Understanding bell's theorem: why hidden variables imply a linear relationship?

[ThomasT]

"I am certain that, if you had 100% detection-efficiency and 100% pairing-efficiency, then QM would hold, as would Einstein-locality. So that suggests to me the need to focus on the R in LR."
Regards, GW

Einstein locality refers to independence, ie., the separability of the joint function vis the functions and λs which determine individual detection, doesn't it? If so, then that way of formalizing locality would continue to be ruled out. I agree with ttn on that. It's the locality condition which effectively creates an LR-predicted correlation between θ and rate of coincidental detection that's incompatible with the QM-predicted correlation.

Realistic models of entanglement are allowed -- as long as they're explicitly nonlocal. This is another reason why, wrt the title question, hidden variables, by themselves, don't imply a linear relationship between θ and rate of coincidental detection.

Of course, the OP was talking about LR models, and, imo, the key to why BIs are violated has to do with how the assumption of locality is expressed in an LR model of entanglement.

 

[lugita15]

If so, then that way of formalizing locality would continue to be ruled out. I agree with ttn on that.

ThomasT, regardless of whether Bell's "way of formalizing locality" restricted it in some way, and regardless of whether that means that Bell's original proof does not apply to all local deterministic theories, the point still remains that not all Bell proofs involve a "formal model". Probably Herbert's version of the proof, and certainly my restatement of Herbert, is not concerned with "encoding" or "formalizing" the philosophical assumption of local determinism to fit some kind of restricted model. The only thing I'm trying to do is deduce the logical consequences of this philosophical assumption, and I claim to have done so in my four steps. If you believe that local determinism IS compatible with the predictions of QM, then the burden of proof is on you to identify the step you disagree with, because if all of my steps are correct how can my conclusion be wrong?

EDIT: For convenience, I just put my four steps in a blog post here.

 

[ThomasT]

lugita, the blog link you gave doesn't seem to work.
But I'll reply to your comments.

ThomasT, regardless of whether Bell's "way of formalizing locality" restricted it in some way, and regardless of whether that means that Bell's original proof does not apply to all local deterministic theories, the point still remains that not all Bell proofs involve a "formal model".

In that case, then they can hardly be called proofs. Proof of nonlocal transmissions would be the objectively recorded observation of nonlocal transmissions. Neither you, nor Bell, nor Herbert, nor Bell tests offer that. Instead, we must, you say, infer from the steps in your lines of reasoning that nature must be nonlocal. I don't conclude that from your, or Bell's, or Herbert's, or ttn's treatments.

Probably Herbert's version of the proof, and certainly my restatement of Herbert, is not concerned with "encoding" or "formalizing" the philosophical assumption of local determinism to fit some kind of restricted model.

But, in effect, that's what you're doing. You're placing certain restrictions on the correlation between θ and rate of coincidental detection. Where do these restrictions come from? Are they warranted? Do they actually show that nature is nonlocal, or might there be some other explanation regarding the effective causes of BI violations?

If you believe that local determinism IS compatible with the predictions of QM, then the burden of proof is on you to identify the step you disagree with, because if all of my steps are correct how can my conclusion be wrong?

Formal, standard, Bell-type LR is incompatible with formal QM. That's an indisputible mathematical fact.

But I think I've shown that wrt at least one conceptualization of the situation the predictions of QM are quite compatible with the assumption of local determinism. Encoding that assumption into a formal model that agrees with QM and experiment is another problem altogether. It, apparently, can't be done.

Extant observations (not necessarily interpretations of those observations) are all in line with the assumption of local determinism, so if you say, via some logical argument, that nature must be nonlocal, then the burden of proof is on you. And that proof, scientifically, wrt your contention, would consist of producing some nonlocal transmissions.

Since no nonlocal transmissions have ever been observed/recorded, then the most reasonable scientific position is to retain the assumption that our universe is evolving in accordance with the principle of locality.

Wrt Bell, Herbert, etc., that means that the most reasonable hypothesis is that there's something in the formalism, or line of reasoning, that has nothing to do with locality in nature, but which nevertheless skews the predictions of a an LR formalism or line of reasoning.

You're a scientist, right? Ok, so just approach this problem from a different perspective, adopting the working hypothesis that maybe, just maybe, there's something in the standard Bell-type LR formalism, or, say, a Herbert-like line of reasoning, that doesn't fit the experimental situation, and that, just maybe, that incompatibility has nothing to do with whether nature is nonlocal or not.

 

[San K]

zonde might be a good person to ask about this. He believes in models in which you would get dramatically different results if you detected all the entangled pairs. He thinks the polarizers are somehow biased towards only detecting the ones that display perfect correlation.

well in that case the above hypothesis can be expanded to apply to various experiments of QM...for example this argument could be stretched to even (single photon, double slit) interference patterns

 

[San K]

.

I'm not sure what you're asking. A photon transmitted by the polarizer and registered by the detector is hypothesized, I think, to have the same polarization orientation, on interacting with the detector, as the orientation of the polarizer that transmitted it.

i am saying

One hypothesis/assumption could be that --

prior to even interacting with the polarizer 50% of the photons have a property that is different from the photons that will pass through...(or how else do we explain why 50% pass thru...;)...)

i.e. the photons that will (or will not) pass through the polarizer are predetermined/marked for any given angle/orientation of the polarizer


that group of photons changes ...with the change in polarizer angle

let me illustrate the above hypothesis with the following example:

lets say we have 360 photons

on average maybe each is at 0, 1, 2...360 degree etc...

so for polarizer at 0 degree...the ones between 270 and 90 degree pass through
for polarizer at 90 degree the ones between 0 and 180 pass through
for polarizer at 180 degree the ones between 90 and 270 pass through etc

to add up to 50% passing through...at any polarizer angle/orientation

 

[lugita15]

the photons that will (or will not) pass through the polarizer are predetermined/marked for any given angle/orientation of the polarizer

If I understand you, all you're saying is that each photon decides in advance which angles to go though and which angles not to go through. And since the two photons in an entangled pair always do the same thing when you send them through polarizers oriented at the same angle, you can conclude that the two photons have agreed on which angles to go through and which ones not to. That's exactly in line with my four-step proof.

 

[DrChinese]

...lets say we have 360 photons

on average maybe each is at 0, 1, 2...360 degree etc...

so for polarizer at 0 degree...the ones between 270 and 90 degree pass through
for polarizer at 90 degree the ones between 0 and 180 pass through
for polarizer at 180 degree the ones between 90 and 270 pass through etc

to add up to 50% passing through...at any polarizer angle/orientation

As lugita15 says, this is exactly the idea (or its equivalent) that was considered PRIOR to Bell. But you will quickly find that works fine when the angle settings are identical, but generally does not work out at many combinations of settings.

0/120/240 are good examples - take the DrChinese challenge! See how close you can get the match rate (comparing AB, BC, AC) to 25% (the QM value) for 10 photons.

Photon 1:
A=0 degrees is +
B=120 degrees is +
C=240 degrees is -

So AB is a match, but AC and BC are not. 1 of 3.

Photon 2:
A=0 degrees is -
B=120 degrees is +
C=240 degrees is -

So AC is a match, but AB and BC are not. 1 of 3.

Photon 3:
A=0 degrees is -
B=120 degrees is -
C=240 degrees is -

So AC, AB and BC are matches. 3 of 3.

Etc. to 10 or whatever.

You win the challenge if your average rate is lower than 1/3. Again, the QM prediction is 1/4. It should be clear that the ONLY way to "win" over a suitably large sample is to know in advance which 2 settings will be selected for each photon in our trial. But if I do that (being independent of you and not knowing whether you marked a + or a - for each photon's settings) after you mark your values, the rate of matches will converge on 1/3 or more.

 

[lugita15]

lugita, the blog link you gave doesn't seem to work.

Sorry, I had to get it approved. Now you can read my post. (It doesn't contain any new info, just the reasoning I've already been giving, for easy reference.)

In that case, then they can hardly be called proofs. Proof of nonlocal transmissions would be the objectively recorded observation of nonlocal transmissions.

No, such an observation would be EVIDENCE of nonlocal transmissions. But I'm trying to do is write logical proofs, not argue about evidence.

Neither you, nor Bell, nor Herbert, nor Bell tests offer that. Instead, we must, you say, infer from the steps in your lines of reasoning that nature must be nonlocal.

No, i do not say that. I say that we must infer from my line of reasoning that local determinism is incompatible with the experimental predictions of quantum mechanics being completely correct.

But, in effect, that's what you're doing. You're placing certain restrictions on the correlation between θ and rate of coincidental detection. Where do these restrictions come from?

I am not arbitrarily placing restrictions. I am *logically deducing* such restrictions, i.e. the Bell inequality, from certain assumptions. If you disagree with my conclusion, you must either disagree with the assumption of local determinism, or you must believe that my reasoning is flawed.

Do they actually show that nature is nonlocal, or might there be some other explanation regarding the effective causes of BI violations?

The proofs show that either nature is nonlocal, nature is nondeterministic, or that quantum mechanics is incorrect, in principle, in at least some of its experimental predictions. As far as actual BI violations in practical Bell tests, zonde will tell you that they reveal nothing at all due to experimental loopholes.

Extant observations (not necessarily interpretations of those observations) are all in line with the assumption of local determinism, so if you say, via some logical argument, that nature must be nonlocal, then the burden of proof is on you.

But I'm not logically proving that nature must be nonlocal. I am trying to logically prove that local determinism leads to certain conclusions that contradict the experimental predictions of QM. So the burden of proof is still on you to either identify a step in my reasoning your disagree with or to agree with the conclusion of my reasoning.

And that proof, scientifically, wrt your contention, would consist of producing some nonlocal transmissions.

If I were interested in proving that this is a nonlocal universe, that might be a worthwhile thing to try to do. But that's not what I'm doing here. I'm trying to demonstrate that two assumptions are logically incompatible.

Since no nonlocal transmissions have ever been observed/recorded, then the most reasonable scientific position is to retain the assumption that our universe is evolving in accordance with the principle of locality.

The reasoning certainly allows you to retain local determinism, but then it forces you to conclude that not all the experimental predictions of QM are correct.

Wrt Bell, Herbert, etc., that means that the most reasonable hypothesis is that there's something in the formalism, or line of reasoning, that has nothing to do with locality in nature, but which nevertheless skews the predictions of a an LR formalism or line of reasoning.

Well there is no formalism in Herbert's proof or my restatement of it, so then the thing you must dispute is the line of reasoning. But which step is it? Step 1 is just a statement of a prediction of QM. Step 3 is completely obvious given step 2 (it's the transitive property of equality: if A=B and B=C then A=C). Step 4 is just an application of the laws of probability using step 3. So the only step left is Step 2. But at least previously, you were unwilling to reject step 2.

You're a scientist, right? Ok, so just approach this problem from a different perspective, adopting the working hypothesis that maybe, just maybe, there's something in the standard Bell-type LR formalism, or, say, a Herbert-like line of reasoning, that doesn't fit the experimental situation, and that, just maybe, that incompatibility has nothing to do with whether nature is nonlocal or not.

I readily concede that Herbert's ideal scenario is not exactly realized in currently practical Bell tests, due to various loopholes. But I maintain the claim that a loophole-free Bell test could, in principle, refute local determinism (as always, excluding superdeterminism). I am also willing to concede that the incompatibility demonstrated by Herbert's reasoning does not automatically mean that nature is nonlocal. I don't think I've ever claimed this.

 

[San K]

If I understand you, all you're saying is that each photon decides in advance which angles to go though and which angles not to go through. And since the two photons in an entangled pair always do the same thing when you send them through polarizers oriented at the same angle, you can conclude that the two photons have agreed on which angles to go through and which ones not to. That's exactly in line with my four-step proof.

Yes it is. Agreed Lugita.

question: why do 50% photons going through a polarizer? What is QM's explanation for that? Is the (indeterminate state) photon's interaction with the polarizer -- totally random or is it cause and effect?

 

[ThomasT]

question: why do 50% photons going through a polarizer? What is QM's explanation for that? Is the (indeterminate state) photon's interaction with the polarizer -- totally random or is it cause and effect?

I see what you mean now, from your post #95. That seems to work for rate of individual detection, but not for rate of coincidental detection. Afaik, QM doesn't provide a causal explanation for either the random individual result sequences, or the random coincidental result sequences, or the predictable correlation between θ and rate of coincidental detection.

 

[San K]

As lugita15 says, this is exactly the idea (or its equivalent) that was considered PRIOR to Bell. But you will quickly find that works fine when the angle settings are identical, but generally does not work out at many combinations of settings.

0/120/240 are good examples - take the DrChinese challenge! See how close you can get the match rate (comparing AB, BC, AC) to 25% (the QM value) for 10 photons.

Photon 1:
A=0 degrees is +
B=120 degrees is +
C=240 degrees is -

So AB is a match, but AC and BC are not. 1 of 3.

Photon 2:
A=0 degrees is -
B=120 degrees is +
C=240 degrees is -

So AC is a match, but AB and BC are not. 1 of 3.

Photon 3:
A=0 degrees is -
B=120 degrees is -
C=240 degrees is -

So AC, AB and BC are matches. 3 of 3.

Etc. to 10 or whatever.

You win the challenge if your average rate is lower than 1/3. Again, the QM prediction is 1/4. It should be clear that the ONLY way to "win" over a suitably large sample is to know in advance which 2 settings will be selected for each photon in our trial. But if I do that (being independent of you and not knowing whether you marked a + or a - for each photon's settings) after you mark your values, the rate of matches will converge on 1/3 or more.

Agreed, could not win the DrChinese challenge...:)

question (and I will search on the net too) what are the QM calculations and assumptions to arrive at 1/4?

 

[San K]

I see what you mean now, from your post #95.

great

That seems to work for rate of individual detection, but not for rate of coincidental detection.

interesting.

what is co-incidental detection? is it (experiments using) entangled photons detected by a co-incidence counter?

Afaik, QM doesn't provide a causal explanation for either the random individual result sequences, or the random coincidental result sequences, or the predictable correlation between θ and rate of coincidental detection.

ok

 

[DrChinese]

Agreed, could not win the DrChinese challenge...:)

question (and I will search on the net too) what are the QM calculations and assumptions to arrive at 1/4?

A - B = -120 degrees
A - C = -240 "
B - C = -120 "

These are all equivalent for the function cos^2(theta), which is the formula for the QM prediction.

cos^2(-120) = .25
cos^2(-240) = .25
cos^2(-120) = .25

So no matter which pair you consider, the QM expectation is 1/4.

 

[ThomasT]

Sorry, I had to get it approved. Now you can read my post. (It doesn't contain any new info, just the reasoning I've already been giving, for easy reference.)

Ok. That makes it handy.

No, i do not say that. I say that we must infer from my line of reasoning that local determinism is incompatible with the experimental predictions of quantum mechanics being completely correct.

What you (and Bell and Herbert) are saying is that expressing coincidental detection in terms of a separable local predetermination is incompatible with the QM-predicted and observed correlation between θ and rate of coincidental detection. Which I agree with.

I am not arbitrarily placing restrictions. I am *logically deducing* such restrictions, i.e. the Bell inequality, from certain assumptions. If you disagree with my conclusion, you must either disagree with the assumption of local determinism, or you must believe that my reasoning is flawed.

Wrt Bell's formulation, it's clear where the restrictions come from and how they affect the predictions of any LR model that encodes those restrictions. Wrt your and Herbert's proofs, it's not so clear to me -- so, if you could clarify that it would help.

The proofs show that either nature is nonlocal, nature is nondeterministic, or that quantum mechanics is incorrect, in principle, in at least some of its experimental predictions.

More precisely, the proofs show that any model or line of reasoning embodying certain restrictions must be incompatible with QM and experiment. What are the restrictions, and how did they become part of the model or line of reasoning? Does employing these restrictions prove that nature is nonlocal? Imo, no.

It's been well established that the QM predictions are correct. Regarding determinism, it's an unfalsifiable assumption. So all you're dealing with is locality. So, what you're saying your proof proves is that nature is nonlocal (which is what Herbert says). But, what you've shown is that a particular way of conceptualizing coincidental detection is incompatible with QM and experiment. You can infer, from a certain conceptualization and line of reasoning that nature is nonlocal, but whether or not that inference is warranted depends on what's involved in the model or line of reasoning, and whether or not that inference is a fact of nature can only be ascertained by observing a nonlocal transmission.

But I'm not logically proving that nature must be nonlocal.

Yet that seems to be what you said above, and it is what Herbert says his proof proves, and you present your steps as a simplified recounting of Herbert's proof.

So the burden of proof is still on you to either identify a step in my reasoning your disagree with or to agree with the conclusion of my reasoning.

I think you (and Bell and Herbert) have proved what I said above. If you don't claim that your proof proves that nature is nonlocal, then we're basically on the same page.

 

[lugita15]

Yes it is. Agreed Lugita.

question: why do 50% photons going through a polarizer? What is QM's explanation for that? Is the (indeterminate state) photon's interaction with the polarizer -- totally random or is it cause and effect?

According to (the standard interpretation of) quantum mechanics, you have a wave function for the two-particle system, so the polarizations of the particles are in a superposition of states, until one of the photons is detected by one of the polarizers (say the first polarizer). Then the wave function of the system collapses (nonlocally and instantaneously), putting both photons in the same definite polarization state. The collapse will either make both particles polarized in the direction of the first polarizer, or make both particles polarized perpendicular to the direction of the first polarizers. Which of these two things will happen is considered to be a 50-50 chance event, because wave function collapse is according to (the standard interpretation of) QM completely random.

So then if the collapse makes the photons polarized in the direction of the first polarizer, the first photon will go through the first polarizer. If the collapse makes the photons polarized perpendicular to the first polarizer, then the first photon doesn't go through. So to someone just looking at the first polarizer, he always sees random 50-50 results.

What about the second polarizer? Well, the second photon is now in a definite polarization state, either parallel or perpendicular to the angle of the first polarizer. So now if the second polarizer is oriented at the same angle as the first one, the second photon will do the same thing the first one did. If the second polarizer is oriented at a different angle, then the second photon will randomly either go through or not go through, with a probability of going through equal to the cosine squared of the difference between the polarization angle of the photon and the angle of the second polarizer. But if someone was just looking at the second polarizer they won't know what angle the first polarizer was turned to or whether the first photon went through or not, so he won't know what angle the second photon was polarized along before it hit, and thus to him it will seem to go through or not go through with random 50-50 chance.

Does that make sense?

 

[San K]

A - B = -120 degrees
A - C = -240 "
B - C = -120 "

These are all equivalent for the function cos^2(theta), which is the formula for the QM prediction.

cos^2(-120) = .25
cos^2(-240) = .25
cos^2(-120) = .25

So no matter which pair you consider, the QM expectation is 1/4.

good answer, however my question was how cos came...:)

cos came from the de broglie waves...

now laws of probability are (linear/simple) additive for particles

are the laws of probability (linear) additive for waves? or do the have cosine in them?

 

[San K]

According to (the standard interpretation of) quantum mechanics, you have a wave function for the two-particle system, so the polarizations of the particles are in a superposition of states, until one of the photons is detected by one of the polarizers (say the first polarizer). Then the wave function of the system collapses (nonlocally and instantaneously), putting both photons in the same definite polarization state. The collapse will either make both particles polarized in the direction of the first polarizer, or make both particles polarized perpendicular to the direction of the first polarizers. Which of these two things will happen is considered to be a 50-50 chance event, because wave function collapse is according to (the standard interpretation of) QM completely random.

i was asking, in general, about non-entangled single photons...sorry forgot to mention

what does "completely random" mean? is there cause and effect?

Does that make sense?

surely and it was good to rehearse the 50-50 logic

however I am asking something else.take 100 photons un-entangled photons (in an indeterminate state)...why do only 50% of them pass through?

is that predetermined, cause and effect, or totally random? what does an indeterminate state mean? what do we mean by "inherent randomness" ?

second question: when we rotate the polarizer by a few degrees:

do the same 50 photons pass through or does the composition changes?

I also realize that we may not have to answer to any of the above questions, however can be important for future researchat some point/interaction ...says QM (?)...we/photons reach the edge...the edge of cause/effect and enter into the world of "inherent" randomness...

 

[lugita15]

What you (and Bell and Herbert) are saying is that expressing coincidental detection in terms of a separable local predetermination is incompatible with the QM-predicted and observed correlation between θ and rate of coincidental detection. Which I agree with.

My steps are concerned with local determinism in general. But what do you mean by separable? Do you mean in the sense of factorization of probability distributions, as Bell did in his original proof? Such a factorization is not used in Herbert's proof.

Wrt Bell's formulation, it's clear where the restrictions come from and how they affect the predictions of any LR model that encodes those restrictions. Wrt your and Herbert's proofs, it's not so clear to me -- so, if you could clarify that it would help.

I don't know how much help I can be, because I honestly don't know where I am "encoding restrictions" in my reasoning. I do ultimately arrive at a restriction, AKA the bell inequality, but I get that restriction as a conclusion of the argument, not an assumption of the argument. So if this conclusion is wrong then one of the steps must be wrong.

To go through the steps again, 1 is a prediction of QM, 3 uses the transitive property of equality, and 4 uses the laws of probability. Thus 2, in my view, is the only step that can possibly be disputed by someone. And yet it seems so obvious to me that a local determinist who accepts 1 must accept 2.

It's been well established that the QM predictions are correct.

I agree that there is ample experimental evidence for many of the predictions of QM. But a key prediction of QM used in the proof is the fact that you get perfect correlation at identical angle settings, and this has not been definitively demonstrated, because there are various experimental loopholes that in principle could be exploited to construct a local deterministic theory. But yes, the preponderance of evidence is in favor of the correctness of QM's experimental predictions.

Regarding determinism, it's an unfalsifiable assumption.

Determinism may be unfalsifiable on its own, but the combination of determinism and other assumptions may be falsifiable.

So all you're dealing with is locality.

I presume you mean locality in the sense of the principle of locality, which is just a synonym for local determinism. But it would be slightly improper to call a theory which violated local determinism a "nonlocal" theory, because "nonlocal" to my mind means that causality can propagate faster than the speed of light. But you can have, for instance, a nondeterministic theory in which there are no FTL influences.

So, what you're saying your proof proves is that nature is nonlocal (which is what Herbert says).

I mean exactly what I said: assuming that QM is completely correct in all its experimental predictions, we may reject local determinism.

But, what you've shown is that a particular way of conceptualizing coincidental detection is incompatible with QM and experiment.

I'm still trying to find out how you think I'm "restricting" or "conceptualizing" local determinism.

You can infer, from a certain conceptualization and line of reasoning that nature is nonlocal, but whether or not that inference is warranted depends on what's involved in the model or line of reasoning, and whether or not that inference is a fact of nature can only be ascertained by observing a nonlocal transmission.

But I'm not deducing facts of nature here, I'm trying to make logical deductions. My argument is of the form "If the universe has property A, then it must have property B." But the question of whether it actually has property B is dependent on whether in fact it has property A. (Property A is local determinism+perfect correlations at identical angle settings, and property B is the Bell inequality.) And the question of whether local determinism is logically incompatible with the experimental predictions of QM is a question to be decided logically, not experimentally. So as I said, the burden of proof is on you to disagree with my steps or agree with my conclusion.

Yet that seems to be what you said above, and it is what Herbert says his proof proves, and you present your steps as a simplified recounting of Herbert's proof.

It is a restatement of Herbert's proof, but I just feel he worded his conclusion a bit too strongly.

I think you (and Bell and Herbert) have proved what I said above. If you don't claim that your proof proves that nature is nonlocal, then we're basically on the same page.

But the only reason I do not make that claim is that current Bell tests have certain practical limitations and loopholes. But assuming that an ideal loophole-free Bell test, of the kind Herbert discusses, were to definitively demonstrate that the predictions of QM are completely correct, then I am certainly willing to reach the conclusion that we can reject local determinism (excluding unfalisifiable assumptions of superdeterminism, of course).

 

[lugita15]

i was asking, in general, about non-entangled single photons...sorry forgot to mention

OK, then the explanation is even simpler. The photon is initially described by a wave function that is in a superposition of polarization states. Then when the photon is hits the polarizer, the wave function collapses, and photon acquires a state of definite polarization, either polarized parallel to the polarizer or polarized perpendicular to the polarizer, each of these two outcomes has a 50% chance of happening.

what does "completely random" mean? is there cause and effect?

In the traditional Copenhagen interpretation, wave function collapse is truly random, in the sense that there is no cause and effect.

take 100 photons un-entangled photons (in an indeterminate state)...why do only 50% of them pass through?

The Cophenhagen interpretation says there is no reason for this, there is just a non-deterministic element to the universe.

is that predetermined, cause and effect, or totally random? what does an indeterminate state mean? what do we mean by "inherent randomness" ?

In the Copenhagen interpretation collapse is totally random, so that absolutely nothing determines what the outcome will be.

second question: when we rotate the polarizer by a few degrees:

do the same 50 photons pass through or does the composition changes?

Copenhagen says that each photon goes through or doesn't go through at random, so which 50 (on average) of the 100 photons are going to go through is not determined in advance at all.

at some point/interaction ...says QM (?)...we/photons reach the edge...the edge of cause/effect and enter into the world of "inherent" randomness...

Yes, at least according to the Copenhagen interpretation, which is the "standard" or "orthodox" view of QM. There are of course many other interpretations. For instance, Bohmian mechanics says that the apparent randomness of particle behavior is just due to our ignorance of (nonlocal) hidden variables associated with the particles. Many Worlds says that all possible outcomes occur in separate universes, and our mind is also there in these multiple universe, so the fact that we seem to observe outcome A rather than outcome B just means we happened to end up in a universe in which outcome A occurs. Roger Penrose's interpretation says that there is no randomness at all, and that the outcomes of all experiments can be determined in advanced just by calculating a mathematical function, but the only problem is that this function cannot be calculated by a computer (or Turing machine); but he believes that this uncomputable mathematical function CAN be calculated by humans, because he believes that the insightful abilities of the human mind surpasses that of any computer, because he believes that the human mind is based on quantum mechanics (see his books The Emperor's New Mind or Shadows of the Mind for more info).

 

[San K]

In the Copenhagen interpretation collapse is totally random, so that absolutely nothing determines what the outcome will be.

Lugita, i agree with all of what you said in your post.

it's hard for the human imagination/mind to comprehend (or think further)...what we mean by no cause and effect...

the below is trivial (not important):

does not the Copenhagen interpretation say let's not go there (not talk about it, shut up and calculate) rather than its totally random? or does it depends upon who you ask about the interpretation of the Copenhagen interpretation? ..:)

 

[lugita15]

good answer, however my question was how cos came...:)?

At a shallow level, the way quantum mechanics works is that you have to calculate the probability amplitude of a particle in state A to be measured in state B. In this case, state A is a superposition of polarization states and state B is the state of definite polarization parallel to the polarizer. Then you take the square of the absolute value of the probability amplitude to find the actual probability. When you do this straightforward calculation, the result happens to be cos^2.

At a more fundamental level, I suppose the cos^2 in this case arises from the the fact that photon polarization is related to spin angular momentum, and angular momentum is based on rotations, so the mathematics of rotations gives us sines and cosines.

cos came from the de broglie waves...

Yes, in some sense you could say that the sinusoidal functions come from the fact that in QM particles are described by wave functions, which is very different than how particles work classically.

now laws of probability are (linear/simple) additive for particles

The laws of probability have the same form regardless of what kinds of objects you're talking about.

are the laws of probability (linear) additive for waves? or do the have cosine in them

The laws of probability are still (sub)additive, for both particles and waves, but that's not the question you should be asking. Rather the issue is, if you take two simple waves, is the square of the amplitude of their sum less than or equal to the sum of the squares of their amplitudes? That is, if wave 1 has amplitude A1, wave 2 has amplitude A2, and wave 3, which is the superposition of waves 1 and 2, has amplitude A3, is A3^2 always less than or equal to A1^2 +A2^2? The answer to that is no.

But we have a problem: the wave function in QM is supposed to represent the probability of getting of a particle getting a certain experimental outcome. So it seems like although we can say that the wave function does describe the probability the photon will be detected at a particular point on the screen of a double slit apparatus, it seems like we cannot say that it describes the probability of the photon going through one slit vs the other slit (where there are no detectors at the slits). The way it looks is that a wave goes through the slits, but then when then there is a detection event, then suddenly the wave function translates into probabilities of the particle being measured having certain attributes. So it's as if the quantum object behaves as a wave until it's measured, behaves as a particle with definite attributes after it's measured. Thus the Copenhagen interpretation was born. If you want to see more discussion along these lines, you can read a chapter from the Feynman Lectures on Physics (I can give you a scan), or watch one of Feynman's Character of Physical Law videos.

Bottom line, in some sense you can say that wave-particle duality is to blame for the strangeness of quantum entanglement.

 

[lugita15]

does not the Copenhagen interpretation say let's not go there (not talk about it, shut up and calculate) rather than its totally random? or does it depends upon who you ask about the interpretation of the Copenhagen interpretation? ..:)

The doctrine of Copenhagen is total randomness of the results of wave function collapse. It's more when you ask questions like "is the wave function real" or "what constitutes a measurement for the purposes of wave function collapse" that Copenhagen people may give you the "shut up and calculate" attitude.

 

[ThomasT]

... what is co-incidental detection? is it (experiments using) entangled photons detected by a co-incidence counter?

Yes, or some other means of pairing individual results. It's what DrC is talking about in his challenge.

Let me say this right now. I feel pretty certain that ttn (Travis Norsen), DrC (David Schneider), zonde, lugita, Demystifier (Nikolic), billschnieder, Gordan Watson, unusualname, harrylin (and anybody I left out) and all the other contributors to this and other 'Bell' threads know a lot more about this stuff than I do. So, it would probably be best if you don't ask me any more questions about this.

The Bell stuff is mainly a philosophical consideration, and wading through the language surrounding it, and eliminating the bs and irrelevant considerations is a daunting task. I hope that you and others stick with it so that maybe one day you can explain it to me and other laypersons in a way that we can understand it.

I've expressed my ideas/opinions, and now I will fade back into the peanut gallery, and hopefully learn something new.

 

[ThomasT]

My steps are concerned with local determinism in general. But what do you mean by separable? Do you mean in the sense of factorization of probability distributions, as Bell did in his original proof? Such a factorization is not used in Herbert's proof.

Herbert says that his line of reasoning embodies the independence of spacelike separated events as the assumption of locality. If your proof is a recounting of Herbert's proof, then your proof does this also. In which step of your proof is this explicated?

I don't know how much help I can be, because I honestly don't know where I am "encoding restrictions" in my reasoning. I do ultimately arrive at a restriction, AKA the bell inequality, but I get that restriction as a conclusion of the argument, not an assumption of the argument. So if this conclusion is wrong then one of the steps must be wrong.

The conclusion isn't wrong if it follows from your assumptions. You say, and I agree, that your conclusion follows from your assumptions. So, what we have to look at is your assumptions in order to ascertain whether we can conclude that an underlying reality, ie., nature, must be nonlocal.

It's not that one of your steps (assumptions) is necessarily wrong, it's that one of your steps might not necessarily be expressing what's actually happening in the underlying reality. The problem, the situation, is that we have no way of knowing, because of the limitations imposed by our sensory faculties.

I agree that there is ample experimental evidence for many of the predictions of QM. But a key prediction of QM used in the proof is the fact that you get perfect correlation at identical angle settings, and this has not been definitively demonstrated, because there are various experimental loopholes that in principle could be exploited to construct a local deterministic theory. But yes, the preponderance of evidence is in favor of the correctness of QM's experimental predictions.

Ok, so we, and most everybody else, agrees on that.

Determinism may be unfalsifiable on its own, but the combination of determinism and other assumptions may be falsifiable.

In which case, then what you might be falsifying would be a certain expression of those other assumptions, such as a particular expression of locality -- but not determinism.

I presume you mean locality in the sense of the principle of locality, which is just a synonym for local determinism.

Locality, in the usual sense, means that nothing propagates faster than the speed of light. Determinism means that events or states at t = 1 are a consequence of events or states at t = 0. Determinism isn't incompatible with ftl propagations. But it is incompatible with instantaneous action at a distance.

I'm still trying to find out how you think I'm "restricting" or "conceptualizing" local determinism.

That's what I'm trying to find out. It's your proof. You tell me.

But I'm not deducing facts of nature here ...

Then we're on the same page. You, and Herbert, and Bell aren't necessarily saying anything about nature.

 

[San K]

So, it would probably be best if you don't ask me any more questions about this.

i won't ask you anymore.

it has been a great discussion/thread...:)

DrChinese, Lugita and others have passionately/patiently answered the posts and shared some interesting new information/knowledge. They has also helped, some of us, understand Bell's theorem faster. thanks DrC, Lugita and others.

 

[ThomasT]

i won't ask you anymore.

But certainly keep on asking the others. They know a bit more. (And of course you can still ask me anything, and if I don't feel certain that I know the answer, then I'll try to find the time to look it up ... but of course you can do that also.)

If you're just starting out in this, then I hope you have the time to keep at it until you're satisfied that you fully understand it.

 

[lugita15]

Herbert says that his line of reasoning embodies the independence of spacelike separated events as the assumption of locality. If your proof is a recounting of Herbert's proof, then your proof does this also. In which step of your proof is this explicated?

Well, if by "independence of spacelike separated events" you mean that the behavior of particle 1 is independent of the setting of polarizer 2, and vice versa, then yes, I am assuming that that is part of the definition of local determinism. Is that what you dispute? If so, then step 2 would be the step you should disagree with me on.

It's not that one of your steps (assumptions) is necessarily wrong, it's that one of your steps might not necessarily be expressing what's actually happening in the underlying reality. The problem, the situation, is that we have no way of knowing, because of the limitations imposed by our sensory faculties.

But there are some things that are the same regardless of the universe we live in. Step 1 is a prediction of quantum mechanics, and this prediction will be the same in every universe, although presumably it will be a correct prediction in some universes and an incorrect prediction in others. Step 3 is an application of the transitive property of equality, and step 4 is an application of the laws of probability, and I hope you agree that those apply equally well in all universes. So we come back to step 2.

Determinism isn't incompatible with ftl propagations. But it is incompatible with instantaneous action at a distance.

This is irrelevant to what we're discussing, but why do you think instantaneous action at a distance is incompatible with determinism?

That's what I'm trying to find out. It's your proof. You tell me.

But I don't think I am assuming some restrictions on what a local deterministic theory can look like. Rather, I am CONCLUDING a restriction, the Bell inequality, from the assumptions of local determinism and perfect correlation at identical angles.

Then we're on the same page. You, and Herbert, and Bell aren't necessarily saying anything about nature.

We're not on the same page, because under the assumption that QM is correct in its experimental predictions, I most definitely AM saying something about nature.

 

[ThomasT]

Well, if by "independence of spacelike separated events" you mean that the behavior of particle 1 is independent of the setting of polarizer 2, and vice versa, then yes, I am assuming that that is part of the definition of local determinism. Is that what you dispute? If so, then step 2 would be the step you should disagree with me on.

But step 2 doesn't specify any particular way of expressing that. That comes with step 3. So, it would seem that step 3 is where the actual restriction is introduced.

... why do you think instantaneous action at a distance is incompatible with determinism?

Because determinism has to do with the temporal causal order of events. Instantaneous action at a distance between A and B precludes this. It says that A and B are happening simultaneously.

But I don't think I am assuming some restrictions on what a local deterministic theory can look like. Rather, I am CONCLUDING a restriction, the Bell inequality, from the assumptions of local determinism and perfect correlation at identical angles.

The restriction has to be introduced before the conclusion of a linear correlation between θ and rate of coincidental detection. Since step 2 doesn't express any particular literal restriction, then it has to be step 3. That is, you've chosen to express the assumption of independence (locality) in a certain way, and expressing it that way entails the conclusion that the correlation between θ and rate of coincidental detection must be linear.

We're not on the same page, because under the assumption that QM is correct in its experimental predictions, I most definitely AM saying something about nature.

The physical interpretation of QM has been an open question since the theory was first formulated. As far as I can tell it will always be an open question.

The only thing that can be concluded from any Bell-LR model of quantum entanglement is that something pertaining to the formal LR restrictions makes the model nonviable. The precise relationship between the model, any model, even viable ones, and an underlying reality remains unknown.

If the source of disagreement between model and results can be precisely identified as something in the model which clearly is incompatible wrt the experimental design and execution, then that should be taken as the effective cause of the nonviability.

Regarding your proof, is your step 3 the only way to conceptualize the experimental situation? If not, then does it establish that nature is nonlocal?

 

[lugita15]

But step 2 doesn't specify any particular way of expressing that. That comes with step 3. So, it would seem that step 3 is where the actual restriction is introduced.

ThomasT, you have the uncanny ability of focusing on steps I consider to be unimportant. Step 3 says "In order for the agreed-upon instructions (to go through or not go through) at -30 and 30 to be different, either the instructions at -30 and 0 are different or the instructions at 0 and 30 are different." Let me ask you this, is the following general statement true? "If A and C are different, either A and B are different or B and C are different." For example, "If the color of your pants and shoes are different, then the color of your pants and socks are different, or the color of your socks and shoes are different." (In this case, A="the instruction at -30", B="the instruction at 0", and C="the instruction at 30".) If you cannot tell that this statement is true, consider the equivalent statement "If A and B are the same, and B and C are the same, then A and C are the same." You should recognize that as the transitive property of equality, and presumably that is not in despite.

You can, of course, dispute that the particles have agreed in advance which angles to go through and which angles not to go through, in which case you should dispute step 2. But if you have accepted step 2, and thus believe that the particles have instructions as to exactly which angles to go through and which angles not to go through, then the transitive property of equality forces you to accept step 3.

Because determinism has to do with the temporal causal order of events. Instantaneous action at a distance between A and B precludes this. It says that A and B are happening simultaneously.

This is entirely irrelevant to our discussion, but do you not consider Newton's theory of gravitation to be deterministic, since it has instantaneous action at a distance? And would consider Bohmian mechanics to be nondeterministic, since it too has instantaneous action at a distance?

The restriction has to be introduced before the conclusion of a linear correlation between θ and rate of coincidental detection. Since step 2 doesn't express any particular literal restriction, then it has to be step 3. That is, you've chosen to express the assumption of independence (locality) in a certain way, and expressing it that way entails the conclusion that the correlation between θ and rate of coincidental detection must be linear.

But I am not making any assumption of locality or independence in step 3! Step 2 is where I say the particles have determined in advance, exactly what angles to go through and what angles not to go through. So they have a list of the instructions of the form "If you see a 20 degree polarizer, go through", "If you see a 40 degree polarizer, don't go through", etc., a list they have agreed upon in advance when they were emitted from the source.

If you agree with me up to there, I don't know how you can disagree with step 3, which is completely trivial.

The physical interpretation of QM has been an open question since the theory was first formulated. As far as I can tell it will always be an open question.

Yes, there are some philosophical views that are indistinguishable experimentally from quantum mechanics, so they can fairly be called interpretations. Copenhagen, Many Worlds, and Bohmian mechanics are good examples of those. But not all possible viewpoints are indistinguishable experimentally from quantum mechanics. For instance, Schrodinger himself originally viewed the wave function as a literal gas that surrounded the nucleus of the atom, and that the magnitude of the wave function was indication the thickness of the gas. But this view was rejected after it was found that when measured, an electron was detected as a particle, not a wave.

Similarly, I see local determinism (excluding superdeterminism) as a view that IS distinguishable experimentally from quantum mechanics, and thus it can't be fairly called an "interpretation".

Regarding your proof, is your step 3 the only way to conceptualize the experimental situation? If not, then does it establish that nature is nonlocal?

As I said, step 3 is not the step where locality is invoked. Step 3 is an unimportant step where I'm just saying something of the form "If A≠C, then A≠B or B≠C" (an application of the transitive property of equality), so that I can apply the laws of probability and say "The probability that A≠B or B≠C is less than or equal to the probablity that A≠B plus the probability that B≠C" and thus conclude that "The probability that A≠C is less than or equal to the probablity that A≠B plus the probability that B≠C", which is the Bell inequality I'm after.

 

[ThomasT]

ThomasT, you have the uncanny ability of focusing on steps I consider to be unimportant.

They must all have some importance, otherwise I suppose that you wouldn't bother expressing them.

Step 3 says "In order for the agreed-upon instructions (to go through or not go through) at -30 and 30 to be different, either the instructions at -30 and 0 are different or the instructions at 0 and 30 are different." Let me ask you this, is the following general statement true? "If A and C are different, either A and B are different or B and C are different." For example, "If the color of your pants and shoes are different, then the color of your pants and socks are different, or the color of your socks and shoes are different." (In this case, A="the instruction at -30", B="the instruction at 0", and C="the instruction at 30".) If you cannot tell that this statement is true, consider the equivalent statement "If A and B are the same, and B and C are the same, then A and C are the same." You should recognize that as the transitive property of equality, and presumably that is not in despute.

No, that's not in dispute. What's in dispute is the manner in which some have chosen to restrict the argument. Is it possible that the transitive property of equality expressed in terms of things that we can count at our level of macroscopic apprehension might have nothing to do with locality/nonlocality in a realm of behavior removed from our sensory apprehension and, presumably, underlying instrumental behavior -- at least wrt the way that the dilemma has so far been framed?

You can, of course, dispute that the particles have agreed in advance which angles to go through and which angles not to go through, in which case you should dispute step 2. But if you have accepted step 2, and thus believe that the particles have instructions as to exactly which angles to go through and which angles not to go through, then the transitive property of equality forces you to accept step 3.

There's at least one other way of conceptualizing the reason for identical detection attributes at identical settings. Namely, that the separated polarizers are analyzing, filtering exactly the same thing wrt any given pair of entangled particles. In which case, the expected result would be in line with the QM predictions and Malus Law.

This is entirely irrelevant to our discussion ...

I think so too. But you're the one who's including determinism in this.

... but do you not consider Newton's theory of gravitation to be deterministic, since it has instantaneous action at a distance?

I'm not aware of any contention or hypothesis of instantaneous action at a distance associated, by Newton, with the relationships that his equations specify. For those who want to infer nonlocality from the equations, then that's on them. The equations express an observationally confirmed relationship. Is it possible that that relationship might be due to local interactions/transmissions? Yes, of course it is, in the sense of gravitational systems.

And would consider Bohmian mechanics to be nondeterministic, since it too has instantaneous action at a distance?

Yes, insofar as dBB is interpreted to explicate nonlocality, then it's nondeterministic. Just relational, just as standard QM is relational, not causal.

But I am not making any assumption of locality or independence in step 3!

But that's where it takes a particular form that must affect the conclusion. Simply assuming locality, in terms of independence, is inconsequential until that assumption is put into a form that will impact the reasoning or the experimental predictions.

Step 2 is where I say the particles have determined in advance, exactly what angles to go through and what angles not to go through.

Yes, but step 2 doesn't put it into a form that will impact the reasoning. Step 3 does that.

Then again, I suppose you could say that step 2 in some sense implies step 3. So, maybe we should look more closely at step 2. The way it's stated is rather ... pedestrian and a bit too anthropomorphic, I must say. What are some other ways of stating the inference(s) that might be drawn from step 1?