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 Ben6993 » Tue Jun 30, 2015 12:27 pm

Jochen wrote:
Additionally, weak measurements are called this because they weakly couple to individual members of an ensemble, thus minimally disturbing the state, and consequently extracting only a minimum amount of information; it is to rectify this that postselection (the preselection is really just the preparation of a definite state, which we do in any Bell experiment) is necessary. As you can see in Fig. 1 of http://arxiv.org/abs/1005.3236, it is indeed the case that all measurements are carried out on a single pair.


I have skim read the paper twice. As I read it, the idea is to generate a host of cloned particles. So the paired partners of the normal Bell test are replaced by a large, single group of particles with identical (as identical as possible but presumably not exactly so ... quite weakly so maybe) spin, orientation and presumably other properties. (Assuming that has been possible ... ) A sequence of measurements on the group is made, one measurement per particle. If this is with photons then the sampling of photons is without replacement as the photon is deleted from the group on measurement. If this is with electrons then after a measurement the electron changes spin value but continues in the group and could be measured again. This is why the group/ensemble needs to be as large as possible to minimise the chance of re-sampling the same electron which now has the exact opposite spin to the rest of the group.

The use of a final strong measurement seems to imply that what I have written above is incorrect and that an individual particle is followed and labelled across its interactions. And how are the weak results for a single particle checked against the final strong result. And how does the strong measurement at the end differ from the weak measurements en route?

It may be that the weak measurements are using aggregations as the "readings are noisy, and the microscopic values cannot be inferred".
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Re: A new simulation of the EPR-Bohm correlations

Postby Schmelzer » Tue Jun 30, 2015 11:35 pm

Joy Christian wrote:
Jochen wrote:Then let me try to improve my understanding. In your one-page paper, you define your hidden variable model in the first two equations: basically, Alice always notes down , while Bob notes down . So in performing the experiment, they will get a measurement table like this one:

Code: Select all
lambda | Alice | Bob
   +1  |   +1  |   -1
   -1  |   -1  |   +1
   +1  |   +1  |   -1
   +1  |   +1  |   -1
   -1  |   -1  |   +1
   +1  |   +1  |   -1
.
.
.

I mean, that's what equations (1) and (2) say, no?

I am afraid not. This is what some of my critics would have us believe.

I would say this is what your formulas (1) and (2) would have us believe. If this is not the case, then your formulas (1) and (2) are simply misleading, and should be replaced by formulas which do not allow such a misinterpretation.

Joy Christian wrote:To see how wrong and naïve the claim of "always -1 correlation" is, you may wish to consult equation (A.9.15) on page 244 of this paper.

Sorry, but I'm unable to make sense of the limiting operator
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Re: A new simulation of the EPR-Bohm correlations

Postby FrediFizzx » Tue Jun 30, 2015 11:52 pm

Schmelzer wrote:I would say this is what your formulas (1) and (2) would have us believe. If this is not the case, then your formulas (1) and (2) are simply misleading, and should be replaced by formulas which do not allow such a misinterpretation.

Well, for the 3-sphere model you have to do a geometric product to get the right results. This is how it is done for GAViewer.

Code: Select all
function getRandomLambda()
{
   if( rand()>0.5) {return 1;} else {return -1;}
}

function getRandomUnitVector() //uniform random unit vector:
     //http://mathworld.wolfram.com/SpherePointPicking.html
{
   v=randGaussStd()*e1+randGaussStd()*e2+randGaussStd()*e3;
   return normalize(v);
}
   batch test()
{
   set_window_title("Test of Joy Christian's arXiv:1103.1879 paper");
   N=20000; //number of iterations (trials)
   I=e1^e2^e3;
   s=0;

   a=getRandomUnitVector();
   b=getRandomUnitVector();
   minus_cos_a_b=-1*(a.b);

   for(nn=0;nn<N;nn=nn+1) //perform the experiment N times
   {
     lambda=getRandomLambda(); //lambda is a fair coin,
                               //resulting in +1 or -1
     mu=lambda * I;  //calculate the lambda dependent mu
     C=-I.a;  //C = {-a_j B_j}
     D=I.b;   //D = {b_k B_k}
     E=mu.a;  //E = {a_k B_k(L)}
     F=mu.b;  //F = {b_j B_j(L)}
     A=C E;  //eq. (1) of arXiv:1103.1879, A(a, L) = {-a_j B_j}{a_k B_k(L)}
     B=F D;  //eq. (2) of arXiv:1103.1879, B(b, L) = {b_j B_j(L)}{b_k B_k}
     q=0;
     if(lambda==1) {q=((-C) A B (-D));} else {q=((-D) B A (-C));} //eq. (6)
     s=s+q; //summation of all terms.
   }
   mean_mu_a_mu_b=s/N;
   print(mean_mu_a_mu_b); //print the result
   print(minus_cos_a_b);
   prompt();
}
//Typical result is:
//mean_mu_a_mu_b = 0.87 + 0.00*e2^e3 + 0.00*e3^e1 + 0.00*e1^e2
//minus_cos_a_b = 0.87
//The scalar parts match and others vanish!  Proving the result is -a.b.
//Thus Dr. Christian's arXiv:1103.1879 paper is a classical local
//realistic counter-example that in fact contradicts Bell's theorem.

http://challengingbell.blogspot.com/201 ... f-joy.html
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Re: A new simulation of the EPR-Bohm correlations

Postby Joy Christian » Wed Jul 01, 2015 12:06 am

Schmelzer wrote:
Joy Christian wrote:To see how wrong and naïve the claim of "always -1 correlation" is, you may wish to consult equation (A.9.15) on page 244 of this paper.

Sorry, but I'm unable to make sense of the limiting operator


Equation (A.9.15) describes a limit of a product of two different quaternions, which belong to S^3. And since S^3 remains closed under multiplication, the product is also a unit quaternion, as shown in equations (A.9.16) and (A.9.17). Also worth noting is that quaternionic S^3 is necessarily "flat", with constant but non-vanishing torsion. The limits in these equations simply describe the limits in which the scalar part of the product quaternion reduces to +/-1 while the bivector part reduces to zero, as shown in equations (A.9.17) to (A.9.19). The purpose of this demonstration is to show that the geometry and topology of the 3-sphere is highly non-trivial.

Schmelzer wrote:I would say this is what your formulas (1) and (2) would have us believe. If this is not the case, then your formulas (1) and (2) are simply misleading, and should be replaced by formulas which do not allow such a misinterpretation.

I disagree. The only people who read my formulae (1) and (2) with jaundiced eyes are those who are committed to Bell's by now comprehensively refuted "theorem."
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Re: A new simulation of the EPR-Bohm correlations

Postby Joy Christian » Wed Jul 01, 2015 12:52 am

Jochen wrote:What I mean by a two-boxes instantiation is simply a program such that I could run one copy on computer A, which gets as input the measurement directions of Alice, and another copy on computer B, which gets the directions of Bob, and then take the output data and compute the correlations from that. In this way, you'd ensure that there is no 'hidden nonlocality', i.e. the measurement outcomes of both Alice and Bob would be computed from data available only locally in an unquestionable way.

Hi Jochen,

I have now consulted Fred and minkwe about this. As I thought, it is straightforward to produce the lists {a, A(a)} and {b, B(b)} on two different computers using two copies of this simulation. If you know R, then you can produce the lists yourself, and then calculate the correlation on a third computer, using the coincident counts Cuu, Cdd, Cud, and Cdu, as done in the simulation. Note that there are no "0" outcomes in the simulation by construction, so only Cuu, Cdd, Cud, and Cdu are needed.
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Re: A new simulation of the EPR-Bohm correlations

Postby Schmelzer » Wed Jul 01, 2015 1:15 am

Joy Christian wrote:
Schmelzer wrote:
Joy Christian wrote:To see how wrong and naïve the claim of "always -1 correlation" is, you may wish to consult equation (A.9.15) on page 244 of this paper.

Sorry, but I'm unable to make sense of the limiting operator


Equation (A.9.15) describes a limit of a product of two different quaternions, which belong to S^3. And since S^3 remains closed under multiplication, the product is also a unit quaternion, as shown in equations (A.9.16) and (A.9.17). Also worth noting is that quaternionic S^3 is necessarily "flat", with constant but non-vanishing torsion. The limits in these equations simply describe the limits in which the scalar part of the product quaternion reduces to +/-1 while the bivector part reduces to zero, as shown in equations (A.9.17) to (A.9.19). The purpose of this demonstration is to show that the geometry and topology of the 3-sphere is highly non-trivial.

Nothing of this explains the meaning of your strange limit operation. Underscoring product is not really helpful, the meaning of remains unclear even if it is the limit of a product . I can think about the following interpretations:


, or, what gives the same here but could be different for noncommutative operations:
.


Joy Christian wrote:I disagree. The only people who read my formulae (1) and (2) with jaundiced eyes are those who are committed to Bell's by now comprehensively refuted "theorem."

This is a triviality, we have all understood already that everybody who disagrees with you is not only wrong (which is self-evident) but has also some mental problems, with symptoms like running around with jaundiced eyes.
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Re: A new simulation of the EPR-Bohm correlations

Postby Joy Christian » Wed Jul 01, 2015 1:37 am

The important point is that there are people who agree with me. Some of these people have been participating in this forum, and some who are not participating have approved the calculations in my one-page paper in this publication. Those who remain unconvinced may benefit from studying at least the last appendix of this paper.

Also worth noting is the numerical simulation of the calculations in my one-page paper Fred has linked above: http://challengingbell.blogspot.co.uk/2 ... f-joy.html.
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Re: A new simulation of the EPR-Bohm correlations

Postby Jochen » Wed Jul 01, 2015 5:07 am

Joy Christian wrote:The individual measurement results are not calculated in the Clifford-algebraic representation of the 3-sphere---i.e., the one used in my one-page paper.

OK, so just to be completely clear about that, by you actually do not mean that the measurement outcome of A is +1 for ? But then, I don't see why you calculate the average of this function times that for B and denote that as the correlator . I mean, if I have a function that gives me the outcome of the measurement of A in direction a given the HV-state , and a similar function , then I could see getting the correlator for them via in the limit of large N, but if the functions don't return the outcomes of A and B, then why can you use them to compute the correlator? (And also, where does the normalization factor come from?)

In reply to your next post:
Joy Christian wrote:Hi Jochen,

I have now consulted Fred and minkwe about this. As I thought, it is straightforward to produce the lists {a, A(a)} and {b, B(b)} on two different computers using two copies of this simulation. If you know R, then you can produce the lists yourself, and then calculate the correlation on a third computer, using the coincident counts Cuu, Cdd, Cud, and Cdu, as done in the simulation. Note that there are no "0" outcomes in the simulation by construction, so only Cuu, Cdd, Cud, and Cdu are needed.

Unfortunately, I'm unfamiliar with R, but from a cursory reading of the code, this doesn't seem to quite do what I'm asking. Basically, I would want something where I can choose the measurements---the measurement directions can be hard-coded, but I would want to be able to tell the computer which one to choose. So, basically, the A-computer gets a list, say of bits, where a 0 tells it to measure in direction , and a 1 to measure in , and likewise for the B-computer. The output would then be a list for each side, containing the measurement directions in one column, and the observed outcomes in the other. From this, I would then compute the calculation. I may be wrong, but I don't see an easy way to make the simulation do this...

Also, I'm somewhat perplexed about the role of the 0-outcomes. I mean, it'd be easier to just assume perfect detectors (we're all theoreticians here after all), and just not bother with them, especially if you say (as you seem to) that they don't contribute, no?
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Re: A new simulation of the EPR-Bohm correlations

Postby Joy Christian » Wed Jul 01, 2015 6:24 am

Jochen wrote:
Joy Christian wrote:The individual measurement results are not calculated in the Clifford-algebraic representation of the 3-sphere---i.e., the one used in my one-page paper.

OK, so just to be completely clear about that, by you actually do not mean that the measurement outcome of A is +1 for ? But then, I don't see why you calculate the average of this function times that for B and denote that as the correlator . I mean, if I have a function that gives me the outcome of the measurement of A in direction a given the HV-state , and a similar function , then I could see getting the correlator for them via in the limit of large N, but if the functions don't return the outcomes of A and B, then why can you use them to compute the correlator? (And also, where does the normalization factor come from?)

The answer to your first question is: Yes and No. in the model is the orientation of the 3-sphere, so the answer is: Yes. But the measurement outcomes are not generated as trivially as you have described. What is going on is that the functions are products of two bivectors, a detector bivector and a spin bivector. The detector bivector knows nothing about what orientation the spin bivector has chosen until the detection of the spin. Upon interaction the detector detects the spin, and depending on the orientation gives the value +1 or -1. The randomness is thus entirely contained in the spin, with detector being a constant number. I say number, because in geometric (or Clifford) algebra a bivector is indeed a grade-2 number, and scalars (i.e., grade-0 numbers) and bivectors are treated on equal footing. And since randomness is entirely contained in the spin bivector, one must use the full product moment correlation coefficient to do the calculation correctly. Thus what I am doing in the one-page paper is a theoretical calculation that predicts what would happen if we simply collect all of the actually observed numbers and from both sides ("raw scores") and calculate the average in the usual manner. I think you really should read the last appendix of this paper to understand what is going on. Then you will understand my sentence you have quoted above. It shouldn't take more than ten minutes of your time to go through it.

Jochen wrote:In reply to your next post:
Joy Christian wrote:Hi Jochen,

I have now consulted Fred and minkwe about this. As I thought, it is straightforward to produce the lists {a, A(a)} and {b, B(b)} on two different computers using two copies of this simulation. If you know R, then you can produce the lists yourself, and then calculate the correlation on a third computer, using the coincident counts Cuu, Cdd, Cud, and Cdu, as done in the simulation. Note that there are no "0" outcomes in the simulation by construction, so only Cuu, Cdd, Cud, and Cdu are needed.

Unfortunately, I'm unfamiliar with R, but from a cursory reading of the code, this doesn't seem to quite do what I'm asking. Basically, I would want something where I can choose the measurements---the measurement directions can be hard-coded, but I would want to be able to tell the computer which one to choose. So, basically, the A-computer gets a list, say of bits, where a 0 tells it to measure in direction , and a 1 to measure in , and likewise for the B-computer. The output would then be a list for each side, containing the measurement directions in one column, and the observed outcomes in the other. From this, I would then compute the calculation. I may be wrong, but I don't see an easy way to make the simulation do this...

I don't know how to do this in R. Perhaps someone more knowledgeable may suggest something. But so far no one has suggested that there is anything nonlocal going on in the simulation. As far as I can see, it is manifestly local.

Jochen wrote:Also, I'm somewhat perplexed about the role of the 0-outcomes. I mean, it'd be easier to just assume perfect detectors (we're all theoreticians here after all), and just not bother with them, especially if you say (as you seem to) that they don't contribute, no?

I agree. But someone here has made a big fuss about the 0-outcomes, so I just wanted to stress that none exist, either in the simulation or in the theoretical model.
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Re: A new simulation of the EPR-Bohm correlations

Postby Jochen » Wed Jul 01, 2015 7:19 am

minkwe wrote:
Jochen wrote:Additionally, weak measurements are called this because they weakly couple to individual members of an ensemble, thus minimally disturbing the state, and consequently extracting only a minimum amount of information; it is to rectify this that postselection (the preselection is really just the preparation of a definite state, which we do in any Bell experiment) is necessary. As you can see in Fig. 1 of this paper, it is indeed the case that all measurements are carried out on a single pair.

I'm afraid you are mistaken about weak measurements.

In what sense? In all the discussions of weak measurements I know, it's simply a measuring device weakly coupled to the system to be interrogated. The weak coupling ensures that the system is biased minimally, but does not collapse to an eigenstate of the measurement; consequently, the information obtained about the observable is very small, and will, in a single system, not yield enough information to produce a definite value (if you could do that, then the system would necessarily have collapsed).

I thought I made it clear that neither locality nor non-disturbance is essential. The only essential component is existence of a Joint PD.

OK, so how do you justify the existence of a joint PD? If I am allowed nonlocal signalling, then I can always alter the PD of one part of the system due to measurements done on the other, and no joint PD exists.

In fact, let me give you another very clear example. The Bell inequalities will apply to 3 spin-half entangled particles measured simultaneously by Alice, Bob and Cindy. This should give you a huge hint that non-locality or disturbance or even any physics is completely irrelevant.

If I read you right, then this is wrong: there are Bell inequalities, such as Mermin's inequality, that are violated by measurements on threepartite entangled states; in fact, their degree of violation can even distinguish between different SLOCC-equivalence classes of entanglement. Actually, you can even derive a BI based on the GHZ-argument, which will be violated in experiment.

This argument has also been addressed. There are no predefined values in a stochastic process which is "discovered". Yet the Bell inequalities would apply for any process. A very simple counter example is a random number generator which generates 4 integers . There are no pre-defined values. Yet the Bell inequalities applies to the outcomes because there is a joint PD P(A,B,C,D).

Take three coins, , , and . If you flip the first and second together, they will always agree, giving both H = heads or T = tails with 50% probability. If you flip the second and third together, they will always land oppositely (again with 50% probability). If you flip the second and third together, they will always agree (50 % HH, 50% TT). Clearly, there does not exist a joint PD . Nevertheless, flipping each coin on its own is a perfectly ordinary stochastic process---for which, however, BIs can't be derived.

Now, maybe you'll want to say that such coins don't occur in nature; but it's easy to build a little machine that implements these correlations. True, you can't execute a joint coinflip of all three---but as I already said, this situation is commonplace in nature.

But again, you've ignored my arguments demonstrating that the above is false. Take the exact same state machine and measure repeatedly in sequence a joint series of 4 outcomes (A,B,C,D) by pressing the 4 buttons in sequence one after the other for every iteration.

Take the machine reproducing the coin throws above: the single coint throw marginals are just those of a fair coin, hence, what you get this way is just a sequence of random heads and tails; but this doesn't suffice to pin down the PD---a product distribution would reproduce this just fine, but fail to account for the correlations.

The point is that the measurement can not be repeated. It is impossible to reproduce the complete space-time properties of the tablet and liquid from original measurement. Therefore your "need" is impossible to fulfil and therefore no joint PD.

Well, then you can't find any probabilistic quantities, if the experiment is nonrepeatable.

First, it is clear that "repetition" of the measurement is impossible. Secondly, the assumption that there must be a fixed fact of the tablet which induces diarrhea, is unnecessarily highly restrictive especially given that you weren't told nor are aware of all the possible mechanisms by which the tablets induce diarrhea.

But that's the assumption that defines a HV-theory: there is a fixed fact of the matter which measurement will produce which outcome, derivable from the hidden state.

This is what degrees of freedom can do. Alice and Bob do not have the freedom to test the same tablet more than once. They do not have the freedom to test all tablets at the same time.

What, exactly, do you mean by 'degrees of freedom'? The way you use it here seems at variance with how the term is usually used.


Jochen wrote:Finally, regarding your point of whether the correlators are the same across different trials

Please, could you remind me where I made such a point or asked such a question. You must be misunderstanding something very important if you think I asked such a question. A quote would be appreciated.

Here:
minkwe wrote:- Since you can't measure all the terms simultaneously, you make the additional assumption , that counterfactual averages , should all have the same value as averages each measured on a separate set of particle pairs . And you think this assumption is justified because the values you actually measure are reproducible?

Just because you can measure repeatedly and reproducibly does not mean


Therefore I hope it is now clear why the Bell's inequalities should not apply to EPRB experiments. In other words, "violation" of the Bell inequalities does not tell us anything about "non-locality" or "disturbance". It tells us there is no joint PD of outcomes in experiment. Which shouldn't be surprising, given that (1) we only sampled paired distributions, (2) the paired distributions were measured at different times (3) the particles involved are space-time dynamic.

I sense there's probably not going to be a real meeting of minds between us, so all I can really do is extend the same invitation to you as I offered to Joy: produce a simulation, such that I can locally enter the measurement directions for party A and party B on separate, noncommunicating computers, then get out a list that gives for each measurement direction the measurement's outcome, which I then use to compute the correlations; and if that then manages to violate a Bell inequality, I will rescind and retract everything I've said so far.

One battle at at a time. Once the Bell theorem is dealt with, then we can push ahead to the next battle, GHZ :D. But our tactic will be the same, since the fault-lines are the same. We will look for theoretical considerations which discuss "single qubit", or "single-particle" within the framework of a probabilistic theory, compare the predictions with outcomes of measurements which they claim were done on a "single particle" or "single qubit". It turns out, when you look closely that combination is a paradox factory.

Well, in the GHZ argument, you really only need to think about the measurements that could be performed on a single state, and observe that no HV-value assignment can be consistent with all the observations as predicted by QM.
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Re: A new simulation of the EPR-Bohm correlations

Postby Jochen » Wed Jul 01, 2015 7:35 am

Ben6993 wrote:I have skim read the paper twice. As I read it, the idea is to generate a host of cloned particles. So the paired partners of the normal Bell test are replaced by a large, single group of particles with identical (as identical as possible but presumably not exactly so ... quite weakly so maybe) spin, orientation and presumably other properties. (Assuming that has been possible ... )

Yes, but this is the same situation as in ordinary Bell tests: there, too, you generate a large number of particles (say, entangled in the singlet state), on which you then perform measurements. The reason is simply that in order to estimate the correlators in a BI, you need large enough statistics. Also, a high-quality source yields systems in a state nigh-indistinguishable from one another.

A sequence of measurements on the group is made, one measurement per particle.

No, all observables are measured on the same particle, albeit weakly. That is, of a pair of particles, one is deliverd to Alice, the other to Bob, and both carry out all their masurements successively on their particle. With strong measurements, the first would 'collapse' the state, and hence, the second would not yield any information about the original state; but in weak measurements, there is only a small disturbance to the state, and thus, information can still be recovered using the subsequent measurement.

If this is with photons then the sampling of photons is without replacement as the photon is deleted from the group on measurement. If this is with electrons then after a measurement the electron changes spin value but continues in the group and could be measured again.

Photons can be detected nondestructively; and as mentioned above, the electron does not jump into an eigenstate of the spin measurement in the weak formalism.

The use of a final strong measurement seems to imply that what I have written above is incorrect and that an individual particle is followed and labelled across its interactions. And how are the weak results for a single particle checked against the final strong result. And how does the strong measurement at the end differ from the weak measurements en route?

TBH, I haven't really grasped the role of the strong measurement in the end myself... And as I said, I'm not ready to vouch for the quality of the paper.
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Re: A new simulation of the EPR-Bohm correlations

Postby Jochen » Wed Jul 01, 2015 8:01 am

Joy Christian wrote:The answer to your first question is: Yes and No. in the model is the orientation of the 3-sphere, so the answer is: Yes. But the measurement outcomes are not generated as trivially as you have described. What is going on is that the functions are products of two bivectors, a detector bivector and a spin bivector. The detector bivector knows nothing about what orientation the spin bivector has chosen until the detection of the spin. Upon interaction the detector detects the spin, and depending on the orientation gives the value +1 or -1.

At the risk of appearing dense, I don't see how this (or the appendix of the other paper) really answers my question. How does relate to what Alice writes down in her lab book?

I don't know how to do this in R. Perhaps someone more knowledgeable may suggest something. But so far no one has suggested that there is anything nonlocal going on in the simulation. As far as I can see, it is manifestly local.

Well, for one thing, the number of events observed seems to depend on both the measurement directions of A and B, so this is not a quantity that could be calculated in this way in my two-boxes version, since box A would not know about the measurement direction of B, and vice versa. And frankly, I'm not sure why this number is needed at all: if we assume perfect detectors, we can simply assume that each measurement yields an outcome, and thus, that the number of events is equal to the number of measurements.
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Re: A new simulation of the EPR-Bohm correlations

Postby Joy Christian » Wed Jul 01, 2015 9:07 am

Jochen wrote:
Joy Christian wrote:The answer to your first question is: Yes and No. in the model is the orientation of the 3-sphere, so the answer is: Yes. But the measurement outcomes are not generated as trivially as you have described. What is going on is that the functions are products of two bivectors, a detector bivector and a spin bivector. The detector bivector knows nothing about what orientation the spin bivector has chosen until the detection of the spin. Upon interaction the detector detects the spin, and depending on the orientation gives the value +1 or -1.

At the risk of appearing dense, I don't see how this (or the appendix of the other paper) really answers my question. How does relate to what Alice writes down in her lab book?

Alice writes down and Bob independently writes down , but that does not mean that always as some have incorrectly suggested, not the least because and are two independent random variables. Therefore it is incorrect to conclude that always. Equation (B10) of the appendix of the paper I suggested is but one of the many proofs of this elementary fact I have provided.

Jochen wrote:
I don't know how to do this in R. Perhaps someone more knowledgeable may suggest something. But so far no one has suggested that there is anything nonlocal going on in the simulation. As far as I can see, it is manifestly local.

Well, for one thing, the number of events observed seems to depend on both the measurement directions of A and B, so this is not a quantity that could be calculated in this way in my two-boxes version, since box A would not know about the measurement direction of B, and vice versa. And frankly, I'm not sure why this number is needed at all: if we assume perfect detectors, we can simply assume that each measurement yields an outcome, and thus, that the number of events is equal to the number of measurements.

Yes, the number of events observed is not needed in the calculation. It has been included as a response to some unfounded criticisms. Moreover, despite appearances the number does not depend on the measurement directions per se, but on the metric {g, t} of the 3-sphere. The number must respect the geometry of the 3-sphere.
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Re: A new simulation of the EPR-Bohm correlations

Postby minkwe » Wed Jul 01, 2015 10:35 am

Jochen wrote:In all the discussions of weak measurements I know, it's simply a measuring device weakly coupled to the system to be interrogated.

I know, that is why I ask you to provide an actual experiment in which weak measurements were done and we can discuss. It is very easy to speak nonsense "theoretically".

Jochen wrote:OK, so how do you justify the existence of a joint PD? If I am allowed nonlocal signalling, then I can always alter the PD of one part of the system due to measurements done on the other, and no joint PD exists.

If you review my response carefully, you will see examples of how to do it. For example, the your state-machine with non-local disturbance, in which the measurements are always done in sequence A,B,C,D, would produce a joint PD. So long as the 4 numbers are jointly measured, it matters not one iota what physical mechanism is generating them, you will get a joint PD of outcomes and Bell's inequalities will apply.

Jochen wrote:
In fact, let me give you another very clear example. The Bell inequalities will apply to 3 spin-half entangled particles measured simultaneously by Alice, Bob and Cindy. This should give you a huge hint that non-locality or disturbance or even any physics is completely irrelevant.

If I read you right, then this is wrong: there are Bell inequalities, such as Mermin's inequality, that are violated by measurements on three partite entangled states

Of course if the original bell inequalities would have been violated by 3 spin-half particles, the goal-posts would not have needed to be shifted. The original Bell inequalities involve 3 simultaneous measurements at settings (a,b,c). That can be done for 3 spin-half particles directly, and the original Bell's inequalities will apply, shouldn't they? And if they are satisfied, as they must be in this case, are you suggesting your "disturbance" or "non-locality" decides to manifest itself only when two particles are being measured at the time, but decides to stays silent when a third is being measured? Otherwise, why would you expect a joint PD (A,B,C) to be present in this case, but absent in the case of only 2 particles, if you refuse to acknowledge that it is the joint measurement that determines whether you have a joint PD, so that when you measure the 3 simultaneously, you get a joint PD P(A,B,C), and when you measure only 2 you do not get a joint PD P(A,B,C). It does not matter what physical mechanism is generating the outcomes.

Jochen wrote:Take three coins, , , and . If you flip the first and second together, they will always agree, giving both H = heads or T = tails with 50% probability. If you flip the second and third together, they will always land oppositely (again with 50% probability). If you flip the second and third together, they will always agree (50 % HH, 50% TT). Clearly, there does not exist a joint PD . Nevertheless, flipping each coin on its own is a perfectly ordinary stochastic process---for which, however, BIs can't be derived.

But your contrived example does not translate into a general truth. Besides your coins lack many crucial relevant components which is the paired correlation between individual pairs of coins, and the impossibility of re-tossing a specific coin more than once. The point was, that contrary to your claim that pre-determination of values is required, a random number generator which generates the 4 numbers (A,B,C,D) without any pre-determination, must obey the CHSH inequality because the outcomes represent a joint PD P(A,B,C,D). Therefore pre-determination is not required to obtain a joint PD. Do you agree or disagree?

Jochen wrote:Take the machine reproducing the coin throws above: the single coint throw marginals are just those of a fair coin, hence, what you get this way is just a sequence of random heads and tails; but this doesn't suffice to pin down the PD---a product distribution would reproduce this just fine, but fail to account for the correlations.

See above why your coin example misses the mark, and the fact that you use "fair" coins makes the example even worse. If you want, to bring it up to par, you should modify it such 1) that all three coins produced by the machine each time will produce the exact same result when tossed together, and 2) The coins are destroyed by the tossing process as soon as the results are read, and 3) that each triple of the coins contains a specific biasing mechanism not necessarily present in other coins. Once you make those modifications and are convinced that your argument can still proceed (which I don't think it can), then present the new argument and I will address it. You have a bigger burden than me. You are trying to argue that it is ALWAYS possible to reconstruct a joint PD for ALL local HV theories. Using specific contrived examples do not serve your purpose. I'm arguing that in some cases where you have a local HV theory, it is not always possible to reconstruct a joint PD from measured pairs. So I can use simple contrived examples to make my point effectively, you cannot.

Jochen wrote:
This is what degrees of freedom can do. Alice and Bob do not have the freedom to test the same tablet more than once. They do not have the freedom to test all tablets at the same time.

What, exactly, do you mean by 'degrees of freedom'? The way you use it here seems at variance with how the term is usually used.

You do not say what you mean by "at variance" so I don't know how to answer a claim that is not substantiated. I use degrees of freedom it in the same way it is usually used. So please explain what you mean by "at variance".

Jochen wrote:
Jochen wrote:Finally, regarding your point of whether the correlators are the same across different trials


minkwe wrote:- Since you can't measure all the terms simultaneously, you make the additional assumption , that counterfactual averages , should all have the same value as averages each measured on a separate set of particle pairs . And you think this assumption is justified because the values you actually measure are reproducible?

Just because you can measure repeatedly and reproducibly does not mean


So you misunderstood me. The fact that averages actually measured on separate sets of particles are always reproducible does not and cannot reasonably be taken to mean that those averages are the same ones represented by the terms in the inequality which were not measured on the same set of particles. It is a fact that the measured averages are reproducible. But that has nothing to do with the fact that the actually measured correlations are not the same as the unmeasured counterfactual ones from the same set of particles. Reproducibility of measured averages does not necessarily translate to equality between measured outcomes and counterfactual outcomes, even for local hidden variable theories. In fact, I have simulations which prove this point (see below).

In the expression , for the particle pair , three of the paired terms are counterfactual and one is actual. Once a measurement has been made at ,
then the rest of the results are fixed. This is what crucial factorization means! The terms are not independent from each other, there are 4 independent values which are free to vary in that expression, and those 4 values are cyclically shared by the paired terms such that they are not independent. Once three of the paired terms are given, the fourth one is determined automatically. That is the origin of the relationship . The problem is that you are trying to take away the feature that gives you that relationship while at the same time claiming that the relationship continues to hold. For example, the expression where each term is an actual outcome measured on a different particle pair, completely lacks that the original relationship, because there are 8 independent values which are free to vary. Knowing three of those paired terms, tells you absolutely nothing about the fourth one. As you can see, the factorization is no longer possible, and the relationship here should be . You haven't presented a convincing argument to support your claim why we should have rather than . All you argued is that since and are reproducible, therefore . That argument does not make sense. You have to start from , and make all the necessary assumptions you need to make to derive . Once you do that, you will realize that it is impossible, unless you also claim that for every , there must exist a function which would permit you to to rearrange the list of outcomes into such that, ie, the number of +1's and -1's are the same, and the patterns are the same. This is the only condition under which is true. But as I have explained in my previous post, this is impossible. The cyclical nature of the terms in the inequality precludes the general existence of such functions. You did not address that argument at all.

Jochen wrote:I sense there's probably not going to be a real meeting of minds between us, so all I can really do is extend the same invitation to you as I offered to Joy: produce a simulation, such that I can locally enter the measurement directions for party A and party B on separate, noncommunicating computers, then get out a list that gives for each measurement direction the measurement's outcome, which I then use to compute the correlations; and if that then manages to violate a Bell inequality, I will rescind and retract everything I've said so far.

I already have written two local realistic simulations of EPRB experiments, which reproduce the QM correlations without any disturbance, and without non-locality. You can find them https://github.com/minkwe/epr-simple/, and https://github.com/minkwe/epr-clocked. But you are not going to understand what is going on there, if you do not understand my arguments. In fact, epr-clocked does exactly what you asked on separate computers. I have written my own analysis program to analyze the results to show you that it closely reproduces the QM results. But actually I would prefer if you take the two output files from my simulation programs, and do your own analysis. It will be very educational as it will reveal quite a few hidden assumptions, even in the phrasing of your request.

The whole point of my simulations and all my arguments here is the following:
1) There is only one assumption required to derive Bell's inequalities (and the CHSH). ie, the existence of a joint probability distribution of outcomes P(A,B,C) for Bell's original, or P(A,B,C,D) for the CHSH. Nothing else. Therefore, the inequalities do not apply to any experiment in which such a joint probability distribution of outcomes does not exist, such as the EPRB experiment, or their simulations such as "epr-simple" or "epr-clocked".
2) The absence of a joint PD, does not necessarily imply non-locality or disturbance, and can easiliy be obtained when sampling in pairs rather than quartets (or triplets, as in the case of Bell's original). This is what the simulations achieve, just like for the experiments and QM, where measurement can only be done in pairs for 2 spin-half particles.
3) Therefore, there is no conflict between QM and local HV theories. Rather, there is a conflict between the assumption of a joint PD P(A,B,C,D) and experiments in which only pairs are measured. It is the assumption that the joint PD can be reconstructed from the separate paired measurements that fails. The simulations show counter-examples for which it is not possible to reconstruct the joint PD from paired measurements. Therefore it is wrong to assume that local HV theories must allow us to reconstruct the joint PD from separate measurements.
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Re: A new simulation of the EPR-Bohm correlations

Postby Jochen » Wed Jul 01, 2015 11:13 am

Joy Christian wrote:Alice writes down and Bob independently writes down , but that does not mean that always as some have incorrectly suggested, not the least because and are two independent random variables.

Well, but if Alice writes down +1 whenever , then I don't see how anything but -1 for the correlator can be reasonable. And if they're instead independent random variables, then the correlations factorize, and you can't violate a BI, so I'm afraid I'm still confused...
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Re: A new simulation of the EPR-Bohm correlations

Postby Joy Christian » Wed Jul 01, 2015 11:40 am

Jochen wrote:
Joy Christian wrote:Alice writes down and Bob independently writes down , but that does not mean that always as some have incorrectly suggested, not the least because and are two independent random variables.

Well, but if Alice writes down +1 whenever , and Bob writes down -1 whenever , then I don't see how anything but -1 for the correlator can be reasonable. And if they're instead independent random variables, then the correlations factorize, and you can't violate a BI, so I'm afraid I'm still confused...

In that case let me suggest a toy example. Ideally I would like you to appreciate the non-trivial geometry and topology of the 3-sphere itself to understand what I am saying. But the next best thing is this toy example in the first appendix of this paper: http://arxiv.org/pdf/1201.0775.pdf. Please read the entire appendix if you can, but if you are impatient then just have a look at eqs. (1.57) to (1.59) on pages 22 and 23. Also, please understand that the toy example can only illustrate a point. It should not be taken too seriously. I am not asking you to believe that Alice and Bob are running around a Mobius strip every time they are performing an experiment.
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Re: A new simulation of the EPR-Bohm correlations

Postby Schmelzer » Wed Jul 01, 2015 12:24 pm

FrediFizzx wrote:Well, for the 3-sphere model you have to do a geometric product to get the right results. This is how it is done for GAViewer.

quite complicate. I could do it easier, simply "right result = -ab".

With a counterexample for Bell's theorem this has anyway nothing to do.
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Re: A new simulation of the EPR-Bohm correlations

Postby Schmelzer » Wed Jul 01, 2015 12:50 pm

Schmelzer wrote:
Joy Christian wrote:
Schmelzer wrote:Sorry, but I'm unable to make sense of the limiting operator

Equation (A.9.15) describes a limit of a product of two different quaternions, which belong to S^3. ...

Nothing of this explains the meaning of your strange limit operation. Underscoring product is not really helpful, the meaning of remains unclear even if it is the limit of a product . I can think about the following interpretations:


, or, what gives the same here but could be different for noncommutative operations:
.


So if is remains unanswered. Or was this supposed to be an answer:
Joy Christian wrote:The important point is that there are people who agree with me.

Or this:
Joy Christian wrote:The purpose of this demonstration is to show that the geometry and topology of the 3-sphere is highly non-trivial.

???
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Re: A new simulation of the EPR-Bohm correlations

Postby FrediFizzx » Wed Jul 01, 2015 7:50 pm

Schmelzer wrote:
FrediFizzx wrote:Well, for the 3-sphere model you have to do a geometric product to get the right results. This is how it is done for GAViewer.

quite complicate. I could do it easier, simply "right result = -ab".

With a counterexample for Bell's theorem this has anyway nothing to do.

It is the same result as QM for EPRB via a classical local realistic model. Sorry that you can't see that. And it is actually not very complicated at all. What don't you understand? Does QM use the +/- 1 outcomes to get its theoretical prediction of -a.b for EPRB? No, it doesn't. Joy's classical local realistic model is simply an explanation for why we get the correlations that QM produces. Mystery solved. The only question remaining is... does it work for a macroscopic singlet scenario? We definitely need a proper macroscopic test to see if it does. If it does, then Bell's theorem for sure will fall by the wayside like other no-go theorems. But the model definitely works for a QM explanation. That alone kills Bell's theorem off.
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Re: A new simulation of the EPR-Bohm correlations

Postby Joy Christian » Wed Jul 01, 2015 9:37 pm

FrediFizzx wrote:
Schmelzer wrote:
FrediFizzx wrote:Well, for the 3-sphere model you have to do a geometric product to get the right results. This is how it is done for GAViewer.

quite complicate. I could do it easier, simply "right result = -ab".

With a counterexample for Bell's theorem this has anyway nothing to do.

It is the same result as QM for EPRB via a classical local realistic model. Sorry that you can't see that. And it is actually not very complicated at all. What don't you understand?

There are none so blind as those who will not see.

PS: The incontrovertible evidence for E(a, b) = -a.b and detailed explanation are presented in Eq. (B10) and the rest of this paper: http://arxiv.org/abs/1501.03393.
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