expressing the fact that a "measurement" perturbs the "measured" system (AKA, Bohr's Insight).

BUT, then, if that's the case: I understand that theory and experiments, pre-dating Bell, had already established this fact. So this brings me back to BNL (with its FTL) being the issue; this being Bell's contribution to the debate via his assumption of CFD?

 

[stevendaryl]

What are those circumstances, please? And what is "nonlocality" (BNL = Bell non-locality) in Bell's sense?

That was the point of post #74. In the figure, I drew 5 regions of spacetime:

1. The region where Alice performs her measurement.
2. The region where Bob performs his measurement.
3. The region in the causal past of Region 1 that is not in the causal past of Region 2. (the "causal past" of a region means events that are capable of sending a light-speed or slower signal to that region)
4. The region in the causal past of Region 2 that is not in the causal past of Region 1.
5. The region in the common causal past of regions 1 and 2.

If Alice, by making measurements in Region 1 can learn something about Bob's results in Region 2, and that information is not available in region 5, then her knowledge is nonlocal. A local theory, in Bell's sense, would have the property that any information about Bob's results in Region 2 must depend on facts about regions 4 and 5.

IF FTL and BNL are not synonymous, then where is the problem with BNL? I mean this: EPR believed in local causality, and Bell (1964; 2nd sentence) specifically links locality and causality to EPR. So EPR believed in non-FTL causality; as do I.

Einstein was not talking about causality, in the sense of the speed of influences. He believed that there were no such FTL influences. He was saying (paraphrased for the current discussion) that if Alice can find out information about Bob's results, then those results must have already existed beforehand. He didn't explicitly enumerate the regions of spacetime, but the FTL limit of propagation of information implies that if Bob's results are predictable by Alice, then they must have already been predictable in Region 5, which is the only region affecting Bob that Alice would have access to.

So Einstein was assuming no-FTL, and then concluding that Alice's prediction implied an "element of reality" to Bob's result before he performed his measurement. I think that it's incorrect to dismiss this as Einstein assuming determinism. He actually did believe that the universe was deterministic, but that is not an assumption to his argument.

Bell tried to clarify what Einstein was implying about elements of reality. I think Bell would say that Einstein was assuming a notion of locality above and beyond there being no FTL. And that notion of locality seems to be refuted by experiment.

this being Bell's contribution to the debate via his assumption of CFD?

I think that CFD is a bad way to think about it. I don't think it clarifies anything.

 

[stevendaryl]

I claimed your definition of non-locality was synonymous with the existence of entangled particles.

The reason for my claim is your statement in post #74, "If Alice's result in Region 1 reveals information about Bob's result in Region 2, and that information is unavailable in Regions 4 & 5, then that means that the information is nonlocal in the sense of Bell."

How would that information be unavailable?

I mean that there is no local state that implies that information. There is no field whose values in Region 5 determine the outcome. There are no particles with properties that determine the outcome.

Not as you point out with a pair of shoes, or even a pair consisting of a positron and electron. Other than an entangled pair do you have an other example?

Are you asking for an example of information being unavailable?

If you have a truly nondeterministic event, such as the decay of a muon, then the information about whether the muon will decay in the next microsecond is just not available until it happens.

If you are asking for an example of a case where somebody can know nonlocal information, I think it is impossible in our world except by entanglement. But it certainly isn't synonymous with entanglement. Entanglement is a feature of wave functions, but the notion of nonlocal information that I described is independent of whether quantum mechanics is the ultimate theory, or not.

If not (and I see nothing that would indicate otherwise) then nonlocal in the sense of Bell is synonymous with an entangled pair.

I think you're using the word "synonymous" in an unusual way. Synonymous means that two words have the same definition. That's certainly not the case. There's probably a philosophical term for what you're talking about---maybe "co-extensive" or something--meaning that one thing is the only example of another thing.

When I asked, "Do the correlations that are manifest in measuring entangled pairs require FTL phenomena?

I wouldn't say no or yes to my question, I don't know. However, the definition I provided in post #54 seems to imply that FTL and non locality are synonymous.

I don't see how it does that. How does your post #54 imply anything about FTL?

Certainly FTL is a way to explain the EPR correlations. But the correlations don't imply FTL. They imply Bell nonlocality.

 

[DrChinese]

When I asked, "Do the correlations that are manifest in measuring entangled pairs require FTL phenomena?

I wouldn't say no or yes to my question, I don't know. However, the definition I provided in post #54 seems to imply that FTL and non locality are synonymous.
I don't see a problem with that. Other than you having a different definition of non locality, do you see a problem? Perhaps there is and I don't see it.

Quantum non-locality is not the same thing as FTL causation, although admittedly it is easy to identify them as one and the same. We know that there are correlations between spacelike separated elements of a system, and such correlations cannot be explained on the basis of a local hidden variable type theory. This is quantum nonlocality. There are many experimental examples of this.

FTL action is different in that there is supposed to be a cause and an effect. Clearly there are many issues with asserting there is such an FTL effect. Which (or where) is the cause? Without a specific mechanism to consider, it is difficult to assess this.

It is probably simpler to agree that there is something called quantum non-locality, the mechanism for which is unknown, that to try to convince people that there is an FTL mechanism driving that. Maybe there is, maybe there isn't.

 

[Zafa Pi]

I think you're using the word "synonymous" in an unusual way. Synonymous means that two words have the same definition. That's certainly not the case. There's probably a philosophical term for what you're talking about---maybe "co-extensive" or something--meaning that one thing is the only example of another thing.

syn·on·y·mous
səˈnänəməs/
adjective

1. (of a word or phrase) having the same or nearly the same meaning as another word or phrase in the same language.
   "aggression is often taken as synonymous with violence"
   • closely associated with or suggestive of something.
     "his deeds had made his name synonymous with victory"

How does your post #54 imply anything about FTL?

It doesn't. However, I did define locality as no FTL, so what does that make non locality mean?

 

[Zafa Pi]

Quantum non-locality is not the same thing as FTL causation, although admittedly it is easy to identify them as one and the same. We know that there are correlations between spacelike separated elements of a system, and such correlations cannot be explained on the basis of a local hidden variable type theory. This is quantum nonlocality. There are many experimental examples of this.

1) What do you mean by local? I said it meant no FTL (not new). I am up for changing my definition in post #54, though i would like it simple. What do you suggest?

2) In other words your nonlocality is such correlations (arising from measurements on entangled particles as the only way we know) that cannot be explained on the basis of a local hidden variable type theory.
This why I say your nonlocality (like stevendaryl) is synonymous with (the correlations) entangled entities.
If you, like stevendaryl, don't care for synonymous, too bad I'm sticking to it.

It is probably simpler to agree that there is something called quantum non-locality, the mechanism for which is unknown, that to try to convince people that there is an FTL mechanism driving that. Maybe there is, maybe there isn't.

Quantum non-locality has such a nice sophisticated ring to it, something of high scientific repute. This in spite of being another term for for the weird correlations due to measurements on entangled particles with no known mechanism. What if we change it to fiddledeedom, then we could see:
"Quantum physicists have shown that the strange correlations observed when measuring entangled entities is due to fiddledeedom."
A little less high falutin. Or even better:
"Quantum physicists have shown that the strange correlations observed when measuring entangled entities is due to the strange correlations observed when measuring entangled entities."

 

[morrobay]

We can picture it this way:

The quantum version does not allow the prediction of Bob's result based on information about Region 5.

Alice and Bobs measurement results in zone 1 and 2 would be determined by the spin 1/2 particles spins at the source in zone 5 and detector settings at time of measurement:
A(a,λ) =±1
B(b,λ) =±1
For a given a and b (that can be chosen after particles leave source in zone 5) and λ. These unique outcomes are determined. (Bell) So if that is an example of quantum non locality it is not synonymous with FTL which would be a superluminal signal from spacelike separated zones 1 and 2 during measurements.
Suppose Alice measures + or - Then probability for double detection at Bob is (sin θ/2)² and for opposite results (cos θ/2 )²
Since θ = setting (a - b) then it seems that the measurement results at A and B are local .Ie. Ontic spin and interaction with detector settings a and b *
If Bell inequality is violated, of the three possibilities: non locality (FTL), non realism, contextual I would favor contextual*

 

[Boing3000]

It doesn't. However, I did define locality as no FTL

Actually you don't. Locality mean "having a location", which in every one's vocabulary, is identical (not synonymous) to having a space-time coordinate.
Incidentally, it happens that every single entity ever observed to have a location/coordinate, do obey the laws of relativity, that happens to include no FLT.
So it is tautological to associate no FLT with locality.

BTW if someone would ever want to include FLT somewhere in the equations, it would have to provide the exact means of computing space-time interval in that framework. Sadly, this is a waste of time because Bell's prove that there is no such interval.
Now I suppose you can always provide a theory where those interval would be smaller then the margin of error of experimental apparatus. But then the simple fact that Alice or Bob would make the measurement first would make a testable difference. In the non-local side of Bell's inequality it doesn't even matter.

so what does that make non locality mean?

It means no coordinate. The state/value is unique and span the whole universe, it is everywhere at once, and testable only at particles sharing this value (we called them entangled, not fiddledeedoomed)
It is not a feature of QM, but a feature of nature, that QM happens to describe successfully.

I am under the impression that the Bohmian pilot wave is also a non-local.

 

[Zafa Pi]

Entanglement is a feature of wave functions, but the notion of nonlocal information that I described is independent of whether quantum mechanics is the ultimate theory, or not.

Entangled particles are created in the lab, they part of nature, independent of whether quantum mechanics is the ultimate theory, or not.

 

[stevendaryl]

Entangled particles are created in the lab, they part of nature, independent of whether quantum mechanics is the ultimate theory, or not.

Maybe this depends on how you define "entanglement", but the definition I've used is that two particles are entangled if they are described by a two-particle wave function that cannot be "factored" into a product of one-particle wave functions. So it's a theoretical description of what goes on in EPR. If QM is false, then so is the description of the particles as "entangled".

 

[stevendaryl]

Alice and Bobs measurement results in zone 1 and 2 would be determined by the spin 1/2 particles spins at the source in zone 5 and detector settings at time of measurement:
A(a,λ) =±1
B(b,λ) =±1

That's true. That's the "superdeterminism". If it's possible to know Alice's and Bob's choices ahead of time, then you can violate Bell's inequality. But in the figure, Alice's choice may potentially depend on facts about Region 3 as well as Region 5. Bob's choice may depend on Region 4. So there is no reason to believe that the information about Alice's and Bob's future settings are determined in Region 5.

For a given a and b (that can be chosen after particles leave source in zone 5) and λ. These unique outcomes are determined. (Bell) So if that is an example of quantum non locality it is not synonymous with FTL which would be a superluminal signal from spacelike separated zones 1 and 2 during measurements.
Suppose Alice measures + or - Then probability for double detection at Bob is (sin θ/2)² and for opposite results (cos θ/2 )²
Since θ = setting (a - b) then it seems that the measurement results at A and B are local .Ie. Ontic spin and interaction with detector settings a and b *
If Bell inequality is violated, of the three possibilities: non locality (FTL), non realism, contextual I would favor contextual*

If I understand you correctly, I agree that for a fixed choice of Alice's and Bob's settings, one can come up with a hidden-variable explanation for their results. But the combination "Bob's setting plus Bob's result" is something that is completely nondetermined by anything in Region 5, even though Alice can find out something about it in Region 1 (that a particular combination did not/will not occur).

 

[Zafa Pi]

Maybe this depends on how you define "entanglement", but the definition I've used is that two particles are entangled if they are described by a two-particle wave function that cannot be "factored" into a product of one-particle wave functions. So it's a theoretical description of what goes on in EPR. If QM is false, then so is the description of the particles as "entangled".

You are giving the QM definition, and I agree with it. However, via various processes (e.g. down conversion) entangled photons are created in nature, and with the measuring devices (polarization analyzers) give the same weird results predicted by QM., thus independent of whether quantum mechanics is the ultimate theory, or not.

 

[stevendaryl]

syn·on·y·mous
səˈnänəməs/
adjective

1. (of a word or phrase) having the same or nearly the same meaning as another word or phrase in the same language.
   "aggression is often taken as synonymous with violence"
   • closely associated with or suggestive of something.
     "his deeds had made his name synonymous with victory"

By that definition of "synonymous", I don't think that any two of "entanglement", "FTL" or "local" are synonymous.
It doesn't.

However, I did define locality as no FTL

Fine. I don't think that's a helpful definition, though. I agree that QM does not provide a way for people to communicate FTL. I think everybody agrees with that. If that's the end of the matter for you, then there is no need to further discuss Bell and EPR.

 

[stevendaryl]

You are giving the QM definition, and I agree with it. However, via various processes (e.g. down conversion) entangled photons are created in nature, and with the measuring devices (polarization analyzers) give the same weird results predicted by QM., thus independent of whether quantum mechanics is the ultimate theory, or not.

Yes, I would just say that the predictions of QM in EPR-type experiments have been verified, so any successor theory must make the same predictions for those experiments. I would not say that a successor theory must have entangled particles.

 

[Zafa Pi]

If Bell inequality is violated, of the three possibilities: non locality (FTL), non realism, contextual I would favor contextual

Can you give me a short, simple example or explanation that distinguishes nonrealism (= nonCFD) from contextual?

 

[Zafa Pi]

By that definition of "synonymous", I don't think that any two of "entanglement", "FTL" or "local" are synonymous.
It doesn't.

Neither do I. This is disheartening, you've missed which two concepts I've claimed were synonymous. I presume you didn't read either post #91 or #100. I feel crushed.

You don't care for my definition of local. What do you prefer?

 

[morrobay]

Can you give me a short, simple example or explanation that distinguishes nonrealism (= nonCFD) from contextual?

No , nonCFD is equated with or subset of contextuality : Measurement outcomes are produced from particle/detector field interactions.

 

[Zafa Pi]

No , nonCFD is equated with or subset of contextuality : Measurement outcomes are produced from particle/detector field interactions.

Cool, I understand your whole sentence. So now all you have to do to make me a happy quantum camper is to give me an example of contextuality that isn't nonCFD.
The classic example of contextually is the Mermin-Peres quantum pseudo-telepathy, but that is also nonCFD.
If you can't provide me with such an example, I hereby threaten to say they are synonymous, just like I did with Bell non locality and measurements on entangled entities, thus earning further derision from PF luminaries.

 

[PeterDonis]

Everyone, please bear in mind that this is an I level thread and some math is expected. Throwing around ordinary language terms without giving them precise mathematical definitions is a recipe for endless discussion with no resolution, and eventually either a closed thread or a warning. This thread is getting close to the latter point now.

 

[morrobay]

Cool, I understand your whole sentence. So now all you have to do to make me a happy quantum camper is to give me an example of contextuality that isn't nonCFD.
The classic example of contextually is the Mermin-Peres quantum pseudo-telepathy, but that is also nonCFD.
If you can't provide me with such an example, I hereby threaten to say they are synonymous, just like I did with Bell non locality and measurements on entangled entities, thus earning further derision from PF luminaries.

For a quantitative example/explanation let's let one of the Masters or PhD's in physics take your question. My background is in Biology/Chemistry and I am not qualified to go any farther with this.

 

[Zafa Pi]

For a quantitative example/explanation let's let one of the Masters or PhD's in physics take your question. My background is in Biology/Chemistry and I am not qualified to go any farther with this.

I notice a while back there was a B level thread on exactly this topic. However, no answers were provided.

 

[stevendaryl]

Neither do I. This is disheartening, you've missed which two concepts I've claimed were synonymous. I presume you didn't read either post #91 or #100.

Post #91 is where you said

Your definition of non-locality in #74 is synonymous with the existence of entangled particles

I specifically said that I disagreed with that statement. You also said:

Do the correlations that are manifest in measuring entangled pairs require FTL phenomena

I specifically said that I don't think so.

So I read your post #91 and specifically responded to it. So don't feel crushed.

You don't care for my definition of local. What do you prefer?

I wrote a very detailed post, complete with a diagram that I spent a good part of an hour creating, several years ago, in an attempt to answer that question. Let me try one more time.

A "nonlocal correlation" is a correlation between distant (spacelike separated) events. A local theory (or model) explains or implements all nonlocal correlations in terms of a chain of two or more local correlations. So in a local theory, if A is correlated with B, then either A is in the causal past of B, or B is in the causal past of A, or there is a set of events C1, C2, ... such that all the Cs are in the causal past of both A and B and A is only correlated with B through its correlations with C1, C2, ...

The events C1, C2, are elements of the model---they aren't necessarily directly observable.

What's an example of a nonlocal model, then? Well, here's a toy example. Suppose there is a pair of coins, and I propose the following theory about those coins: The nth flip of one coin always produces the opposite result of the nth flip of the other coin.

That's a falsifiable theory about those coins. You can certainly test it by just flipping the coins a bunch of times. But it's a nonlocal theory, since it predicts a correlation between possibly distant coins and does not explain or implement the correlation in terms of local correlations.

In this case, I could come up with a different, local theory that made the same predictions as the first theory. But the original theory is nonlocal.

I believe that in the same way, quantum mechanics in the standard way that it is applied is nonlocal. Einstein et al believed that there might be a local theory that made the same predictions as quantum mechanics, but Bell proved them wrong.

 

[Zafa Pi]

So I read your post #91 and specifically responded to it. So don't feel crushed.

When I said, "Neither do I. This is disheartening, you've missed which two concepts I've claimed were synonymous. I presume you didn't read either post #91 or #100."
I was referring to your comment,

By that definition of "synonymous", I don't think that any two of "entanglement", "FTL" or "local" are synonymous.

And it appeared that you were misquoting me. I'm sorry I made you go through that again. I did understand your post #74. I feel uncrushed.

It seems that your definition of local (post #116) is the negation of your nonlocal, as it should be. Whereas my definition of nonlocal is the negation of local (post #54).
That our definitions disagree is ok with me. We've each said what we dislike about the other's definitions.

You did clear up Bell's definition for me that he made in OP's cited paper, to wit:
"It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past", which I found vague.

I'm sorry you hate CFD, I hope it doesn't feel crushed.

 

[stevendaryl]

I'm sorry you hate CFD, I hope it doesn't feel crushed.

It's just that I don't think it clarifies anything. A local, nondeterministic theory violates CFD, so violating CFD is not a big deal, it seems to me, and it doesn't do anything to understand the difference between a quantum theory and a classical theory.

 

[N88]

Everyone, please bear in mind that this is an I level thread and some math is expected. Throwing around ordinary language terms without giving them precise mathematical definitions is a recipe for endless discussion with no resolution, and eventually either a closed thread or a warning. This thread is getting close to the latter point now.

Thanks for this. The OP was intended to be a straight-forward (but highly relevant) question and I do not see that it has been satisfactorily answered. In my view, without Bell's assumption, his theorem fails. If he was mimicking EPR, then EPR fails. But I do not see that the failure of EPR would mean the failure of local realism.

Maybe a clearer example of my concern is this attachment from Isham's "Lectures on Quantum Theory" (1995). More recent examples exist.

In Isham's equation (9.33), he sums over the same set of particles on 4 occasions! It would never occur to me to do that: for, if I did , I would expect to get an outcome that applied to objects that I could meaningfully test 4 times. Classical objects would meet this criteria; quantum objects would not. So back to my question in the OP please.

 

[PeterDonis]

In Isham's equation (9.33), he sums over the same set of particles on 4 occasions! It would never occur to me to do that: for, if I did , I would expect to get an outcome that applied to objects that I could meaningfully test 4 times.

They don't have to be the same objects; they just have to be taken from an ensemble of objects all prepared in the same state.