A new simulation of the EPR-Bohm correlations

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Re: A new simulation of the EPR-Bohm correlations

Postby Jochen » Sat Jul 04, 2015 5:47 am

Joy Christian wrote:I have given an explicit formula analogous to Bell's formula for Alice's results for all directions etc., both in the simulation and in the theoretical paper on which the simulation is based.

So I hacked together my own simulation of your model in Mathematica, and you'll be pleased to hear that I can indeed reproduce the vioaltion of the CHSH inequality. However, I also now understand somewhat better where that violation comes from: basically, you have a very low detection efficiency, where certain events are rejected depending on the measurement of the experimenter. That is, effectively, the experimenter is not free to perform any measurement they want: for a certain value of (e,s), certain measurement directions do not yield a result, hence measurement along these directions is impossible. This yields a violation of the fair sampling assumption, and hence, the violation of the CHSH inequality in this case is not in conflict with Bell's theorem. And indeed, if one uses instead the adjusted value of Larsson, , where is the detection efficiency, for the bound, then no violation is observed anymore.

Here's the code I used in order to compute individual measurement outcomes, just so you can review it and tell me if I made any mistakes:
Code: Select all
g[u_, v_] := If[Abs[u.v] > f, u.v, 0]

In[329]:= a1 = {1, 0, 0};

In[330]:= a2 = {0, 1, 0};

In[331]:= b1 = -(a1 + a2)/Sqrt[2];

In[332]:= b2 = -(a1 - a2)/Sqrt[2];

In[333]:= CHSH = -a1.b1 - a1.b2 - a2.b1 + a2.b2

Out[333]= 2 Sqrt[2]

In[416]:= Aout = {};
Bout = {};
Ameas = {};
Bmeas = {};
For[i = 1, i < 10000, i++,
 s = RandomReal[]*Pi;
 e = Normalize@RandomReal[{-1, 1}, 3];
 f = -1 + (2/Sqrt[1 + ((3*s)/Pi)]);
 Ameas = Append[Ameas, Sign[RandomReal[{-1, 1}]]];
 a = If[Ameas[[i]] > 0, a1, a2];
 Bmeas = Append[Bmeas, Sign[RandomReal[{-1, 1}]]];
 b = If[Bmeas[[i]] > 0, b1, b2];
 Aout = Append[Aout, Sign[g[a, e]]];
 Bout = Append[Bout, -Sign[g[b, e]]];
 Data = {Ameas, Bmeas, Aout, Bout}\[Transpose]
 ]


First, I define the function g, which returns the scalar product of its inputs if its absolute value exceeds the constraint f, and 0 else. Then, I set four measurement directions for A and B, and check whether they violate CHSH. Then, in the for loop, I calculate a random angle s between 0 and pi, a random unit vector e, and the constraint f. To get the measurement directions of A and B, a random real number between -1 and 1 is generated, and if it is positive, then the first measurement direction is used, if it is negative, the second. The measurement performed is also stored in the lists Ameas and Bmeas. Then, the observed value is computed, and stored in Aout resp. Bout. The whole thing is then for convenience packaged into Data.

To analyze the data, I throw out all the 0-results, and compute the correlation for the four possible settings for the remaining data points, and get a nice violation of CHSH. Does this look about right to you?
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Re: A new simulation of the EPR-Bohm correlations

Postby Joy Christian » Sat Jul 04, 2015 6:46 am

Jochen wrote:...I also now understand somewhat better where that violation comes from: basically, you have a very low detection efficiency, where certain events are rejected depending on the measurement of the experimenter. That is, effectively, the experimenter is not free to perform any measurement they want: for a certain value of (e,s), certain measurement directions do not yield a result, hence measurement along these directions is impossible. This yields a violation of the fair sampling assumption...

My theoretical model or its simulation has nothing to do with detection loophole, detector efficiency, fair sampling, or any other loophole. Nor does it depend on compromising experimenter's freedom to chose any measurement direction they like. If for certain values of (e,s) certain measurement directions do not yield a result as you say, then why should that be a problem? To begin with these are the states that do not exist in S^3 to begin with. And one cannot detect that which does not exist in the first place! Moreover, even if certain states existing within S^3 do not yield a result as you say, then, again, why is that a problem? There are plenty of other states (e,s) existing within S^3 that would yield good results. The fair sampling assumption has to do with certain restrictions experimenters impose on Nature due to their own limitations. In my model there are no restrictions imposed by the experimenters, or on the experimenters, in what and how the measurement events are observed. If there appear to be such restrictions from the perspective of R^3, then that is a limitation of that flat perspective and not of my model based on S^3.

In short, you have now got the model working in Mathematica. That is good, but it will not surprise the participants and readers of this forum. In order to understand my model, however, what you must now do is imagine yourself as residing within S^3 instead of R^3 and try to reinterpret all the details you have found in your code.

On the practical side, Fred, among others, knows Mathematica well, so he will be able to comment on your code in more detail when the Sun rises in Los Angeles.

By the way, I do not care about Bell and his "theorem." What I care about is that what I have produced is a perfectly legitimate and satisfactory local-realistic model.
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Re: A new simulation of the EPR-Bohm correlations

Postby minkwe » Sat Jul 04, 2015 9:56 am

I just want to remind everyone that Guest and Heinera have stated categorically that the following

is impossible in Quantum mechanics. That if the pair going to Alice and Bob can be described by a singlet state, and the pair going to Cindy and Bob can be describe by a singlet state, then it doesn't make sense in Quantum Mechanics to talk of correlation between Alice and Cindy. In other words, the correlation is zero.

Here is what Guest said:
Guest wrote:The statistics of measurements of all four particles will exhibit the singlet correlations between A and B, and the singlet correlations between C and D, and zero correlation between those two pairs.


They think they've successfully dodged the bullet, only to go from the frying pan to the fire. Note following:

1) The derivation of the CHSH starts as follows: . Where A,B,C,D represent measurements on a single pair of spin-half particles. This is exactly equivalent to having two 4 particles in which , where the particle pair used to measure the CD term is identical to the particle pair used to measure AB, just like I describe. An expression like the CHSH inequality was derived precisely by assuming the exact scenario my friends now say is meaningless in QM! The expectation values in the final CHSH expression represents exactly the ones <AB> <AD>, <CB>, <CD>, which the bell believers now either claim QM can not make predictions for, or two of them must be zero :shock:

2) The question I asked them about 4 particles, is exactly the same question Bell asked himself in proving the celebrated Bell's theorem. What predictions does QM make for the expectation values <AB> <AD>, <CB>, <CD> in the CHSH expression :?: According to our esteemed guest, the answer is . Now please tell me how this can ever violate the inequality. You see, Bell's followers don't even realize that they believe contradictory things at the same time. So let me ask the question again, and see what they will answer this time What predictions does QM make for the expectation values in the CHSH expression?

If QM is unable to predict those expectations, then Bell's theorem is a fraud. If QM can provide predictions for the terms of the CHSH, then QM can predict them for the scenario I gave. For those who may still have any shred of doubt left. Consider that when the inequality is derived the starting point is always . But if the CB, CD, AB, and AD measurements are performed on independent particle pairs , then the factorization is not possible. When presented with this fact, Bell's followers often claim that ... even though the factorization fails, the inequality still applies because the averages from different sets of particles will be the same as those from a single set. They argue that since
,
therefore
, must also hold

According to them, the randomized experimental design causes the independent ensembles of pairs used to calculate the second expression to be equal to the ensemble of pairs used in the first, ie , therefore, according to them . But if the ensembles are equivalent, then for every particle of a pair of spin-half particles, there must be an identical particle in the other ensembles. Again, identical in the sense that it always produces the same outcomes at the same setting as the first one. But our friends now say this is impossible in quantum mechanics. Therefore either the CHSH is impossible for QM to calculate, or the result is not the celebrated violations our friends like to call Bell's theorem.

Check mate! :ugeek: :mrgreen:
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Re: A new simulation of the EPR-Bohm correlations

Postby Heinera » Sat Jul 04, 2015 1:47 pm

minkwe wrote:The derivation of the CHSH starts as follows: . Where A,B,C,D represent measurements on a single pair of spin-half particles. This is exactly equivalent to having two 4 particles in which , where the particle pair used to measure the CD term is identical to the particle pair used to measure AB, just like I describe. An expression like the CHSH inequality was derived precisely by assuming the exact scenario my friends now say is meaningless in QM!

Yes, indeed. That's excactly why QM can violate the inequalitiy, because the assumptions used to derive the inequality doesn't apply to QM (or, in other words, they are incorrect in QM). I know you've struggled with this simple fact for years now, but honestly, how hard can it be to get a grip on this?
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Re: A new simulation of the EPR-Bohm correlations

Postby FrediFizzx » Sat Jul 04, 2015 1:54 pm

Heinera wrote:
minkwe wrote:The derivation of the CHSH starts as follows: . Where A,B,C,D represent measurements on a single pair of spin-half particles. This is exactly equivalent to having two 4 particles in which , where the particle pair used to measure the CD term is identical to the particle pair used to measure AB, just like I describe. An expression like the CHSH inequality was derived precisely by assuming the exact scenario my friends now say is meaningless in QM!

Yes, indeed. That's excactly why QM can violate the inequalitiy, because the assumptions used to derive the inequality doesn't apply to QM (or, in other words, they are incorrect in QM). I know you've struggled with this simple fact for years now, but honestly, how hard can it be to get a grip on this?

LOL! How hard is it for you to get a grip on the fact that nothing can violate the inequalities. It is a mathematical impossibility. Above just shows you how the "goal posts are moved" illegally.
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Re: A new simulation of the EPR-Bohm correlations

Postby minkwe » Sat Jul 04, 2015 3:18 pm

Heinera wrote:Yes, indeed. That's excactly why QM can violate the inequalitiy

LOL! I just showed you that QM cannot violate the inequality, duh!

Heinera wrote:because the assumptions used to derive the inequality doesn't apply to QM (or, in other words, they are incorrect in QM).

I just showed you that it is not the assumption that is used to derive the inequality that is at conflict with QM. It is the assumption that the expectation values from different independent sets are the same as those from a single set. An assumption, mind you, that I've already shown to be false, even for local HV theories. Bell's theorem doesn't say it is impossible for QM to predict the expectation values in the CHSH. It says the values predicted by QM for the expectations in the CHSH violate the CHSH. You are in denial. You've been in denial for years and I doubt you will ever pull your head out of the sand.

You've probably already forgotten the following from a couple of pages ago (or wish it would dissapear):

minkwe wrote:The expression means that for every single individual pair of particles in the series which produced the outcome pair , there is an equivalent pair of particles in the series. This means a function exists which maps a specific particle pair in set , to a specific particle pair in set . Let us call that function . Similarly, ... there must exist other independent functions , , , , , . etc.

Imagine a spreadsheet with two columns labelled , and containing all the outcomes for the series of measurements on its rows. Now let us try to apply the function so that we can place the outcomes from the series of measurements on the next two columns, and we must be able to apply all those functions to all the measurement outcomes and at the end all the columns labelled with similar upper case letters must be identical in numbers of +1's and -1's, and also in the pattern of switching back and forth. Only then can you assume that are all true and the upper bound of 2 should apply.


minkwe wrote:
Can be factored if we apply our mapping functions such that the series of equivalent outcome sequences have the same numbers of +1's and -1's and the same pattern of occurences of those numbers. That is, for the above expression we can use our functions to generate new sequences of outcomes from measured data such that and , where the prime , represents the fact that the sequence of outcomes has been rearranged using the mapping function. Thus we have


With our new re-ordered sets of outcomes we invoke the equivalence and do the factorization to get


But then we immediately face a wall. For this expression to obey the inequality , we also need to be able to rearrange so that and which is for all practical purposes impossible. Note that both and have already been rearranged independently of each other, and since any rearrangement will shuffle both outcomes in the set of pairs, any new rearrangement to make agree with will undo the previous rearrangements. The same for and . Different independent and conflicting rearrangements are required to make the inequality work for 4 separate sets of paired outcomes.

Therefore it is simply not true that the inequality
Derived assuming a single set of quartets of outcomes , should Should apply to 4 different independent sets of pairs of outcomes


The above explanation does not rely on QM or anything spooky in any way yet demonstrates that the argument from Bell's supports is nonsense. Therefore your claim that it is only impossible in QM is also nonsense.

But let us see how intellectually honest you are. For the CHSH inequality

Could you please tell us what Quantum Mechanics predicts for the 4 expectation values ?
Can you answer this question as honestly you possibly can. I'll leave it up to you to hammer the final nail into the coffin of Bell's theorem, with your answer to that question.
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Re: A new simulation of the EPR-Bohm correlations

Postby Heinera » Sat Jul 04, 2015 3:54 pm

minkwe wrote:
Heinera wrote:Yes, indeed. That's excactly why QM can violate the inequalitiy

LOL! I just showed you that QM cannot violate the inequality, duh!

You showed no such thing at all. In fact, you just showed why QM can violate the inequality, since your Gedanken experiment is a theoretical inpossibilty in QM. As Schmelzer has already hinted, your knowledge and understanding of QM seems to be limited, to put it mildly. Perhaps you should start with a good QM textbook and then revisit Bell's theorem at a later time.
Last edited by Heinera on Sat Jul 04, 2015 4:25 pm, edited 1 time in total.
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Re: A new simulation of the EPR-Bohm correlations

Postby minkwe » Sat Jul 04, 2015 4:00 pm

:D Mr Handwaver, let us see how intellectually honest you are. For the CHSH inequality

Could you please tell us what Quantum Mechanics predicts for the 4 expectation values ?
Can you answer this question as honestly you possibly can. I'll leave it up to you to hammer the final nail into the coffin of Bell's theorem, with your answer to that question.

Or did the dog eat your tongue/keyboard. Aren't you tired of always ending up with the short end of the stick? It must be very infuriating, for you. Just when you thought you had done a houdini trick to avoid the trap, you find yourself confined in an even bigger trap.

So please tell us, Mr Quantum Expert™, what are the Quantum Mechanical predictions for ?

http://arxiv.org/abs/quant-ph/0006014
A Refutation of Bell's Theorem

Adenier wrote:Bell's Theorem was developed on the basis of considerations involving a linear combination of spin correlation functions, each of which has a distinct pair of arguments. The simultaneous presence of these different pairs of arguments in the same equation can be understood in two radically different ways: either as `strongly objective,' that is, all correlation functions pertain to the same set of particle pairs, or as `weakly objective,' that is, each correlation function pertains to a different set of particle pairs.
It is demonstrated that once this meaning is determined, no discrepancy appears between local realistic theories and quantum mechanics: the discrepancy in Bell's Theorem is due only to a meaningless comparison between a local realistic inequality written within the strongly objective interpretation (thus relevant to a single set of particle pairs) and a quantum mechanical prediction derived from a weakly objective interpretation (thus relevant to several different sets of particle pairs).


I suggest you read the above article very carefully before you go around regurgitating stuff you've heard other people say but don't actually understand yourself.
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Re: A new simulation of the EPR-Bohm correlations

Postby Heinera » Sat Jul 04, 2015 4:59 pm

minkwe wrote:So please tell us, Mr Quantum Expert™, what are the Quantum Mechanical predictions for ?

The problem wtih your question is that its premise

There is no copying or cloning involved. I'm asking what the answers to those questions would be if the source produced the particles just like described. If you think such a source is impossible, then QM cannot predict any correlations at all. But what would QM predict if such a source produced the particles just as described in the gedankenexperiment such that A and B can be described by a singlet state and so can C and D, and the outcomes of A and C are correlated in the sense that if a measurement is done on A at setting "a", a simultaneous measurement on C at the same setting will always produce exactly the same outcome as A. In other words for all values of a. Same between B and D. So it is not correct to say A and B are completely independent of C and D. I've specified exactly how they are correlated.

is just plain rubbish.

"But what would QM predict if such a source produced the particles just as described in the gedankenexperiment such that A and B can be described by a singlet state and so can C and D, and the outcomes of A and C are correlated in the sense that if a measurement is done on A at setting "a", a simultaneous measurement on C at the same setting will always produce exactly the same outcome as A. "

When you do pick up that textbook, you will hopefully realize that this is impossible in QM, and that the impossibility can be rigorously proved.
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Re: A new simulation of the EPR-Bohm correlations

Postby minkwe » Sat Jul 04, 2015 6:29 pm

minkwe wrote::D Mr Handwaver, let us see how intellectually honest you are. For the CHSH inequality

Could you please tell us what Quantum Mechanics predicts for the 4 expectation values
?


The poor guy can't even tell us what QM predicts for the CHSH inequality, yet he believes Bell's theorem.
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Re: A new simulation of the EPR-Bohm correlations

Postby minkwe » Sat Jul 04, 2015 8:24 pm

Jochen wrote:To analyze the data, I throw out all the 0-results, and compute the correlation for the four possible settings for the remaining data points

Why do you have to throw away anything in order to calculate
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Re: A new simulation of the EPR-Bohm correlations

Postby Joy Christian » Sat Jul 04, 2015 11:56 pm

minkwe wrote:
Jochen wrote:To analyze the data, I throw out all the 0-results, and compute the correlation for the four possible settings for the remaining data points

Why do you have to throw away anything in order to calculate

Besides, as evident from both my theoretical model and its simulation, the {0,+}, {0,-}, {+,0}, {-,0}, and {0,0} outcomes simply do not exist within S^3. An elementary fact that flatlanders like Gill are having a great deal of difficulty understanding. One cannot measure, or "throw out", that which is not there in S^3 in the first place.
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Re: A new simulation of the EPR-Bohm correlations

Postby FrediFizzx » Sun Jul 05, 2015 1:09 am

Joy Christian wrote:
minkwe wrote:
Jochen wrote:To analyze the data, I throw out all the 0-results, and compute the correlation for the four possible settings for the remaining data points

Why do you have to throw away anything in order to calculate

Besides, as evident from both my theoretical model and its simulation, the {0,+}, {0,-}, {+,0}, {-,0}, and {0,0} outcomes simply do not exist within S^3. An elementary fact that flatlanders like Gill are having a great deal of difficulty understanding. One cannot measure, or "throw out", that which is not there in S^3 in the first place.

Yep, the fact they don't understand it is really mystifying. From Albert Jan's blog.

I suspect it is the case that they don't want to understand it because then they would have to accept it.
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Re: A new simulation of the EPR-Bohm correlations

Postby Joy Christian » Sun Jul 05, 2015 1:43 am

FrediFizzx wrote:
Joy Christian wrote:Besides, as evident from both my theoretical model and its simulation, the {0,+}, {0,-}, {+,0}, {-,0}, and {0,0} outcomes simply do not exist within S^3. An elementary fact that flatlanders like Gill are having a great deal of difficulty understanding. One cannot measure, or "throw out", that which is not there in S^3 in the first place.

Yep, the fact they don't understand it is really mystifying. From Albert Jan's blog.

I suspect it is the case that they don't want to understand it because then they would have to accept it.

Here is the link to Albert Jan Wonnink's blog page, which also has a nice video demonstration: http://challengingbell.blogspot.co.uk/2 ... tians.html.

By the way, I have revised the simulation again and now also calculate the "N vectors" that appear in Eq. (B10) of this paper: http://arxiv.org/abs/1501.03393.

These are the N vectors for which Gill owes me 10,000 euros + interest + inflation (also, Scott Aaronson owes me 100,000 US dollars + 8 Yr interest + 8 Yr inflation).
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Re: A new simulation of the EPR-Bohm correlations

Postby Jochen » Sun Jul 05, 2015 3:42 am

minkwe wrote:Good that you agree. Who cares about unmeasured distributions? The only outcomes you can calculate with are the ones that are measured. So your so-called "actual probability distribution" is a fantasy.

But the question is exactly whether such a probability distribution can possibly exist, and explain the measured values. If no Bell inequality is violated, then such a distribution does exist, if there is a violation, then you can't find one. I mean, we want to find whether there could be a theory more fundamental than QM that accounts for all of QM's predictions, while assigning definite values to all observables at all times. Such a theory will have a PD over all possible outcomes in a given experiment. So if there is such a PD possible, then likewise, such a theory is possible; and if not, then no such theory exists.

This is thus not about the PD that you get by making a certain subset of measurements only, but rather, the PD that is actually prepared by nature---the actual ensemble of hidden variable value assignment. That we can do a certain set of measurement in which we simply neglect correlations and hence, obtain a PD that does not include any correlations is completely beside the point. The correlations are what we are interested in---failure to measure them then just means that we did our experiment stupidly, not anything about local realistic completions of QM.

minkwe wrote:The point is that there is a joint PD P(A,B,C,D) of outcomes based on how the experiment was performed, irrespective of whatever mechanism is producing the outcomes, and the corollary is that even if the process producing the outcomes may have a fantastic unmeasurable "actual distribution", you could still obtain measurement outcomes which do not have a joint PD P(A,B,C,D) simply by choosing to measure the outcomes in a certain way, such as is done in EPRB experiments.

No, this isn't possible. If there exists a fundamental joint PD, then no experimental outcomes exist that aren't compatible with the existence of that PD, no matter how you perform the measurements, since all the outcomes are just sampled from this distribution.

minkwe wrote:I take it then you believe that a system producing 3 correlated spin-half particles heading towards Alice, Bob and Cindy, with Cindy simply ignoring her particles, and Alice and Bob measuring theirs like a typical EPRB cannot violate a Bell inequality no matter the setting combination they use, and no matter the nature of the correlation between them? Yes or no?

That depends: if the state is separable wrt both the Alice-Cindy and Bob-Cindy splits, but maximally entangled across the Alice-Bob split, then they will be able to violate the CHSH inequality maximally. If there is some entanglement present between Cindy and Alice-Bob, then there won't be a maximal violation, and the violation will decay in proportion to the amount of this entanglemen.

minikwe wrote:And if you believe the fact that it doesn't violate Bell's inequality can be used to conclude that there is no-disturbance present, and no non-locality present.

The fact that no Bell violation exists does entail that there is a local realistic model for the particular scenario. But the fact that there are scenarios where Bell violation exists means that there is no such model that can be used to explain every quantum prediction.

minkwe wrote:If you believe that then, I'm asking you if you believe the claimed non-locality or disturbance only shows up for specific states, but decides to hide if you have more particles that can actually be measured.

Just like for any other characteristic, you must make the right measurement on the system in order to detect the nonlocality. Making the wrong measurements won't tell you anything.

minkwe wrote:Take for example the CHSH in which 2 spin-half particles in the singlet state are measured at 4 settings , in the pairs . If instead of producing just the 2 particles each time, our source produces 4 entangled particles heading towards 4 stations, Alice, Bob, Cindy, and Dave, such that the particles pair going to Alice and Bob are always in a singlet state, those going to Cindy and Dave are also always in a singlet state, and the particles going to Alice and Cindy are identical to each other, just like the particles going to Bob and Dave. Thus all the paired measurements are by themselves measurements on a pair of spin-half particles in a singlet state.

This characterizes the state fully to be , i.e. the state is maximally entangled between Alice and Bob, respectively between Cindy and Dave, and completely uncorrelated between the A-B and C-D pairs. Thus, correlations , while . Hence, , and there is no CHSH violation predicted by QM.

minkwe wrote:Would those values be different if Cindy and Dave simply ignored their particle pairs, so that Alice and Bob did all the measurements at different times and different settings on different ensembles?

Since the state is separable along the A-B|C-D split, what Cindy and Dave do or don't do doesn't affect the results that Alice and Bob get from their measurements. Thus, if Alice and Bob add measurements c and d to their repertoire, they're now measuring the full CHSH-correlations on an ensemble of maximally entangled particles, and will obtain .

minkwe wrote:Nope, you did not understand. I say the presence or absence of a joint PD is based on how you do the measurement, not due to disturbance or non-locality, I've given you examples (tablets) in which even with locality and no-disturbance, you did not not have a joint PD of outcomes based on how you did the measurement.

In this case, there is a joint PD (trivially), but you can't find it because you can't repeat the measurements. From throwing a coin once, you can't know the probability of it coming up heads.

minkwe wrote:I have given examples (non-local state machine pressed in sequence ) in which a joint PD of outcomes was present even with disturbance or non-locality to prove this point.

A joint PD is trivially present if you neglect all correlations, because then you can just use a product distribution. But that distribution won't be able to explain all measurements, i.e. the outcomes of joint measurements. Again, throw two correlated coins, only noting down the outcome of one, and you can write down a joint PD; but according to that PD, the coins will be completely uncorrelated, so it's just not in any sense the PD of those coins.

minkwe wrote:I have also given another example (see above) using 4 spin-1/2 particle particles in which a joint PD is present and the inequalities must be satisfied. I hope you will address that example because I think it shows clearly the problem with your argument.

I don't see any problem; there's clear predictions from quantum mechanics, which will agree with experiments.

minkwe wrote:So let me ask you again the questions I asked you are the beginning. A simple yes/no answer will resolve all the word games
1) Is locality required or necessary in order to have a joint PD? Yes or no.
2) Is pre-determination required or necessary in order to have a joint PD? Yes or no.
3) Is no-disturbance required or necessary in order to have a joint PD? Yes or no.

1) No. There are nonlocal models which nevertheles admit a joint PD; however, whenever a joint PD is absent, then we know that there is no local (realistic) model. This is what Bell is about.
2) Again, no. But again, the question is: "We have this data. Can it be explained by a local realistic model?", and if there is a joint PD, then it can; otherwise, it can't, since any local realistic model admits a joint PD. There are nonlocal, nonrealistic models that nevertheless do, but those are simply besides the issue. We don't want to know whether the data is compatible with non-local antirealism, we want to know whether it is compatible with local realism, which it is if and only if there is no BI violation.
3) No. See above.

If you want to change your answers to no, no, no. Then we can put this issue to bed and proceed to other things.

The problem is, however, that you seem to think that answering no to all of the above would resolve the issue, but you've still simply got the logic backwards: if we find data compatible with a joint PD, then (and only then) can we write down a local realistic model that replicates the data, because any local realistic model will have a joint PD---local realism is sufficient for the existence of a joint PD. So if there is no joint PD, then local realism doesn't hold.

minkwe wrote:The problem is that you continue to argue that the inequality should hold even in the scenario I have shown it does not apply to. You continue to argue that a joint PD must be possible if the model is a local HV one. There is no disturbance in my simulations, and there is no non-locality.

And hence, there is a local realistic model; in fact, your model just is that model. The simulation is intended to argue that local realistic models can violate Bell inequalities, but it misses its mark, in violating a Bell inequality that would not be expected to hold in this scenario anyway, since one needs a higher detection efficiency than you provide in order to perform a conclusive test.

minkwe wrote:The simulations are completely local realistic, and yet they reproduce the QM predictions very well. So it must be false that a joint PD can always be constructed if the model is local realistic and does not have any disturbance. If you disagree, show me the disturbance or non-locality that my simulations are using to produce their outcomes. They are designed to be run on separate unconnected computers.

And one can explicitly write down a joint PD for your model; it's just that some samples from that PD will be rejected, i.e. not lead to a detection.

minkwe wrote:All you have to do is admit that based on how the measurements are done, it is not always possible to reconstruct a joint PD, even if the model is local and realistic, just like is the case in the EPRB experiment. If you admit that, then we can put this issue to bed.

I can't admit it, because it happens to be false. If the model is realistic, then there is always some value assignment prior to measurement. If there is no disturbance, then that value assignment is not influenced by other measurements. Hence the convex combination of value assignments according to their frequency in the ensemble is a joint probability distribution, from which measurement outcomes are sampled.
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Re: A new simulation of the EPR-Bohm correlations

Postby Jochen » Sun Jul 05, 2015 3:55 am

Joy Christian wrote:My theoretical model or its simulation has nothing to do with detection loophole, detector efficiency, fair sampling, or any other loophole. Nor does it depend on compromising experimenter's freedom to chose any measurement direction they like. If for certain values of (e,s) certain measurement directions do not yield a result as you say, then why should that be a problem?

Because most typical Bell inequalities are derived under an assumption that measurements always yield a result, or yield a result at least probabilistically with some high enough efficiency; hence, these BIs, for instance, the CHSH inequality, simply doesn't apply to your model. In your model, the data obtained is not a fair sample of the data produced, since data is rejected based on the measurement direction (a fair sample would produce a result with some certain probability independently of what is measured). Hence, CHSH violation isn't in conflict with Bell's theorem in this case. Using an appropriate inequality, such as Larsson's modification, sees the violation disappear, and hence, your model is completely in line with Bell's theorem.


Joy Christian wrote:To begin with these are the states that do not exist in S^3 to begin with. And one cannot detect that which does not exist in the first place! Moreover, even if certain states existing within S^3 do not yield a result as you say, then, again, why is that a problem? There are plenty of other states (e,s) existing within S^3 that would yield good results. The fair sampling assumption has to do with certain restrictions experimenters impose on Nature due to their own limitations. In my model there are no restrictions imposed by the experimenters, or on the experimenters, in what and how the measurement events are observed. If there appear to be such restrictions from the perspective of R^3, then that is a limitation of that flat perspective and not of my model based on S^3.

The thing is, that your model then predicts a certain maximum detector efficiency; if that given by your implementation is indicative, then you have a maximum of , if I have made my estimation right, i.e. that for any given instance, only 68% of measurement directions will yield a detection; but we already have detectors more efficient than that, and hence, your model seems experimentally ruled out.

Joy Christian wrote:By the way, I do not care about Bell and his "theorem." What I care about is that what I have produced is a perfectly legitimate and satisfactory local-realistic model.

Not one that replicates the quantum predictions, however, since it doesn't violate the inequality appropriate to your setting.
Last edited by Jochen on Sun Jul 05, 2015 3:56 am, edited 1 time in total.
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Re: A new simulation of the EPR-Bohm correlations

Postby Jochen » Sun Jul 05, 2015 3:56 am

minkwe wrote:
Jochen wrote:To analyze the data, I throw out all the 0-results, and compute the correlation for the four possible settings for the remaining data points

Why do you have to throw away anything in order to calculate

As you can see yourself, they don't enter in the calculation of the above quantity; hence, I can just throw them away.
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Re: A new simulation of the EPR-Bohm correlations

Postby Joy Christian » Sun Jul 05, 2015 4:44 am

Jochen wrote:
Joy Christian wrote:My theoretical model or its simulation has nothing to do with detection loophole, detector efficiency, fair sampling, or any other loophole. Nor does it depend on compromising experimenter's freedom to chose any measurement direction they like. If for certain values of (e,s) certain measurement directions do not yield a result as you say, then why should that be a problem?

You have cut off my argument in the middle, which allows you to continue to misinterpret my model. My full response (which you do continue quoting later) was:

Joy Christian wrote:My theoretical model or its simulation has nothing to do with detection loophole, detector efficiency, fair sampling, or any other loophole. Nor does it depend on compromising experimenter's freedom to chose any measurement direction they like. If for certain values of (e,s) certain measurement directions do not yield a result as you say, then why should that be a problem? To begin with these are the states that do not exist in S^3 to begin with. And one cannot detect that which does not exist in the first place! Moreover, even if certain states existing within S^3 do not yield a result as you say, then, again, why is that a problem? There are plenty of other states (e,s) existing within S^3 that would yield good results. The fair sampling assumption has to do with certain restrictions experimenters impose on Nature due to their own limitations. In my model there are no restrictions imposed by the experimenters, or on the experimenters, in what and how the measurement events are observed. If there appear to be such restrictions from the perspective of R^3, then that is a limitation of that flat perspective and not of my model based on S^3.

Until you liberate yourself from the "flatland" perspective of R^3, you will not be able to comprehend my 3-sphere model, and most likely continue to misinterpret it:

Jochen wrote:Because most typical Bell inequalities are derived under an assumption that measurements always yield a result, or yield a result at least probabilistically with some high enough efficiency; hence, these BIs, for instance, the CHSH inequality, simply doesn't apply to your model. In your model, the data obtained is not a fair sample of the data produced, since data is rejected based on the measurement direction (a fair sample would produce a result with some certain probability independently of what is measured). Hence, CHSH violation isn't in conflict with Bell's theorem in this case. Using an appropriate inequality, such as Larsson's modification, sees the violation disappear, and hence, your model is completely in line with Bell's theorem.

I cannot agree with a single word of what you have written above, because what you have written has nothing whatsoever to do with my model. At best it describes your model, not mine. In my 3-sphere model measurements always yield a result. All detectors in the model are of 100% efficiency. The data obtained is a fair sample of the data produced. No data has been rejected based on the measurement direction. Every single initial state (e,s), or particle w, is detected. There is one-to-one correspondence between the initial states w = (e,s) and the measurement results A and B. Both CHSH and CH inequalities are duly "violated", since all 13 probabilistic predictions of the model match exactly with the corresponding predictions of quantum mechanics. Bell's theorem has thus been put to rest, and constructively so, not just formally. The only reason you seem not to recognize this is because you seem to be stuck in R^3. But we do not live in R^3. We live in S^3. That is the model.

Jochen wrote:The thing is, that your model then predicts a certain maximum detector efficiency; if that given by your implementation is indicative, then you have a maximum of , if I have made my estimation right, i.e. that for any given instance, only 68% of measurement directions will yield a detection; but we already have detectors more efficient than that, and hence, your model seems experimentally ruled out.

As noted above, all detectors involved in my model are of 100% efficiency. Mine is not a detection loophole model, or exploiting fair sampling model. It is S^3 model.

Jochen wrote:
Joy Christian wrote:By the way, I do not care about Bell and his "theorem." What I care about is that what I have produced is a perfectly legitimate and satisfactory local-realistic model.

Not one that replicates the quantum predictions, however, since it doesn't violate the inequality appropriate to your setting.


My model replicates all 13 of the probabilistic predictions of QM exactly, with detectors of 100% efficiency. You have missed the understanding of my model by a mile.
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Re: A new simulation of the EPR-Bohm correlations

Postby Jochen » Sun Jul 05, 2015 4:50 am

Joy Christian wrote:I cannot agree with a single word of what you have written above, because what you have written has nothing whatsoever to do with my model. At best it describes your model, not mine. In my 3-sphere model measurements always yield a result. All detectors in the model are of 100% efficiency. The data obtained is a fair sample of the data produced. No data has been rejected based on the measurement direction. Every single initial state (e,s), or particle w, is detected. There is one-to-one correspondence between the initial states w = (e,s) and the measurement results A and B.

OK, so what do you do with the events in which in which A(a,e,s)=0?
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Re: A new simulation of the EPR-Bohm correlations

Postby Joy Christian » Sun Jul 05, 2015 4:57 am

Jochen wrote:OK, so what do you do with the events in which A(a,e,s)=0?

There are no such events. Please read through the simulation carefully. You will see what I mean.
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