Nick Herbert's Proof: Quantum Non-Locality Explained

[harrylin]

This is a spin-off from the thread on Bell's theorem, following this post:
https://www.physicsforums.com/showthread.php?p=3819552

Instead of discussing about λ and the way to account for it, Nick Herbert seems to have provided a stunningly simple and convincing proof of "quantum non-locality" here (thanks for the link Lugita15):

- http://quantumtantra.com/bell2.html
The essential part is in the last drawing, with the text just above it:

simple arithmetic and the assumption that Reality is Local leads one to confidently predict that the code mismatch at 60 degrees must be less than 50%.

It surely looks very convincing to me!
Thus my questions:

- are there known issues with that proof?
- I thought that models exist that reproduce the characteristic of QM of a greater "mismatch". However, according to Herbert's proof, that is not possible. What's going on?

 

[gill1109]

That's a perfectly good proof. Nothing wrong with it.

What do you mean by "I thought that models exist that reproduce the characteristic of QM of a greater 'mismatch'"?

There are published models which are wrong (as they must be: you can't contradict a true theorem).

There are published models which simply exploit the so-called detection loophole, but without making that explicit.

Imagine the standard Bell situation where two particles fly to two distant locations where they are each measured in one of two possible ways resulting in a binary outcome. Suppose the two particles, just before departing from the source, agree what pair of settings they would like to see and what pair of outcomes they will then generate. They then set off on their journey. Each of them arrives at a detector and sees that one particular setting has been chosen. If the setting which has been chosen by the experimenter is different from the setting which the two particles had agreed on in advance, then that particle decides to vanish. It's not detected at all.

If real settings and if "guessed settings" are all chosen completely at random, half of the particles will fail to arrive at each detector. Both will be detected one quarter of the times. And on those quarter of all the times, they can produce any correlation they like, for instance, they can go all the way to 4 in the Bell inequality (QM only goes to 2 sqrt 2).

It's well known that even if only 10% of the particles fail to be detected (or something like that), they can perfectly violate Bell inequality at the 2 sqrt 2 level predicted by QM.

In real experiments many, many particles are not detected. The non-detection rate is more like 95%.

 

[gill1109]

By the way the link between Nick Herbert's proof and Bell's proof is to think of lambda as being the set of four measurement outcomes of the two particles under each of the two settings. After all, Bell's encoding of "local realism" is that if you knew the values of hidden variables located in the photons or in the measuring devices or anywhere else, then the outcomes of either measurement, on either particle, is just some deterministic function of the values of all these variables.

Then in Bell's formulas for the correlation between the outcomes of two measurements, replace integration over the possible values of the hidden variables, weighted according to their probabiity density, by a sum over the 16 possible values of the four binary outcomes.

Well, it still maybe looks like different mathematics, but in fact we are now getting very close to a simple combinatorial argument - just running through a finite number of different possibilities.

 

[ThomasT]

- I thought that models exist that reproduce the characteristic of QM of a greater "mismatch". However, according to Herbert's proof, that is not possible. What's going on?

local hidden variable theory

You should be able to find examples of LR models that produce a nonlinear correlation between θ and P(a,b) via Google and arxiv.org searches.

Here are a couple of statements of the issues regarding Bell-type or Herbert-type proofs by a couple of physicists who think that the assumption of nonlocality in nature might be unwarranted.

One general issue raised by the debates over locality is to understand the connection between stochastic independence (probabilities multiply) and genuine physical independence (no mutual influence). It is the latter that is at issue in “locality,” but
it is the former that goes proxy for it in the Bell-like calculations.

How clearly and convincingly to exorcise nonlocality from the foundations of physics in spite of the violations of Bell inequalities. Nonlocality has been egregiously oversold. On the other hand, those who briskly dismiss it as a naive error
are evading a direct confrontation with one of the central peculiarities of quantum
physics. I would put the issue like this: what can one legitimately require of
an explanation of correlations between the outcomes of independently selected tests
performed on systems that no longer interact?

 

[gill1109]

Fine is wrong. Bell gave sufficient conditions for his inequality to hold, not necessary and sufficient conditions. The issue is not statistical independence. The issue is the possibility to add into the model the outcomes of the measurements which were not performed, alongside of those which were performed, in a way which respects locality. In the Bell-CHSH set-up (two parties, two measurements per party, two possible outcomes per measurement) all Bell-CHSH inequalities hold if and only if the unperformed measurements can also have outcomes attributed to them, in a local way.

 

[gill1109]

The only models which are correct and which reproduce P(a,b) are models exploiting the detection loophole.

 

[ThomasT]

Fine is wrong. Bell gave sufficient conditions for his inequality to hold, not necessary and sufficient conditions. The issue is not statistical independence. The issue is the possibility to add into the model the outcomes of the measurements which were not performed, alongside of those which were performed, in a way which respects locality. In the Bell-CHSH set-up (two parties, two measurements per party, two possible outcomes per measurement) all Bell-CHSH inequalities hold if and only if the unperformed measurements can also have outcomes attributed to them, in a local way.

Not sure what you're saying. Have Herbert and Bell proven that nature is nonlocal?

 

[DrChinese]

Not sure what you're saying. Have Herbert and Bell proven that nature is nonlocal?

Don't forget the realism requirement. If that is dropped, locality is possible.

 

[bohm2]

Don't forget the realism requirement. If that is dropped, locality is possible.

What is the difference between local non-realism vs non-local non-realism?

 

[DrChinese]

What is the difference between local non-realism vs non-local non-realism?

To me (and not everyone has the exact same definitions): It is non-realistic if you deny existence of counterfactual outcomes. In EPR terms, you are essentially denying the existence of "elements of reality independent of the act of observation." EPR would say that perfect correlations are a manifestation of these elements of reality. While the Copenhagen view would be that perfect correlations are the mathematical outcome you get as a result of the cos^2(theta) relationship.

So I guess the non-local version of the above adds in the idea that the measurement device settings are effectively in communication with the particles being observed.

 

[ThomasT]

What do you mean by "I thought that models exist that reproduce the characteristic of QM of a greater 'mismatch'"?

I think he's referring to LR models that produce a nonlinear angular dependence.

In real experiments many, many particles are not detected. The non-detection rate is more like 95%.

For the purposes of the OP, assuming 100% detection efficiency and 100% attribute-pairing efficiency, wouldn't the predictions of any Bell-type or Herbert-type LR model of entanglement (wrt a simple setup where you have two parties, one measurement per party per entangled pair, and two possible outcomes per measurement) still disagree with most of the QM predictions? That is, even in the ideal, an LR model necessarily produces a correlation between θ and P(a,b), from linear to something approching cos²θ, that will, necessarily, be incongruent with the QM correlation.

 

[ThomasT]

Don't forget the realism requirement. If that is dropped, locality is possible.

The way I think about this is that the realism requirement is the association of the individual measurement outcomes (either +1 and -1, or 1 and 0, denoting detection and nondetection, respectively, wrt a coincidence interval) with a function describing individual detection, which includes both λ and the polarizer setting, a (or b), such that, as Bell wrote, A(a,λ) = ±1. While the locality requirement is the separation of the functions determining individual detection in the formulation of the function determining joint detection, such that, as Bell wrote,
P(a,b) = ∫dλρ(λ)A(a,λ)B(b,λ) .

So, if the realism requirement is dropped, then how would locality be expressed/encoded?

 

[ThomasT]

Fine is wrong. ... The issue is not statistical independence.

Apparently, something gets lost (or confused) in the translation of the assumption of locality (independence) into a testable mathematical model.

Assuming a local reality means that, for each A photon, whatever hidden mechanism determines the output of Miss A's SPOT detector, the operation of that mechanism cannot depend on the setting of Mr B's distant detector. In other words, in a local world, any changes that occur in Miss A's coded message when she rotates her SPOT detector are caused by her actions alone.

And the same goes for Mr B. The locality assumption means that any changes that appear in the coded sequence B when Mr B rotates his SPOT detector are caused only by his actions and have nothing to do with how Miss A decided to rotate her SPOT detector.

The vital assumption is that the result B for particle 2 does not depend on the setting a, of the magnet for particle 1, nor A on b.

One general issue raised by the debates over locality is to understand the connection between stochastic independence (probabilities multiply) and genuine physical independence (no mutual influence). It is the latter that is at issue in “locality,” but
it is the former that goes proxy for it in the Bell-like calculations.

 

[DrChinese]

The way I think about this is that the realism requirement is the association of the individual measurement outcomes (either +1 and -1, or 1 and 0, denoting detection and nondetection, respectively, wrt a coincidence interval) with a function describing individual detection, which includes both λ and the polarizer setting, a (or b), such that, as Bell wrote, A(a,λ) = ±1. While the locality requirement is the separation of the functions determining individual detection in the formulation of the function determining joint detection, such that, as Bell wrote,
P(a,b) = ∫dλρ(λ)A(a,λ)B(b,λ) .

So, if the realism requirement is dropped, then how would locality be expressed/encoded?

I don't know, as it is essential to all Bell-type arguments including Herbert's.

To me, the locality requirement is tested by having the Alice and Bob measurement settings be determined while spacelike separated. This has the effect of proving that no classical communication is occurring between Alice and Bob.

 

[ThomasT]

- are there known issues with that proof?

Herbert goes from this:

Assuming a local reality means that, for each A photon, whatever hidden mechanism determines the output of Miss A's SPOT detector, the operation of that mechanism cannot depend on the setting of Mr B's distant detector. In other words, in a local world, any changes that occur in Miss A's coded message when she rotates her SPOT detector are caused by her actions alone.

And the same goes for Mr B. The locality assumption means that any changes that appear in the coded sequence B when Mr B rotates his SPOT detector are caused only by his actions and have nothing to do with how Miss A decided to rotate her SPOT detector.

To this:

Starting with two completely identical binary messages, if A's 30 degree turn introduces a 25% mismatch and B's 30 degree turn introduces a 25% mismatch, then the total mismatch (when both are turned) can be at most 50%. In fact the mismatch should be less than 50% because if the two errors happen to occur on the same photon, a mismatch is converted to a match.

What has he overlooked?

 

[harrylin]

That's a perfectly good proof. Nothing wrong with it.

It was indeed my first impression that it is a perfect proof: it seems to be necessarily valid for all possible scenarios - that is, without any exceptions or "loopholes".

What do you mean by "I thought that models exist that reproduce the characteristic of QM of a greater 'mismatch'"?

I meant models that predict observations that reproduce such observations - and which therefore are impossible according to Herbert's proof. Consequently, either Herbert's proof has a weakness that I did not perceive, or such models are erroneous.

[..] There are published models which simply exploit the so-called detection loophole, but without making that explicit.

Imagine the standard Bell situation where two particles fly to two distant locations where they are each measured in one of two possible ways resulting in a binary outcome. Suppose the two particles, just before departing from the source, agree what pair of settings they would like to see and what pair of outcomes they will then generate. They then set off on their journey. Each of them arrives at a detector and sees that one particular setting has been chosen. If the setting which has been chosen by the experimenter is different from the setting which the two particles had agreed on in advance, then that particle decides to vanish. It's not detected at all.

Perhaps I misunderstood Herbert's proof; I thought that such particles participate in generating the differences that are recorded, on each side independently. Then it's not clear to me how it matters, how his proof could be affected by this (see next).
And evidently Herbert also did not realize that his proof could fail for such situations... He only considerd the observed patterns, and his only condition is that "reality is local" - detection yield doesn't play any role in his argument.

If real settings and if "guessed settings" are all chosen completely at random, half of the particles will fail to arrive at each detector. Both will be detected one quarter of the times. And on those quarter of all the times, they can produce any correlation they like, for instance, they can go all the way to 4 in the Bell inequality (QM only goes to 2 sqrt 2).

It's well known that even if only 10% of the particles fail to be detected (or something like that), they can perfectly violate Bell inequality at the 2 sqrt 2 level predicted by QM.

In real experiments many, many particles are not detected. The non-detection rate is more like 95%.

Thank you! Clearly I overlooked something. Regretfully I still don't get it, as Herbert's proof looks robust for such cases - your proposed model is just another possible hidden mechanism that "determines the output", as Herbert described.
His conclusion that "simple arithmetic and the assumption that Reality is Local leads one to confidently predict that the code mismatch at 60 degrees must be less than 50%", sounds rock solid.

isn't the possible loss of particle detections included in the 25% mismatch? Thus, how can in such a case 25% + <=25% > 50% ??

 

[ThomasT]

To me, the locality requirement is tested by having the Alice and Bob measurement settings be determined while spacelike separated. This has the effect of proving that no classical communication is occurring between Alice and Bob.

The experiments do structure out c or sub c communications between spacelike separated events per coincidence interval.

The problem is that the independence encoded in LR formulations involves statistical independence, while also requiring coincidental detection to be expressed in terms of a variable (via the individual detection functions) that, as far as I can tell, doesn't determine it.

Also, the possibility remains of some sort of superluminal communication between whatever -- even though lower bounds have been calculated wrt various experiments. There's no way to falsify the assumption of >c transmissions wrt optical Bell tests, is there?

 

[gill1109]

Herbert's argument (which is informal) relies on 25% and 25% and 75% being percentages of the same photon pairs. In a model which violates Bell through the detection loophole, it would be different photon pairs which are not detected with each pair of detector settings. 25% of a smaller subset of photons, 25% of another small subset of photons, 75% of yet another small subset of photons.

He is silently assuming realism by imagining the same population of photon pairs being measured in different ways.

 

[gill1109]

The only statistical independence required is that between the experimentally chosen measurement settings and the set of counterfactual measurement outcomes (the two pairs of outcomes of both possible measurements on both particles).

 

[harrylin]

The only statistical independence required is that between the experimentally chosen measurement settings and the set of counterfactual measurement outcomes (the two pairs of outcomes of both possible measurements on both particles).

Herbert's argument (which is informal) relies on 25% and 25% and 75% being percentages of the same photon pairs. In a model which violates Bell through the detection loophole, it would be different photon pairs which are not detected with each pair of detector settings. 25% of a smaller subset of photons, 25% of another small subset of photons, 75% of yet another small subset of photons.

He is silently assuming realism by imagining the same population of photon pairs being measured in different ways.

I still don't get it... Herbert's proof doesn't even consider particles, let alone both particles or the same photon pairs.

Here is how I apply Herbert's proof to the scenario of incomplete detection, following his logic by the letter and adding my comments:

---------------------------------------------------------------------
Step One: Start by aligning both SPOT detectors. No errors are observed.

[harrylin: for example the sequences go like this:

A 10010110100111010010
B 10010110100111010010]

Step Two: Tilt the A detector till errors reach 25%. This occurs at a mutual misalignment of 30 degrees.

[harrylin: for example (a bit idealized) the sequences go like this:

A 10010100110110110110
B 10110100111010010010

This mismatch could be partly due to the detection of different photon pairs.]

Step Three: Return A detector to its original position (100% match). Now tilt the B detector in the opposite direction till errors reach 25%. This occurs at a mutual misalignment of -30 degrees.

[harrylin: for example the sequences go like this, for the same reasons:

A 10100100101011010011
B 10010101101011010101]

Step Four: Return B detector to its original position (100% match). Now tilt detector A by +30 degrees and detector B by -30 degrees so that the combined angle between them is 60 degrees.

What is now the expected mismatch between the two binary code sequences?

[..] Assuming a local reality means that, for each A photon, whatever hidden mechanism determines the output of Miss A's SPOT detector, the operation of that mechanism cannot depend on the setting of Mr B's distant detector. In other words, in a local world, any changes that occur in Miss A's coded message when she rotates her SPOT detector are caused by her actions alone.

[harrylin: apparently that includes whatever mechanism one could imagine - also non-detection of part of the photons]

And the same goes for Mr B. [..] So with this restriction in place (the assumption that reality is local), let's calculate the expected mismatch at 60 degrees.

Starting with two completely identical binary messages, if A's 30 degree turn introduces a 25% mismatch and B's 30 degree turn introduces a 25% mismatch, then the total mismatch (when both are turned) can be at most 50%. In fact the mismatch should be less than 50% because if the two errors happen to occur on the same photon, a mismatch is converted to a match.

[harrylin: and if the errors happen to occur on different photons that are compared, still sometimes a mismatch will be converted to a match. Thus now for example the sequences go like this, for the same reasons as +30 degrees and -30 degrees:

A 10101010110101010011
B 10100100101011010101]
----------------------------------------------------------------------------

So far Herbert's proof, which is simply comparing binary code sequences. Nowhere is there any assumption about detection efficiency, as there is even no assumption about what happens at the detectors or about what happens at the source. The only assumptions concern independent detections and reproducibility of % of matching in sufficiently long sequences.

Where is the error?

 

[DrChinese]

I still don't get it... Herbert's proof doesn't even consider particles, let alone both particles or the same photon pairs.

Here is how I apply Herbert's proof to the scenario of incomplete detection, following his logic by the letter and adding my comments:

---------------------------------------------------------------------
Step One: Start by aligning both SPOT detectors. No errors are observed.

[harrylin: for example the sequences go like this:

A 10010110100111010010
B 10010110100111010010]

Step Two: Tilt the A detector till errors reach 25%. This occurs at a mutual misalignment of 30 degrees.

[harrylin: for example (a bit idealized) the sequences go like this:

A 10010100110110110110
B 10110100111010010010

This mismatch could be partly due to the detection of different photon pairs.]

Step Three: Return A detector to its original position (100% match). Now tilt the B detector in the opposite direction till errors reach 25%. This occurs at a mutual misalignment of -30 degrees.

[harrylin: for example the sequences go like this, for the same reasons:

A 10100100101011010011
B 10010101101011010101]

Step Four: Return B detector to its original position (100% match). Now tilt detector A by +30 degrees and detector B by -30 degrees so that the combined angle between them is 60 degrees.

What is now the expected mismatch between the two binary code sequences?

[..] Assuming a local reality means that, for each A photon, whatever hidden mechanism determines the output of Miss A's SPOT detector, the operation of that mechanism cannot depend on the setting of Mr B's distant detector. In other words, in a local world, any changes that occur in Miss A's coded message when she rotates her SPOT detector are caused by her actions alone.

[harrylin: apparently that includes whatever mechanism one could imagine - also non-detection of part of the photons]

And the same goes for Mr B. [..] So with this restriction in place (the assumption that reality is local), let's calculate the expected mismatch at 60 degrees.

Starting with two completely identical binary messages, if A's 30 degree turn introduces a 25% mismatch and B's 30 degree turn introduces a 25% mismatch, then the total mismatch (when both are turned) can be at most 50%. In fact the mismatch should be less than 50% because if the two errors happen to occur on the same photon, a mismatch is converted to a match.

[harrylin: and if the errors happen to occur on different photons that are compared, still sometimes a mismatch will be converted to a match. Thus now for example the sequences go like this, for the same reasons as +30 degrees and -30 degrees:

A 10101010110101010011
B 10100100101011010101]
----------------------------------------------------------------------------

So far Herbert's proof, which is simply comparing binary code sequences. Nowhere is there any assumption about detection efficiency, as there is even no assumption about what happens at the detectors or about what happens at the source. The only assumptions concern independent detections and reproducibility of % of matching in sufficiently long sequences.

Where is the error?

Realism is assumed. That is because there are 3 detector positions: 0, +30, -30. In a Bell type proof, you are looking for a setup in which there is a counterfactual setting. These are exactly equivalent to the Mermin example, which I often use, which is 0/120/240 degrees.

 

[harrylin]

Realism is assumed. That is because there are 3 detector positions: 0, +30, -30. In a Bell type proof, you are looking for a setup in which there is a counterfactual setting. These are exactly equivalent to the Mermin example, which I often use, which is 0/120/240 degrees.

Realism is definitely assumed in simulations that make use of detection time windows; and surely the detection times at A are not affected by the detection times at B. Such simulations demonstrate that there has to be a glitch in this nice looking proof by Herbert... and as you and gill say, it's similar with Mermin's example as well as with Bell's calculation. There is thus a glitch in all these "proofs" that I just don't get...

 

[DrChinese]

Realism is definitely assumed in simulations that make use of detection time windows; and surely the detection times at A are not affected by the detection times at B. Such simulations demonstrate that there has to be a glitch in this nice looking proof by Herbert... and as you and gill say, it's similar with Mermin's example as well as with Bell's calculation. There is thus a glitch in all these "proofs" that I just don't get...

No glitch. Realism has nothing to do with detection or efficiency of same.

Realism is essentially the requirement of EPR that there are elements of reality *independent* of the act of observation. So they believe in the reality of counterfactual cases, i.e. the probability of occurance is in the range 0 to 100%.

 

[harrylin]

No glitch. Realism has nothing to do with detection or efficiency of same.

Realism is essentially the requirement of EPR that there are elements of reality *independent* of the act of observation. So they believe in the reality of counterfactual cases, i.e. the probability of occurance is in the range 0 to 100%.

Then please point out (if you found it) where the error is in applying Herbert's proof with the "detection loophole"; as his proof is not concerned at all with what happens at the detectors but only with the generated data strings, I obtain the exact same conclusion with or without it... Is the error in step 1, 2, 3 or 4, and where exactly?

 

[DrChinese]

Then please point out (if you found it) where the error is in applying Herbert's proof with the "detection loophole"; as his proof is not concerned at all with what happens at the detectors but only with the generated data strings, I obtain the exact same conclusion with or without it... Is the error in step 1, 2, 3 or 4, and where exactly?

What detection loophole? This is an idealized case so loopholes are not an issue.

 

[zonde]

I still don't get it... Herbert's proof doesn't even consider particles, let alone both particles or the same photon pairs.

Here is how I apply Herbert's proof to the scenario of incomplete detection, following his logic by the letter and adding my comments:

---------------------------------------------------------------------
Step One: Start by aligning both SPOT detectors. No errors are observed.
...
Where is the error?

If you consider detection loophole error is right in step 1.
In case of inefficient detection not all detection are perfectly paired up for maximum correlation settings. So you have something like 10% coincidences and you just normalize this number to 100%. Then you use proportion between coincidences/singles at max correlation as normalization factor for correlations at other settings.

So you have something like:
step 1: 10%
step 2: 7.5%
step 3: 7.5%
step 4: 2.5%
and after normalization you get:
step 1: 100%
step 2: 75%
step 3: 75%
step 4: 25%

 

[harrylin]

If you consider detection loophole error is right in step 1.
In case of inefficient detection not all detection are perfectly paired up for maximum correlation settings. So you have something like 10% coincidences and you just normalize this number to 100%. Then you use proportion between coincidences/singles at max correlation as normalization factor for correlations at other settings.

So you have something like:
step 1: 10%
step 2: 7.5%
step 3: 7.5%
step 4: 2.5%
and after normalization you get:
step 1: 100%
step 2: 75%
step 3: 75%
step 4: 25%

OK thanks for the clarification - that looks very different!

So one then has in reality for example:
- step 1: 90% mismatch
- step 2: 92.5% mismatch
- step 3: 92.5% mismatch
- step 4: 97.5% mismatch.

Based on local reality and applying Herbert's approach, I find that in case of a mismatch of 90% at step 1, the mismatch of step 4 should be <= 185%. Of course, that means <=100%.

 

[ThomasT]

Realism is definitely assumed in simulations that make use of detection time windows; and surely the detection times at A are not affected by the detection times at B.

They're connected, necessarily, due to the design of optical Bell tests. The point is that the individual detection attributes have to be combined. They're combined based on their time stamps. The time stamps refer to a common cause, which, presumably, is creating a relationship between the entangled photons. This relationship is, presumably, not varying from pair to pair. So, it can't be the variable, λ, which is determining individual detection.

Such simulations demonstrate that there has to be a glitch in this nice looking proof by Herbert... and as you and gill say, it's similar with Mermin's example as well as with Bell's calculation. There is thus a glitch in all these "proofs" that I just don't get...

I don't think there's anything necessarily wrong, in a certain sense, with Herbert's proof. But there is a question wrt what, exactly, it proves. So, if we want to say that there's something wrong, or right, with Herbert's proof, then we have to specify a criterion wrt which that can be ascertained.

Herbert asserts that his line of reasoning proves that nature is nonlocal. But that's prima facie absurd. The only proof that there are nonlocal propagations in nature would be the detection and recording of such nonlocal propagations. And there is no such evidence. So, what, exactly, does Herbert's proof prove?

 

[gill1109]

A mathematical proof proves a mathematical theorem. The mathematical theorem in this case is that quantum mechanics predicts correlations which cannot be reproduced by a local realistic theory of nature.

 

[gill1109]

Whether nature is non-local or not depends on what you mean by "local", "non-local". I think that these concepts are only defined relative to a theory. "Realism" is another word which has to be looked at carefully. In fact, "realism" could better be called "idealism". It says that we add into our picture of reality not only the outcomes of the measurements which were actually done, also the outcomes of the measurements which might have been done, but weren't actually. We moreover attribute these counter-factual outcomes of un-performed measurements not only the status of being "real", we also attribute them to a definite region of space-time. And then we discover that the only way to do this so as to fit to quantum mechanics' predicitions, is to allow instantaneous dependence between *which* measurement was performed in one wing of the experiment, and the outcomes (both factual and counterfactual) in the other wing.

If you want to call that non-locality, that's fine. But please note that it's non-locality of objects which you created yourself in some theoretical description of the world, it's not non-locality of objects which are there in the real world, independent of any theoretical framework.

 

[gill1109]

I think that Bell's (and Herbert's) arguments show that nature is non-classical. It is very definitely non-deterministic. There are phenomena out there in nature which cannot be explained by a determinisitic billiard-balls-moving-around-and-bouncing-off-one-another picture of the universe.

There's a beautiful paper by Masanes, Acin and Gisin which shows that quantum non-locality (which just means: violation of Bell inequalities) together with no-signalling (no action-at-a-distance) implies that Nature must be random. Also other implications like no-cloning follow from this combination.

And this randomness is at the heart of quantum mechanics, therefore at the heart of chemistry, therefore at the heart of life; also because it's at the heart of quantum mechanics, it's at the heart of cosmology, at the heart of the existence of the universe as we know it.

I find that a rather exciting thought.

 

[harrylin]

[..] I don't think there's anything necessarily wrong, in a certain sense, with Herbert's proof. But there is a question wrt what, exactly, it proves. So, if we want to say that there's something wrong, or right, with Herbert's proof, then we have to specify a criterion wrt which that can be ascertained.

I already gave a criterion in my first post: Herbert's proof pretends to prove that "local quantum facts that we observe in every experiment" - the kind of "twin light" experiments that have been successfully explained with ad hoc local realistic models - cannot be explained by such models.

Herbert asserts that his line of reasoning proves that nature is nonlocal. But that's prima facie absurd. The only proof that there are nonlocal propagations in nature would be the detection and recording of such nonlocal propagations. And there is no such evidence. So, what, exactly, does Herbert's proof prove?

It now appears to me that in reality he proved that idealised quantum theory (but perhaps not even realistic quantum theory) makes surprising predictions...

 

[harrylin]

[..] There's a beautiful paper by Masanes, Acin and Gisin which shows that quantum non-locality (which just means: violation of Bell inequalities) together with no-signalling (no action-at-a-distance) implies that Nature must be random. Also other implications like no-cloning follow from this combination. [..]

That sounds like an interesting take on this topic! - a link (or just the title) would be appreciated.

 

[gill1109]

General properties of Nonsignaling Theories
Ll. Masanes, A. Acin, N. Gisin
http://arxiv.org/abs/quant-ph/0508016

 

[billschnieder]

From the conclusion from the above paper (page 8):

Hence, some properties traditionally attributed to QM are generic within this family of physical theories. For example: the fact that two observables cannot be simultaneously measured on the same system (incompatibility), becomes necessary to explain the correlations observed in some experiments [violation of CHSH [2]], independently of the fact that we use models based on noncommuting operators to explain such experiments (see also [12]).

 

[ThomasT]

It now appears to me that in reality he proved that idealised quantum theory (but perhaps not even realistic quantum theory) makes surprising predictions...

The QM predicted correlation isn't surprising if one takes into account the known behavior of light. Herbert's conclusion that the correlation between θ and rate of coincidental detection should be linear goes against what's known about light. So, it would seem that Herbert's conclusion is the more surprising one.

 

[ThomasT]

I think that Bell's (and Herbert's) arguments show that nature is non-classical. It is very definitely non-deterministic.

I think you're reading too much into it. We know that LR models give incorrect predictions. What is it in the models that causes their predictions to diverge from QM and experimental results? When this is ascertained, then the question is whether this informs wrt deep reality -- which, imo, it doesn't.

And this randomness is at the heart of quantum mechanics, therefore at the heart of chemistry, therefore at the heart of life; also because it's at the heart of quantum mechanics, it's at the heart of cosmology, at the heart of the existence of the universe as we know it.

I find that a rather exciting thought.

I find it rather an unwarranted stretch. Randomness refers to unpredictable (experimental) phenomena.

 

[morrobay]

Realism is definitely assumed in simulations that make use of detection time windows; and surely the detection times at A are not affected by the detection times at B. Such simulations demonstrate that there has to be a glitch in this nice looking proof by Herbert... and as you and gill say, it's similar with Mermin's example as well as with Bell's calculation. There is thus a glitch in all these "proofs" that I just don't get...

The glitch in all these "proofs" are that they accept non-locality, which has no
known mechanism, and is bizarre. For example from Herbert :
No local reality can explain these facts. ( yet )
Therefore reality is non- local

 

[salvestrom]

One thing I've failed to get clear is why locality meant additive (25+25 and 30+30) while non-locality was "proven" by the sinusidol wave results. Given the results, anything local must explain why the results are sinusidal. Yet in the proof, the callibration, which is purely local, does indeed produce a sinusoidal wave result. Which brings me back round to the question of why the local expectation is additive and not sinosuidal, for the non-polarised light during the experiment.

I may have spelt sinosuidal corrently once out of the five times I used it...

 

[gill1109]

When I said randomness I did not refer to unpredictable (experimental) phenomena. When you toss a coin, the result depends deterministically on the initial conditions. That is familiar everyday randomness which is merely practical unpredictability.

QM on the other hand says that nature is intrinsically random. There is no hidden layer "explaining" what actually will happen. The randomness is spontaneous. Inexplicable. Without antecedent. Effects without a cause.

 

[harrylin]

The glitch in all these "proofs" are that they accept non-locality, which has no known mechanism, and is bizarre. For example from Herbert :
No local reality can explain these facts. ( yet )
Therefore reality is non- local

Actually, zonde pointed out in post #26 that Herbert had the facts wrong. At best there are only a few published experiments that "closed the detection loophole", and I suspect that they were done with different set-ups than the one on which he based his proof.

However, you do put your finger on another weak point in the proof. As you say, non-locality has no known mechanism and as far as I know, no non-local model exists that could explain these non-facts. Which shows that the reasoning [no local reality can explain these facts, THEREFORE reality is non- local], is flawed. And this was to be expected: flawed reasoning is typical for paradoxes.

 

[harrylin]

One thing I've failed to get clear is why locality meant additive (25+25 and 30+30) while non-locality was "proven" by the sinusidol wave results. Given the results, anything local must explain why the results are sinusidal. Yet in the proof, the callibration, which is purely local, does indeed produce a sinusoidal wave result. Which brings me back round to the question of why the local expectation is additive and not sinosuidal, for the non-polarised light during the experiment.

I may have spelt sinosuidal corrently once out of the five times I used it...

It sounds to me as if you misunderstand Herbert's argument, and perhaps also what is meant with "localist". Please have a look at my post #20, in which I elaborated on Herbert's proof. Do you see an error, assuming that step 1 is correct?

 

[gill1109]

Harrylin, that's the whole point, that quantum non-locality (violation of Bell etc) has no known (local) mechanism.

There are non-local models a-plenty which reproduce the predictions of quantum mechanics, for instance Bohmian models.

On the other hand, there are *no* published experiments which closed the detection loophole while at the same time having the measurement completed in each wing of the experiment, before the chosen setting in the other could have become known. Every published experiment to date does allow a local realistic explanation. But none of them are plausible. If messages can be sent faster than the speed of light in order to engineer the singlet correlations, why does nature not also use this to create action at a distance? The hidden layer where instantenous communication takes place is still mysteriously insulated from the "real world". (QM does not allow instant messaging, for instance). And is it really plausible that the physical mechanism of tossing a coin to choose a setting on one apparatus is linked to the physical mechanism of the measured polarization of a photon far away?

 

[harrylin]

Harrylin, that's the whole point, that quantum non-locality (violation of Bell etc) has no known (local) mechanism.

There are non-local models a-plenty which reproduce the predictions of quantum mechanics, for instance Bohmian models.

On the other hand, there are *no* published experiments which closed the detection loophole while at the same time having the measurement completed in each wing of the experiment, before the chosen setting in the other could have become known. Every published experiment to date does allow a local realistic explanation. But none of them are plausible. If messages can be sent faster than the speed of light in order to engineer the singlet correlations, why does nature not also use this to create action at a distance? The hidden layer where instantenous communication takes place is still mysteriously insulated from the "real world". (QM does not allow instant messaging, for instance). And is it really plausible that the physical mechanism of tossing a coin to choose a setting on one apparatus is linked to the physical mechanism of the measured polarization of a photon far away?

Thanks for reminding me of Bohmian models!
To me all those explanations ("localist" as well as "non-localist") seem implausible; only the hypothesis of a "non-localist" cause seems much more implausible to me than that of a "localist" cause. Of course, such estimations are very personal. For example, if no plausible explanation could be found for this trick , then some people may find magic (that is, the usage of unknown laws of physics) the most plausible, while I will keep on looking for a more down-to-earth explanation. Maybe I'm too stubborn?

Note that I don't think that nature is playing tricks on us; it's more us playing tricks on ourselves, due to misinterpretation of what we see.

 

[lugita15]

harrylin, this point was already made by gill1109 and DrChinese, but just to reiterate the place where Herbert invokes counterfactual definiteness AKA realism, is when he says that the probability of mismatch at -30 and 30 is less than or equal to the probability of mismatch at -30 and 0 plus the probability at 0 and 30. So Herbert is assuming it makes sense to ask what *would have* occurred if you oriented one the SPOT detectors at 0 degree angle, even when the detectors are actually oriented at -30 degrees and 30 degrees. So the assumption is that regardless of what measurements you actually do, there are still well-defined answers (although unknown to the experimenters) for the results of measurements you did not do.

That's why quantum mechanics itself does not fall victim to Bell's theorem: because it's not realistic. If you measure the position of a particle, in QM it doesn't make sense to ask what result you would have gotten if you had instead measured momentum.

 

[ThomasT]

That's why quantum mechanics itself does not fall victim to Bell's theorem: because it's not realistic. If you measure the position of a particle, in QM it doesn't make sense to ask what result you would have gotten if you had instead measured momentum.

I agree with you on this (finally, eh? ).

 

[ThomasT]

When I said randomness I did not refer to unpredictable (experimental) phenomena. When you toss a coin, the result depends deterministically on the initial conditions. That is familiar everyday randomness which is merely practical unpredictability.

QM on the other hand says that nature is intrinsically random. There is no hidden layer "explaining" what actually will happen. The randomness is spontaneous. Inexplicable. Without antecedent. Effects without a cause.

The words spontaneity and randomness refer to our ignorance of, and inability to specify the mechanics of, an assumed (if only tacitly) local deterministic evolution of a system from a prior state.

If QM isn't a realistic theory, then it can't be saying much, if anything, about deep reality. To paraphrase a statement by Bohm from his 1950 textbook, maybe a more appropriate name for the theory would be quantum nonmechanics.

It's interesting to me that LR models of individual detection are compatible with QM. That is, in the case of individual detection, in the words of J. S. Bell:

So in this simple case there is no difficulty in the view that the result of every measurement is determined by the value of an extra variable, and that the statistical features of quantum mechanics arise because the value of this variable is unknown in individual instances.

So, why is it that the joint (entanglement) observational context is impossible to viably describe in the same LR terms that, wrt individual measurements, are compatible with QM?

The most parsimonious working hypothesis would seem to me to be that there's something about the encoding of the standard LR modelling requirements that is at odds with the experimental design of Bell tests. If so, then BI violations wouldn't be informing wrt deep reality -- while still definitively ruling out a certain class of LR models of quantum entanglement.

Ascertaining the precise source of the assumed discrepancy has been the subject of much debate. I have my own ideas on it, but they're not rigorously developed, certainly not definitive, and the possibility remains that nature might be nonlocal. But, while that's a possibility, I don't think it's the best working hypothesis. So, with many others, I continue to assume that our universe is evolving deterministically in accordance with the principle of locality.

Herbert's line of reasoning, which fails to take into account the known behavior of light (wrt crossed polarizers), certainly doesn't rule out those assumptions.

 

[harrylin]

[..] just to reiterate the place where Herbert invokes counterfactual definiteness AKA realism, is when he says that the probability of mismatch at -30 and 30 is less than or equal to the probability of mismatch at -30 and 0 plus the probability at 0 and 30.

What I found so great about Herbert's proof, is that it doesn't invoke lambda's and even not probabilities, but just direct comparisons of statistical measurement data. That is of course strongly related to probabilities, but it's great not to have to make that step.

So Herbert is assuming it makes sense to ask what *would have* occurred if you oriented one the SPOT detectors at 0 degree angle, even when the detectors are actually oriented at -30 degrees and 30 degrees. So the assumption is that regardless of what measurements you actually do, there are still well-defined answers (although unknown to the experimenters) for the results of measurements you did not do. [...]

More or less so. Herbert simply uses the "fact" that when "aligning both SPOT detectors, No errors are observed." Thus his assumption is that detector settings do not affect whatever is sent towards the detectors, if that is what you mean

Also, the successful "local realist" models that I referred to in my first post, no doubt do allow for well-defined answers (although unknown to the experimenters) for the results of measurements you did not do.

 

[harrylin]

[..] Herbert's line of reasoning, which fails to take into account the known behavior of light (wrt crossed polarizers), certainly doesn't rule out those assumptions.

Please elaborate - you seem to suggest to have spotted another flaw in Herbert's proof, but it's not clear to me what you mean.

 

[lugita15]

More or less so. Herbert simply uses the "fact" that when "aligning both SPOT detectors, No errors are observed." Thus his assumption is that detector settings do not affect whatever is sent towards the detectors, if that is what you mean

No, that's not what I meant, but that's also an important assumption, known as the "no-conspiracy condition". There are people known as superdeterminists who try to get around Bell's theorem by violating this condition, e.g. by saying that the particles know in advance what the detector settings will be because the universe is totally deterministic, so the two particles use this information to coordinate in just the right way so that Bell's inequality appears to be false even though it would really be true if measurement decisions were free and independent. Superdeterminism is a pretty small fringe, but it counts Nobel laureate Gerard t'Hooft as one of it's adherents.

Anyway, what I was talking about was when Hebert says this "Starting with two completely identical binary messages, if A's 30 degree turn introduces a 25% mismatch and B's 30 degree turn introduces a 25% mismatch, then the total mismatch (when both are turned) can be at most 50%."He's assuming whenever you get a mismatch between the -30 degree polarizer and the 30 degree polarizer, this really represents a deviation of one of the polarizer measurements from the "identical binary messages" that would have been gotten if you had put both polarizers at 0 degrees. Without the assumption that there is counterfactual definiteness at 0 degrees, you can't conclude that the percentage (i.e. the probability) of mismatches at -30 and 30 is less than or equal to the percentage of mismatches at -30 and 0 plus the percentage of mismatches at 0 and 30.

Also, the successful "local realist" models that I referred to in my first post, no doubt do allow for well-defined answers (although unknown to the experimenters) for the results of measurements you did not do.

The "successful" local hidden variable models you're talking about, like the ones zonde was referring to, do not actually reproduce all the experimental predictions of quantum mechanics. Rather, they exploit some loophole or the other of Bell test experiments to say that Bell tests experiments to date have not definitively disproven their particular theories, but they claim that an "ideal experiment" would prove them right and QM wrong.

Remember, all Bell's theorem shows is that a local hidden variable theory cannot reproduce all the experimental predictions of QM. It says nothing at all about theories which claim that some of the predictions of QM are wrong and can in principle be disproven experimentally.