Boole vs. Bell - the latest paper of De Raedt et al

[harrylin]

There is no flaw in Bell's derivation. The issue is that the expectation values from QM or experiments are not compatible with those in Bell's inequality, as explained in the "Violation of Bell's inequality" thread.
[..] Note that it is not possible to do the factorization as Bell assumed [..]

Bill,

Thanks for your nice summary in post #47.

Regretfully I did not yet find the time to work through it; when I do I'll come back to it.

Just a comment on your appraisal: in my book an invalid mathematical operation is an error, or, to be less severe, a flaw.

 

[JesseM]

In contrast, Bell's theorem is about the correspondence between sets of measurement results from the interactions - not between idealised input and output values.

No, the simplest form of Bell's theorem deals with contradictions between local realism and the theoretical predictions of QM in ideal experiments with perfect detection (which is certainly allowed by the laws of physics even if it's not practical to do with present technology), not real experiments with realistic detectors. Of course there are also modified versions of Bell's theorem that deal with imperfect detectors, and these are the ones that are used in actual experiments, but the original point of the theorem was simply to show a theoretical conflict between local realism and the fundamental equations of quantum mechanics (if two theories have predictions which are at odds in idealized experiments that would be possible in principle but are realistically impractical, that is sufficient for a theoretical proof that the two theories are incompatible; for example, we know general relativity and QM are incompatible based on different predictions about things going on at the Planck scale which are far outside of the energy ranges we can actually test in practice).

Again: my point was that as Tim Maudlin indicated, QM does in fact predict imperfect correlations between realistic measurement results; and Bell's Theorem is that no local hidden variable theory can reproduce those predictions.

No, you've quite misunderstood what Bell's theorem is about here. All of Bell's papers that I've read deal with idealized experiments with perfect detection rates, and they are intended as theoretical proofs that the laws of QM are incompatible with local realism, not guides to experiment. Again you can find modified Bell inequalities that do take into account limits on detector efficiency, but Bell's original arguments were not concerned with such practical issues.

 

[harrylin]

No, the simplest form of Bell's theorem deals with contradictions between local realism and the theoretical predictions of QM in ideal experiments with perfect detection (which is certainly allowed by the laws of physics even if it's not practical to do with present technology), not real experiments with realistic detectors. [..]
you've quite misunderstood what Bell's theorem is about here. All of Bell's papers that I've read deal with idealized experiments with perfect detection rates [..].

Jesse thanks for the clarification to my question if QM actually predicts a perfect correlation in principle (that is, zero theoretical precision limit). I was not thinking about detection limits (for which I suppose that there is no relevant theoretical limit) but about such things as Heisenberg's uncertainty principle and detection time windows.

QM doesn't make claims about flying photons (that is a semi-realistic interpretation based on one out of several models); instead it predicts photon observations at detectors. I was under the impression that in QM no certain and precise correlation between two photons is possible in principle, and the mention in De Raedt's paper of the timing events of stochastic processes suggested to me that this may be relevant.

Thus, can someone clarify if indeed, and how, QM predicts no theoretical precision limit for the correlation between two photon detection events?

 

[harrylin]

In post #47:

[...] The issue is that the expectation values from QM or experiments are not compatible with those in Bell's inequality, as explained in the "Violation of Bell's inequality" thread.

The summary of the De Raedt argument is the following:
Bell's inequality

1 + <bc> >= |<ab> - <ac>|

is derived in a way that requires that the following factorization MUST be possible

1 + <bc> >= |<a(b - c)>|

Such a factorization is possible if all three observables are results of a single experiment, such as (a1, b1, c1). If you are in doubt about this factorizability requirement, see this post and the next one, where I go through Bell's derivation in detail to show where this requirement comes in (https://www.physicsforums.com/showpost.php?p=2830780&postcount=1211, https://www.physicsforums.com/showpost.php?p=2830781&postcount=1212)

However the expectation values from QM and Experiments, correspond to three different experiments (a1,b1), (b2,c2), (a3,c3). So that substituting these into Bell's inequality, you get

1 + <b2c2> >= | <a1b1> - <a3c3> |

Note that it is not possible to do the factorization as Bell assumed because a1 is different from a3. However, if you naively think a1 is equivalent to a3, then you might be tempted to drop the indices and say

1 + <b2c2> >= | <a(b1 - c3)> |

By dropping all the indices, Bell proponents naively think the variables from QM and experiments should be compatible. De Raedt et al show using the doctors example that such operations are wrong. But you do not need the doctors example to see the error in the above.

From the above, ai,bi,ci correspond to three list of values (+1, -1) which correspond to the outcome at when the angle is a,b,c. Take for example a1 corresponds to the list of outcomes when Alice set her detector to angle a, and b1 corresponds to the list of outcomes when Bob set his detector to angle b, during experiment (1).

Same for b2,c2 and same for a3,c3.

Bill, thanks for the link to that one year old thread which elaborates on eq.2 in Bell's paper, as well as the derivation of eq.15. This summary was really helpful for me.

Now if I correctly understand it, it is argued that the unknown lambda in Bell's derivation must be of the same value (or of the same average value, this certainly is an issue!):

1. between each photon pair
and also
2. between consecutive measurements with different angle settings.

Correct? Thanks for the improved understanding. :-)

Meanwhile I found back the paper of Bell on Bertlmann's socks:
http://cdsweb.cern.ch/record/142461?ln=en

There he seems to be aware of that kind of issues - even with mention of patients in Lyon and Lille. He argues near the end of his paper that common influences should average out. And he claims without hesitation that a similar inequality must be valid for the socks, based on the fair sampling hypothesis.

Comments on his sock washing inequality are welcome.

 

[billschnieder]

That's better for me: as an onlooker I do prefer the example in which the tablets stand for photons and the glasses for detectors (please do not present flying glasses with liquids that fall on tablets, that just causes confusion ).

I agree,

- Three liquids correspond to three angles, two tablets correspond to two photons which for our case are identical. Bitter = +, sweet = -.

It is very important not to confuse this simple analogy by changing the glasses to now be photons as DrC wants to do. If I accept this, we by the time we are done, we will not have any clarity. We want clarity not obfuscation and I am baffled why DrC is resisting it. We have a clear correspondence between the EPR experiment and the analogy that should be enough so I continue to ask the same question I have been asking and getting no response from DrC.

 

[billschnieder]

Ditto, ace. We are using your analogy my way.

3 tabs = 3 angles
X/Y/and whatever else you want, unknown liquids
Bitter=+, Sweet=-

ONE PHOTON PER DATA ITEM, NOT TWO.

NO! The analogy as I phrased it is clearly similar to the EPR case. If you want to give a different analogy, you will have to explain it in a similar manner as I've done below so that it is clear to anyone that it corresponds to the EPR case. What you have suggested is a joke.

- The two photons will correspond to two tablets of a given kind produced at a time, one given to Alice and the other to Bob, each of whom has three different liquids (a,b,c). The experiment at each station will involve a random choice of one of the liquids, an aliquot of which they then mix with the given tablet and drink to obtain either the "sweet" (+) outcome or the "bitter"(-) outcome.
- The tablet properties (chemicals), being hidden are not specified. We do not know how many of them there are, but we can say each particle pair has a well defined "chemical composition" (elements of reality) which interacts with the liquids (a,b,c) (detector settings) to produce the observables ("sweet", "bitter").


1) What does each data point of triples represent that is supposed to be realistic?
2) How are you going to select pairs from these triples in a way that is consistent with the way pairs are selected in Bell test experiments?

This is not Hard at all, the fact that you keep bobbing and weaving tells alot.
Now phrase your dataset according to the above description which you have already agreed is a good analogy. Or explain why you can not do it unless you switch glasses with tablets.

 

[JesseM]

Jesse thanks for the clarification to my question if QM actually predicts a perfect correlation in principle (that is, zero theoretical precision limit). I was not thinking about detection limits (for which I suppose that there is no relevant theoretical limit) but about such things as Heisenberg's uncertainty principle and detection time windows.

The uncertainty principle only applies when you have non-commuting operators. If you measure both particles at the same detector angle, the two measurement operators should commute, so there should be no uncertainty.

QM doesn't make claims about flying photons (that is a semi-realistic interpretation based on one out of several models); instead it predicts photon observations at detectors. I was under the impression that in QM no certain and precise correlation between two photons is possible in principle

No, that's incorrect. If both polarizers are set to the same angle, and there are no issues with detector efficiency, then QM predicts they will either both pass through the polarizers or both be reflected by them, with probability 1. In general, if one polarizer is set to angle a while the other is set to angle b, then the probability they will both pass through (the probability that both are "vertically polarized" relative to the polarizer) is given by the equation P_VV = (1/2)*cos²(a-b) -- see the top of p. 3 of this intro to entanglement and Bell's inequalities for example. That paper also notes that the probability that both are "horizontally polarized" is given by P_HH = (1/2)*cos²(a-b), while the probability that one photon is horizontally polarized while the other is vertically polarized is given by P_HV = P_VH = (1/2)*sin²(a-b). So if a=b, since cos²(0) = 1 the probability both are vertically polarized or both are horizontally polarized is 1/2 + 1/2 = 1, and since sin²(0)=0 the probability that one is vertically polarized while the other is horizontally polarized is 0.

 

[harrylin]

The uncertainty principle only applies when you have non-commuting operators. If you measure both particles at the same detector angle, the two measurement operators should commute, so there should be no uncertainty. [..] If both polarizers are set to the same angle, and there are no issues with detector efficiency, then QM predicts they will either both pass through the polarizers or both be reflected by them, with probability 1.

Do those measurement operators include the detector atoms and the timing precision for identifying entangled photons? I still think that they don't...

[..] So if a=b, since cos²(0) = 1 the probability both are vertically polarized or both are horizontally polarized is 1/2 + 1/2 = 1, and since sin²(0)=0 the probability that one is vertically polarized while the other is horizontally polarized is 0.

Your interpretation implies that there is in principle no limit to the accuracy of such things as detection angle, timing accuracy, etc...
I keep thinking that this is at odds with Maudlin's "at best allow some approximation"; and although Bell thought along the lines that you sketched, he did not want to rely on that argument in "Bertlemann's socks". There he admitted that Bohm's example is "idealized" and he stressed that his general argument does not rely on such unattainable perfection.

Harald

 

[DrChinese]

NO! The analogy as I phrased it is clearly similar to the EPR case. If you want to give a different analogy, you will have to explain it in a similar manner as I've done below so that it is clear to anyone that it corresponds to the EPR case. What you have suggested is a joke.


This is not Hard at all, the fact that you keep bobbing and weaving tells alot.
Now phrase your dataset according to the above description which you have already agreed is a good analogy. Or explain why you can not do it unless you switch glasses with tablets.

It's my challenge, ace. And you STILL refuse to take it. One photon, 3 angles. Not 2. One less than 2. That's ONE. How many ways can I say it? So you can represent a set of photons with a set of tabs. 3 glasses correspond to 3 angles. Outcomes are binary, bitter or sweet or red or green, I don't care. Lemme know when you can come up with a dataset.

I have a nap to take now, while you bob some more. Can you please help my Mavs? They need a little extra something right now, and you appear to be doing a good job.

 

[billschnieder]

It's my challenge, ace. And you STILL refuse to take it.

Sure it is your challenge, which does not make sense and I've been trying to extract a coherent description of the challenge from you. Apparently it is harder than a root-canal extraction. If you want someone else to actually respond to the challenge, then you will have to put aside your pride and make an effort to actually explain the challenge in detail.

So you can represent a set of photons with a set of tabs. 3 glasses correspond to 3 angles. Outcomes are binary, bitter or sweet or red or green, I don't care. Lemme know when you can come up with a dataset.

So you finally agree with my description but do not specify what the dataset means. From the discussion so far (summarized below), I will have to infer what you mean by "dataset"

Do you want me to give you a dataset in which each point is a triple of angles, or a triple of outcomes?

Yes, a triple of outcomes...The outcomes are for observations that may or may not be performed.

you are asking for a dataset from an impossible experiment, as evidenced from the fact that you are unable to describe to me the experiment that is supposed to produce this dataset.

no, there is no experiment implied here (impossible or otherwise). Just asking you to tell me what possibilities there are for the triples.

Given the above, I can infer that your "dataset" is a list of triples of *possible outcomes* of the experiment as described in the analogy which you now agree to. In other words, you want a list containing something like (+,-,+) for each identical pair of tablets (photons) corresponding to the *possible outcomes* when mixed with three different liquids (a,b,c) (angles).

Here is the dataset you are requesting. I am providing it despite the fact that you have refused to specify how you will derive terms involving pairs from this dataset to substitute in Bell's inequality 1 + <bc> >= |<ab> - <ac>|, in a manner that is similar to what is done in Bell test experiments.

a, b, c
-----------
-1, +1, -1
+1, -1, -1
+1, +1, -1
-1, -1, -1
-1, -1, -1
-1, +1, +1
-1, +1, -1
+1, +1, -1
+1, +1, -1
+1, -1, -1
+1, -1, +1
+1, -1, +1
-1, +1, +1
+1, +1, +1
-1, +1, -1
+1, +1, +1
+1, +1, +1
-1, +1, -1
-1, -1, -1
-1, -1, +1

 

[billschnieder]

That is the OPPOSITE of the EPR argument, which was: that individual elements of reality exist simultaneously, and that the possibility of specifying same proves QM is incomplete..

No. My definition of realism is consistent with the EPR one. If you disagree, provide a quote from EPR which shows otherwise

If, without in anyway disturbing a system, we can predict with certainty (...) the value of a physical quantity, then there exists an element of physical reality that corresponds to this physical quantity.

Note, the distinction between element of physical reality and physical quantity.

Just because you can predict the value of a physical quantity with certainty, does not mean all such physical quantities which you can predict, must necessarily exist simultaneously. This has been hashed extensively in the "Violation of Bell's inequality" thread.

 

[billschnieder]

Another one, with 16 data points:

a, b, c
-----------
+1, +1, -1
-1, -1, +1
+1, +1, -1
-1, -1, +1
+1, +1, -1
+1, +1, -1
-1, -1, +1
+1, +1, -1
+1, +1, -1
+1, +1, -1
-1, -1, +1
+1, +1, -1
+1, +1, -1
+1, +1, -1
-1, -1, +1
+1, +1, -1Just let me know how many points you want. For example here is another 20 point dataset followed by a 30 point one.

a, b, c
-----------
+1, -1, -1
-1, +1, -1
-1, +1, -1
-1, +1, -1
-1, -1, -1
+1, -1, +1
+1, -1, +1
+1, +1, +1
-1, -1, +1
-1, +1, -1
-1, -1, +1
+1, +1, +1
-1, +1, +1
+1, -1, +1
+1, -1, +1
-1, +1, -1
+1, +1, +1
-1, -1, +1
+1, -1, +1
+1, +1, +1 a, b, c
-----------
+1, -1, +1
-1, +1, -1
-1, +1, -1
-1, +1, -1
+1, -1, -1
-1, +1, +1
-1, +1, -1
+1, -1, +1
-1, -1, -1
-1, -1, -1
-1, -1, +1
-1, +1, +1
+1, -1, -1
+1, -1, -1
-1, -1, +1
-1, -1, -1
+1, -1, +1
-1, +1, -1
-1, +1, -1
+1, +1, +1
+1, -1, -1
-1, -1, +1
+1, -1, +1
+1, -1, +1
+1, +1, +1
-1, -1, -1
+1, +1, +1
-1, -1, -1
-1, +1, -1
+1, -1, +1

 

[DrChinese]

... In other words, you want a list containing something like (+,-,+) for each identical pair of tablets (photons) corresponding to the *possible outcomes* when mixed with three different liquids (a,b,c) (angles).

Here is the dataset you are requesting. I am providing it despite the fact that you have refused to specify how you will derive terms involving pairs from this dataset to substitute in Bell's inequality 1 + <bc> >= |<ab> - <ac>|, in a manner that is similar to what is done in Bell test experiments.

a, b, c
-----------
-1, +1, -1
+1, -1, -1
+1, +1, -1
-1, -1, -1
-1, -1, -1
-1, +1, +1
-1, +1, -1
+1, +1, -1
+1, +1, -1
+1, -1, -1
+1, -1, +1
+1, -1, +1
-1, +1, +1
+1, +1, +1
-1, +1, -1
+1, +1, +1
+1, +1, +1
-1, +1, -1
-1, -1, -1
-1, -1, +1

OK, great start. The above is for ONE stream of photons. Now according to the EPR entanglement model*, we would be able to predict any ONE of those in advance (use Bob to predict Alice or vice versa). We could also measure any TWO different of ab, bc or ac (one from Alice and a different one from Bob). That would give us more information about Alice than the HUP allows (as EPR argued). Now, my question is: when you run that for any pair of columns I pick, what is your estimate of the match rate? In other words, for the sample you provided: ab has a match rate of 10/20, bc has a rate of 10/20, and ac has a rate of 12/20. I.e. an average of just over 50%.

So in our analogy, I am not asking for any simultaneous triples where we can only measure doubles. So I am not asking for 1 + <bc> >= |<ab> - <ac>| or similar. I am simply asking you: what is your estimate of the coincidence rate for a typical dataset as above? I am guessing that it might be ultimately somewhere between 1/3 and 1/2, would that be fair as an estimate? Keeping in mind, of course, that we are drawing from something constrained as in our analogy.

BTW: my next step will be to ask you to what is the lowest rate of pair coincidences (fewest) you could express in a dataset as above. I.e. if you were trying to minimize coincidences.

* Using Type I PDC entanglement, where you get identical polarization values for Alice and Bob.

 

[billschnieder]

OK, great start. The above is for ONE stream of photons. Now according to the EPR entanglement model*, we would be able to predict any ONE of those in advance (use Bob to predict Alice or vice versa).

What are you talking about. You said I should give you only one of the two stream of tablets, which are identical in the above example. So Alice and Bob have exactly the same streams since two tablets are produced at a time. There is no need to predict anything.

We could also measure any TWO different of ab, bc or ac (one from Alice and a different one from Bob).

The above dataset as you requested, consists of the "possible outcomes" of measuring the given tablet(s) using three different liquids (a,b,c). What do you mean now by the statement in bold. This is the reason I wanted this clearly specified upfront so that you don't obfuscate the issue latter as you are now doing. You have the dataset, all that is remaining for you to do is to determine your ab, bc, and ac terms from THAT list and then do your calculation. You asked for the list, I'm assuming you had a reason for asking for the dataset. Now let us see that reason -- do the calculation.

Now, my question is: when you run that for any pair of columns I pick, what is your estimate of the match rate? In other words, for the sample you provided: ab has a match rate of 10/20, bc has a rate of 10/20, and ac has a rate of 12/20. I.e. an average of just over 50%.

What is the match rate supposed to correspond to?

So in our analogy, I am not asking for any simultaneous triples where we can only measure doubles. So I am not asking for 1 + <bc> >= |<ab> - <ac>| or similar. I am simply asking you: what is your estimate of the coincidence rate for a typical dataset as above?

You are confused. Coincidence rate does not come in. Coincidence means the two tablets are measured. For photons, it means the two photons measured, are from the same pair, so that we discount stray photons, and those where only one is measured, in order to ensure that we are measuring a single pair. That does not come into this situation because according to the description you agreed to, both tablets are identical, and I have given you the dataset for one which should be the same as the other, so in a sense the coincidence is 100%. Coincidence does not mean perfect correlation. Even if it meant that, both tablets being identical will still give you a 100% perfect correlation. What's the beef?

I am guessing that it might be ultimately somewhere between 1/3 and 1/2, would that be fair as an estimate?

No. Coincidence does not come into the picture here. You must have something different in mind so spell it out clearly.

BTW: my next step will be to ask you to what is the lowest rate of pair coincidences (fewest) you could express in a dataset as above. I.e. if you were trying to minimize coincidences.

Again, coincidence does not come in here. In real bell test experiments, coincidence is a solution to the problem of imperfect detectors. In this case, we are not losing any tablets.

* Using Type I PDC entanglement, where you get identical polarization values for Alice and Bob.

Again, although I kept insisting on two tablets, you insisted that you wanted just one tablet at a time. I accepted because it does not matter since both tablets are identical anyway so your comment above is moot. You get identical outcome for identical liquids on both tablets.

 

[DrChinese]

...You get identical outcome for identical liquids on both tablets.

Sure. Glad we are on the same page. To summarize:

a) You have provided a sample REALISTIC dataset for the 3 liquids (potential angle settings of 0/120/240 degrees, although you may not have yet tweaked them for this specifically). This is for a stream of photons seen by (say) observer Alice.
b) We agree that each individual photon (tab) can be tested with only a single liquid (angle). There are no impossible doubles or triples.
c) We agree that when you prepare a duplicate of Alice's stream, and provide that to Bob, that when Bob checks the same liquids (angles) as Alice, this information is redundant (by definition) because Alice has this. This is following the spirit of the EPR program.

Next steps:

d) We are going to compare when Bob uses a different liquid (angle) to measure than Alice does. Using your example data, my estimate of result matches (Alice with one liquid and Bob with another) is around 1/3 to 1/2. For the specific example you provided, it is just over 1/2 but as I said already, you will get an opportunity to tweak the dataset as you like to obtain a result which is higher or lower. You accept that this is a physically viable experiment and does not involve any impossible triples.

e) Lastly, I will request that you provide a revised dataset - similar to your previous but you can hand pick the values. I would ask that you provide the lowest possible average match rate, again I get to pick the pairings that Alice and Bob will use and will do so without regard to what you provide. All I am asking for is something reasonably low, you don't need to use any special technique.

f) I presume you are intelligent enough to realize that the result of step e) will be a value somewhere around 1/3. But hey, give it your best (or alternately just concede the point and save us both the time). Remember, I have yet to mention any experiment which is not physically feasible. There are no triples, no mixing of possibilities with actualities.

-DrC

 

[billschnieder]

Sure. Glad we are on the same page. To summarize:
a) You have provided a sample REALISTIC dataset for the 3 liquids (potential angle settings of 0/120/240 degrees, although you may not have yet tweaked them for this specifically). This is for a stream of photons seen by (say) observer Alice.
b) We agree that each individual photon (tab) can be tested with only a single liquid (angle). There are no impossible doubles or triples.
c) We agree that when you prepare a duplicate of Alice's stream, and provide that to Bob, that when Bob checks the same liquids (angles) as Alice, this information is redundant (by definition) because Alice has this. This is following the spirit of the EPR program.

No we are not on the same page!
a) What I presented is NOT a realistic dataset. It is a dataset of "possiblities". If you still do not understand this point, please review post #49 (https://www.physicsforums.com/showpost.php?p=3335444&postcount=49), and post #186 (https://www.physicsforums.com/showpost.php?p=3333711&postcount=186) in the the "Violation of Bell's theorem" thread.

b) Every tablet can only be tested with one liquid. We have three liquids and two tablets at a time. It is obvious that no experimenter dead or alive could possibly test all three liquids for a given tablet pair. So contrary to your statement, the triple in the dataset is the result of an impossible experiment, even a cave man can understand this. However, you did not ask for the result of an experiment. You asked for a triple of "possibilities" for a given pair for the three liquids. Therefore the triplet (+,-,+) is equivalent to the following three statements together:

(one tablet tested with liquid a, gives bitter taste;
one tablet tested with liquid b, gives sweet taste;
one tablet tested with liquid c, gives bitter taste)

This data point is a triple of possibilities of testing one type of tablet (two of which constitute the the given pair), with the three liquids (a,b,c).

This is not a realistic dataset because the dataset consists of triplets, which can never be simultaneously realized) -- again, because for all three to be realized, we need three tablets but we only have 2.

If you insist to call what I provided you a REALISTIC dataset, it shows that you do not know what realism means and this whole exercise is moot.

Next steps:

d) We are going to compare when Bob uses a different liquid (angle) to measure than Alice does. Using your example data, my estimate of result matches (Alice with one liquid and Bob with another) is around 1/3 to 1/2. For the specific example you provided, it is just over 1/2 but as I said already, you will get an opportunity to tweak the dataset as you like to obtain a result which is higher or lower. You accept that this is a physically viable experiment and does not involve any impossible triples.

The terms ab, bc, and ac are terms corresponding to when Alice and Bob choose a different liquid. Those are the only terms relevant in Bell's inequality which I provided ealier.
* Have you calculated the expectation values for those terms from my list?
* How did you do that? (Please copy the relevant dataset prior to your explanation and results so that I can verify)
* Have you substituted them into Bell's inequality?
* Was it violated or not?

These are the relevant questions you are skirting. Without specifying exactly how you calculated the terms, how am I supposed to know if it corresponds to a possible experiment or not? So unless you clearly explain how you are calculating the terms, I will not agree with what you claim.

e) Lastly, I will request that you provide a revised dataset - similar to your previous but you can hand pick the values. I would ask that you provide the lowest possible average match rate, again I get to pick the pairings that Alice and Bob will use and will do so without regard to what you provide. All I am asking for is something reasonably low, you don't need to use any special technique.

f) I presume you are intelligent enough to realize that the result of step e) will be a value somewhere around 1/3. But hey, give it your best (or alternately just concede the point and save us both the time). Remember, I have yet to mention any experiment which is not physically feasible. There are no triples, no mixing of possibilities with actualities.

One thing at a time. Address the questions above before you start requesting new datasets and predicting what those new datasets might show. The questions above should reveal a lot already about your misunderstanding.

As concerns the part in bold, you haven't presented anything of sufficient detail to enable me to determine that your suggested experiments are physically feasible or not.

 

[DrChinese]

No we are not on the same page!
...

Arggh! It is my challenge, and we keep going in circles. So let's start again, Mr. Weaver.

- Glass containing Liquid=Angle setting.
- There are 3 types of Liquid used for the test.
- Bottle of Tabs=Stream of Photons
- No idea how many different types of tabs there are, could be 3 or 3000.
- They all look alike, although they are numbered from 1 to N.
- Place a tab in a liquid, you always get Bitter or Sweet.
- Bitter=+1, Sweet=-1.
- You cannot place the same tab in more than one glass. The process destroys the tab completely.

Alice picks tabs out of her bottle. She has a bunch of glasses of liquids, she knows which is which but know nothing about the tabs until she places it in a glass. One tab per glass, and vice versa. Then she tastes the glass and says: Bitter or Sweet! And writes it down.

There is NO second identical bottle of tabs for Bob - yet. We are just trying to create a realistic dataset. Now if you cannot follow this simple example and agree it is realistic a la EPR, I really don't understand how you put your pants on in the morning. EPR says that reality for Alice does NOT depend on Bob. Essentially that means that reality for Alice depends only on Alice (and what is close/local to Alice). Now I am sure that you can map this example to the first dataset of 20 elements and conclude it was in fact a realistic dataset. Because the possible outcomes all exist and are essentially predetermined once Alice starts pulling them out of the bottle in order from 1 to N and testing them in one of the glasses with the liquid of her choosing. But to her, the results seem capriciously random.

So we start with a realistic example. If you can't agree this is a realistic example, then you are essentially ceding my entire argument. Here we have an example where the tabs have simultaneous properties but they cannot be simultaneously tested. The moon exist even when not being observed. So are we in agreement about our example? There are no forbidden triples here.

 

[harrylin]

No we are not on the same page!
a) What I presented is NOT a realistic dataset. It is a dataset of "possiblities".
[..]
Therefore the triplet (+,-,+) is equivalent to the following three statements together:

(one tablet tested with liquid a, gives bitter taste;
one tablet tested with liquid b, gives sweet taste;
one tablet tested with liquid c, gives bitter taste)

This data point is a triple of possibilities of testing one type of tablet (two of which constitute the the given pair), with the three liquids (a,b,c).

This is not a realistic dataset because the dataset consists of triplets, which can never be simultaneously realized) -- again, because for all three to be realized, we need three tablets but we only have 2.

If you insist to call what I provided you a REALISTIC dataset, it shows that you do not know what realism means and this whole exercise is moot.

To me it sounds like a small misunderstanding only: certainly it's a realistic description of conditional observation data. Knowledge of the hidden secrets of this tablet would allow us to tell that IF this tablet would be tested with liquid a, it would yield a bitter taste as data. Correct? That is not experimental output data, but still it is input data for us in this discussion.

The terms ab, bc, and ac are terms corresponding to when Alice and Bob choose a different liquid. Those are the only terms relevant in Bell's inequality which I provided earlier.
[..]

There should also be agreement for the same liquids. However for that requirement your tablets and liquids correspond to the ideal case of 100% correlation.

 

[DrChinese]

The terms ab, bc, and ac are terms corresponding to when Alice and Bob choose a different liquid. Those are the only terms relevant in Bell's inequality which I provided ealier.
* Have you calculated the expectation values for those terms from my list?
* How did you do that? (Please copy the relevant dataset prior to your explanation and results so that I can verify)
* Have you substituted them into Bell's inequality?
* Was it violated or not?

I am ignoring the Bell inequality precisely because you don't like the triples. I do not know how to be any more accommodating.

 

[billschnieder]

Arggh! It is my challenge, and we keep going in circles. So let's start again, Mr. Weaver.

- Glass containing Liquid=Angle setting.
- There are 3 types of Liquid used for the test.
- Bottle of Tabs=Stream of Photons
- No idea how many different types of tabs there are, could be 3 or 3000.
- They all look alike, although they are numbered from 1 to N.
- Place a tab in a liquid, you always get Bitter or Sweet.
- Bitter=+1, Sweet=-1.
- You cannot place the same tab in more than one glass. The process destroys the tab completely.

Alice picks tabs out of her bottle. She has a bunch of glasses of liquids, she knows which is which but know nothing about the tabs until she places it in a glass. One tab per glass, and vice versa. Then she tastes the glass and says: Bitter or Sweet! And writes it down.

Agreed! This is exactly what I explained.

We are just trying to create a realistic dataset. Now if you cannot follow this simple example and agree it is realistic a la EPR, I really don't understand how you put your pants on in the morning.

We do not yet agree as to what a "realistic dataset" means. This is the point of contention. I have described to you what "realism means" and as a result what "realistic dataset" means. You have done neither. So either you accept my definition and concede that what you request is not a realistic dataset, or provide your own definition of "realism" and your own definition of what "realistic dataset" means. And by providing that you also have to admit that any outcome based on your definitions can not be interpreted to mean my definition is not tenable. This is very simple. You can not use your definition, to draw a conclusion that my definition is not tenable. This the whole point of this exercise.

EPR says that reality for Alice does NOT depend on Bob. Essentially that means that reality for Alice depends only on Alice (and what is close/local to Alice). Now I am sure that you can map this example to the first dataset of 20 elements and conclude it was in fact a realistic dataset.

This is a whole different can of worms we should not be opening here, about what is the difference between ontological dependence and logical dependence. But I agree that nothing Alice does, can have any causal influence over what Bob does according to EPR.

Because the possible outcomes all exist and are essentially predetermined once Alice starts pulling them out of the bottle in order from 1 to N and testing them in one of the glasses with the liquid of her choosing. But to her, the results seem capriciously random.

The bolded statement shows your misunderstanding very clearly. You do not yet understand the difference between something being TRUE and something EXISTING. I have explained this multiple times, in different ways without any statement from you whether you disagree with my explanation, or agree with it. A statement about a conditional possibility is True, but that does not mean the possibility is ACTUALIZED/REALIZED. (See the definition of realized). If you would admit this point, this whole discussion might not be necessary.

So we start with a realistic example. If you can't agree this is a realistic example, then you are essentially ceding my entire argument.

See the above. Just because I point out that you do not understand what is meant by a realistic dataset does not mean I concede your argument. This is at the core of the issue in this thread that we need to reach a consensus on this point in order to proceed. Either you accept my definition and concede that the dataset is not realistic, or you clearly state what you mean by realism and we proceed with your definition with the understanding that any future conclusion will be limited to your definition. The ball is in your court.

Here we have an example where the tabs have simultaneous properties but they cannot be simultaneously tested. The moon exist even when not being observed. So are we in agreement about our example?

Yes. Agreed. According to my definition of realism, a dataset containing triplets of these simultaneousl properties will be a realistic dataset.

There are no forbidden triples here.

But you just said they could not be simultaneously tested. That is an admission that something is impossible. Testing produces outcomes, that is why according to my definition of realism, if all the outcomes in the triplet can not all be simultaneously tested, it is not a realistic dataset according to my definition.

 

[billschnieder]

To me it sounds like a small misunderstanding only

I disagree. It is the central issue -- what does realism mean.

certainly it's a realistic description of conditional observation data

Phrased like that, it seems like it might make sense. But let us expand it and to (if a then +, if b then -, if c then +), you see then that If a, and if b, then definitely not c, which means
(if a then +, if b then -, if c then +) =/= (+,-,+)

In the LHS the possibilities are all simultaneously True, but that does not mean the outcomes in the RHS are simultaneously real. They can never be.

Knowledge of the hidden secrets of this tablet would allow us to tell that IF this tablet would be tested with liquid a, it would yield a bitter taste as data. Correct?

Correct.

That is not experimental output data, but still it is input data for us in this discussion.

It is input data for the discussion, that is why I provided the dataset. However, the next part now is to discuss how this is compatible with any experiment that could ever be performed.

There should also be agreement for the same liquids. However for that requirement your tablets and liquids correspond to the ideal case of 100% correlation.

It is a moot point since we already agreed that Bob and Alice could get the exact same tablet type which corresponds to 100%. The reason I say it is not relevant is because Bell's inequality does not contain "aa", "bb", "cc" terms.

 

[billschnieder]

DrC.
So I'm waiting for your answers to these questions

1 + <bc> >= |<ab> - <ac>|

* Have you calculated the expectation values for those terms from any of the dataset I presented?
* How did you do that? (Please copy the relevant dataset prior to your explanation and results so that I can verify)
* Have you substituted them into Bell's inequality?
* Was it violated or not?

I am explicitly asking you these questions, you can't simply ignore them. They are relevant.

 

[DrChinese]

DrC.
So I'm waiting for your answers to these questions

1 + <bc> >= |<ab> - <ac>|

* Have you calculated the expectation values for those terms from any of the dataset I presented?
* How did you do that? (Please copy the relevant dataset prior to your explanation and results so that I can verify)
* Have you substituted them into Bell's inequality?
* Was it violated or not?

I am explicitly asking you these questions, you can't simply ignore them. They are relevant.

No, because you don't like that. So no need to do that.

 

[billschnieder]

No, because you don't like that. So no need to do that.

Who is bobbing and weaving now. I ask you a question and you refuse to answer because according to you, I do not like the question? Huh?

For those following, note that DrC has refused to answer the question twice and he knows why. It is because he has calculated it and realized that based on how you calculate <ab>, <bc> and <ac>, the inequality can be violated. If you calculate it in a way consistent with Bell test experiments, the inequality is violated. If you calculate it the way Bell intended, the inequality is satisfied but the corresponding experiment is impossible as it will require measuring tablets more than once. This is the real reason DrC does not want to answer the question.

Again, it doesn't make sense to say I do not like the question I asked. I'm asking it which means I like the question. If there was any doubt that I did not like the question, I am declaring in the open that I do like the questions I asked and here they are again:

First one of the datasets (you can pick anyone you like other than this one):

a, b, c
-----------
+1, -1, +1
-1, +1, -1
-1, +1, -1
-1, +1, -1
+1, -1, -1
-1, +1, +1
-1, +1, -1
+1, -1, +1
-1, -1, -1
-1, -1, -1
-1, -1, +1
-1, +1, +1
+1, -1, -1
+1, -1, -1
-1, -1, +1
-1, -1, -1
+1, -1, +1
-1, +1, -1
-1, +1, -1
+1, +1, +1
+1, -1, -1
-1, -1, +1
+1, -1, +1
+1, -1, +1
+1, +1, +1
-1, -1, -1
+1, +1, +1
-1, -1, -1
-1, +1, -1
+1, -1, +1

Then Bell's inequality:
1 + <bc> >= |<ab> - <ac>|

Then the relevant questions for DrC, which I like very much:

* Have you calculated the expectation values for those terms from any of the datasets I presented?
* How did you do that? (Please copy the relevant dataset prior to your explanation and results so that I can verify)
* Have you substituted them into Bell's inequality?
* Was it violated or not?

 

[DrChinese]

...Again, it doesn't make sense to say I do not like the question I asked. I'm asking it which means I like the question. If there was any doubt that I did not like the question, I am declaring in the open that I do like the questions I asked and here they are again:

First one of the datasets (you can pick anyone you like other than this one):

a, b, c
-----------
+1, -1, +1
-1, +1, -1
-1, +1, -1
-1, +1, -1
+1, -1, -1
-1, +1, +1
-1, +1, -1
+1, -1, +1
-1, -1, -1
-1, -1, -1
-1, -1, +1
-1, +1, +1
+1, -1, -1
+1, -1, -1
-1, -1, +1
-1, -1, -1
+1, -1, +1
-1, +1, -1
-1, +1, -1
+1, +1, +1
+1, -1, -1
-1, -1, +1
+1, -1, +1
+1, -1, +1
+1, +1, +1
-1, -1, -1
+1, +1, +1
-1, -1, -1
-1, +1, -1
+1, -1, +1

Then Bell's inequality:
1 + <bc> >= |<ab> - <ac>|

Then the relevant questions for DrC, which I like very much:

1. Have you calculated the expectation values for those terms from any of the datasets I presented?
2. How did you do that? (Please copy the relevant dataset prior to your explanation and results so that I can verify)
3. Have you substituted them into Bell's inequality?
4. Was it violated or not?

Let's see: you were in the act of accepting my challenge (bob, weave) and now you have issued the billschnieder challenge. I don't get it, but it seems easy enough.

1. Yes
2. I used the entire universe of the following which you provided, it is the first 10 rows.

+1, -1, +1
-1, +1, -1
-1, +1, -1
-1, +1, -1
+1, -1, -1
-1, +1, +1
-1, +1, -1
+1, -1, +1
-1, -1, -1
-1, -1, -1

ab=.2 (2/10)
bc=.4 (4/10)
ac=.8 (8/10)

3. Yes, the result is:

1+.4>=| .2 - .8 |
1.4 >= .6

4. No.

Care to repeat this (futile) exercise again? Or why don't you just give me your answer? Because I am going to tell you that Bell's Inequality is not going to be violated. You can try to manipulate things, but the issue is whether the realistic condition - that out of 8 permutations (+++, ++-, etc.), all have a likelihood of 0 to 1. And they will, in any realistic dataset, by definition.

 

[harrylin]

[..]
1. Yes
2. I used the entire universe of the following which you provided, it is the first 10 rows.

+1, -1, +1
-1, +1, -1
-1, +1, -1
-1, +1, -1
+1, -1, -1
-1, +1, +1
-1, +1, -1
+1, -1, +1
-1, -1, -1
-1, -1, -1

ab=.2 (2/10)
bc=.4 (4/10)
ac=.8 (8/10)

3. Yes, the result is:

1+.4>=| .2 - .8 |
1.4 >= .6

4. No.

[..].

That is strange... DrC, I don't understand how you got those numbers. How could you use a data set of 10 rows for sets of 3 liquids? I can only use the data in multiples of 3. This is what I get with your selection (omitting the last row), arbitrarily sampling in the sequence that the combinations appear in the inequality:

a b c
+1, -1, +1 -> bc1= -1
-1, +1, -1 -> ab1= -1
-1, +1, -1 -> ac1= -1
-1, +1, -1 -> bc2= -1
+1, -1, -1 -> ab2= 1
-1, +1, +1 -> ac2= 1
-1, +1, -1 -> bc3= -1
+1, -1, +1 -> ab3= -1
-1, -1, -1 -> ac3= 1

<bc> = SUM(bc)/N = (-1 + -1 + -1) = -3/3
<ab> = SUM(ab)/N = (-1 + 1 + -1) = -2/3
<ac> = SUM(ac)/N = (-1 + 1 + 1) = 1/3

1 + <bc> >=? |<ab> - <ac>|
1 + -1 >=? |-2/3 - 1/3|
0 >=? +1

That is invalid; thus I get for this example that the inequality is violated.
Did I do something wrong?

Thanks,
Harald

 

[DrChinese]

That is strange... DrC, I don't understand how you got those numbers. How could you use a data set of 10 rows for sets of 3 liquids? I can only use the data in multiples of 3. This is what I get with your selection (omitting the last row), arbitrarily sampling in the sequence that the combinations appear in the inequality:

a b c
+1, -1, +1 -> bc1= -1
-1, +1, -1 -> ab1= -1
-1, +1, -1 -> ac1= -1
-1, +1, -1 -> bc2= -1
+1, -1, -1 -> ab2= 1
-1, +1, +1 -> ac2= 1
-1, +1, -1 -> bc3= -1
+1, -1, +1 -> ab3= -1
-1, -1, -1 -> ac3= 1

<bc> = SUM(bc)/N = (-1 + -1 + -1) = -3/3
<ab> = SUM(ab)/N = (-1 + 1 + -1) = -2/3
<ac> = SUM(ac)/N = (-1 + 1 + 1) = 1/3

1 + <bc> >=? |<ab> - <ac>|
1 + -1 >=? |-2/3 - 1/3|
0 >=? +1

That is invalid; thus I get for this example that the inequality is violated.
Did I do something wrong?

Thanks,
Harald

We are drifting off into the ozone, because we have made the method of calculation for one of bill's assertions our focus - and it shouldn't be. The reason I always set up the examples myself is to prevent situations like this where we argue pointlessly over the assignment of values. In my calculation, I took the matches to be 1 and mismatches to be 0. So ++ or -- is 1, +- or -+ is 0. I don't really care for bill's form of Bell's Inequality, though to be fair it is the original from Bell. And the reason is precisely this, because it entirely obscures the point. Which is that the assertion of realism imposes a burden on a theory which, when expressed mathematically, cannot be met by one which is also local. So I am simply asking any realist to present their version of a mathematical requirement associated with realism.

My goal had been to address his point that Bell tests don't make sense because they involve "impossible" experiments. I was going to do that by showing that if you start with a realistic dataset, you cannot get agreement with QM in possible experiments. That was Bell's essential point.

If you deny that observables corresponding to particle properties (EPR's "elements of reality") have definite values at all times: that IS the mainstream view and it is labeled by the scientific community as "non-realism". But you can call it Al or anything you want.

 

[DrChinese]

I think you will find this a better expression of Bell's idea for this case:

Matches(ab) + Mismatches(ac) - Matches(bc) >= 0

Doesn't matter what you label as a, b or c. Using the first 10 data points bill provided:

a b c
+1, -1, +1
-1, +1, -1
-1, +1, -1
-1, +1, -1
+1, -1, -1
-1, +1, +1
-1, +1, -1
+1, -1, +1
-1, -1, -1
-1, -1, -1

ab matches=2
ac mismatches=2
bc matches=4

2+2-4 >= 0

Try it on a few datasets and you should quickly agree that it works for all.

 

[DrChinese]

In fact, use just 1 datapoint and make it anything you like:

a b c
+ - +
or
? ? ?

Matches(ab) + Mismatches(ac) - Matches(bc) >= 0

0 + 1 - 1 >= 0

or

? + ? - ? >= 0

Obviously, if it works for the single case you hand pick to violate it, it works also for all cases.

 

[harrylin]

We are drifting off into the ozone, because we have made the method of calculation for one of bill's assertions our focus - and it shouldn't be.

I don't think so: we test here a realistic illustration of Bell's Theorem with Bell's method of calculation that corresponds to his theorem as he originally wrote it. Just as easy as Bertlmann's socks, but better matching the photon and electron experiments.

The reason I always set up the examples myself is to prevent situations like this where we argue pointlessly over the assignment of values. In my calculation, I took the matches to be 1 and mismatches to be 0. So ++ or -- is 1, +- or -+ is 0. I don't really care for bill's form of Bell's Inequality, though to be fair it is the original from Bell. And the reason is precisely this, because it entirely obscures the point. [...]

OK that is indeed a minor problem, I had forgotten about the two conventions. Thanks for pinpointing that issue!
In the paper on which this discussion is based, De Raedt writes:

It is often convenient to work with variables S = ±1 instead of x = 0, 1

As far as I can see, from thereon he uses S throughout his paper, and not x. So, in order to avoid confusion, please stick in this thread to that calculation convention which Bell also used in his original paper.

Anyway, perhaps due to the distraction by that minor issue, you did not notice the main issue which I brought up, and which probably relates to what Bill intended to show - indeed it's even the main point, I think, of De Raedt's paper:
How could you use a data set of 10 rows for tests with 3 liquids? I can only use the data in multiples of 3, in the way I showed. One row corresponds to the hidden possible experience of one tablet as well of its double (just like a pair of Bertlmann's socks). Thus only two experiences (with two liquids) are possible per row of data. Bell elaborates about that same issue in "Bertlmann's socks" (there it concerns two new socks that cannot be tested for three temperatures).

PS in a follow-up post you write:

In fact, use just 1 datapoint and make it anything you like [...]
Obviously, if it works for the single case [...]

In this example, a single input data point such as [a,b,c] = [+ + -] corresponds to the hidden possible experiences of one pair of tablets with the three liquids a, b and c. If you insist on only one tablet, then you reduce it to only one tablet that dissolves in one liquid. It is impossible to test with one or two tablets a prediction concerning tests of dissolving whole tablets in three different liquids!