Recommendations for EPR-type simulations

[gill1109]

Do you want to bet on this, too?

I won't want to deprive your family of your hard earned money just to prove a point. You claim something is impossible, and I do it. That proves you were wrong and you learn from it. No need for bets.

Now what about the abstract simulation I suggested earlier. Are you going to do it or not. It is just a slight modification of your R-innovations.

No you still haven't done what I said was impossible. Perhaps you didn't read carefully enough, exactly what it is you have to do.

By the way I earn cash from time to time by doing statistical consulations for lawyers. I put the money into science (I have a day job to feed my family). So you needed worry about my wife and kids going hungry.

[minkwe]

I'm awaiting your response to my abstract thought experiment I asked yesterday. Here it is again in case you missed it:

The question we are trying to answer is: "What happens if instead of substituting actual results from a different set of particles, we use counterfactual results from the same set of particles as was intended in the original CHSH?"

We will proceed as follows:
* Generate pairs of particles as done previously.
* Instead of measuring at just "alice" and "bob", we will add two more "ghost" stations called "cindy" and "dave". We will send an exact copy of Alice's particle to Cindy and an exact copy of Bob's particle to Dave. This way we will have counterfactual results for Alice's particle at Cindy, and the same for Bob at Dave.
* We will do the data analysis in two steps. In the first step, we will ignore Cindy and Dave and simply use Alice and Bob as we have been doing until now. This scenario is equivalent to substituting actual results on different sets of particles for counterfactual results on a single set.
* The next step of data analysis will involve using all 4 outcomes for calculating the correlations. So that we use Alice and Bob to calculate C(a,b), Cindy and Bob to calculate C(a',b), Alice and Dave to calculate C(a,b') and Cindy and Dave to calculate C(a',b'). This step is equivalent to using counter-factual correlations just as is intended in the CHSH.
* We will then compare the results between the two scenarios and be able to answer our main question.

You can see my own results of this abstract simulation experiment in my previous post. Note this endeavour is quite separate from your claim that it is impossible to simulate a clocked experiment ....

[gill1109]

I don't have anything to say about this particular thought experiment of yours, Minkwe. (So far, I don't think the experiment interesting. Also, I don't know where you are going. I don't know what you are trying to prove. I'm waiting to hear a punch-line or a question.)

I *am* interested in a slightly different thought experiment. It runs like this:

There are only Alice and Bob, no Cindy and Dave, but instead we are going to clone Alice's computer and Bob's computer. We're going to compare the normal situation in which they each have one computer, and an artificial situation in which they each have two.

In my experiment, like in a real CHSH experiment, Alice and Bob each choose settings at random. Alice chooses in each run (each pair of particles) between a and a', Bob between b and b'. I suppose they do this with fair coin tosses. All this is exactly the same in both situations. In fact, they do their coin tosses at their homes in advance (in secret) and use the same coin tosses whether, when they come to work the next morning, they find one computer or two on their desk.

So in the "normal situation" (= the original situation = no clones ...) Alice has *one* computer, and per run, chooses a or a' and gets one *outcome*. Similarly for Bob. In the "situation with the cloned computers" I let Alice's computer 1 always use setting a, and Alice's computer 2 always use setting a'. She just uses her coin toss, per run, to decide which setting to take "for real" and hence which outcome to write down in the laboratory log-book. However, she did get to see both, and could just as well have written down both.

I'm assuming that the computer program is not using the memory loophole. It doesn't need to take account of past settings and outcomes when doing the work for the n'th run. I'm assuming the usual kind of pseudo random number generators, a fixed number of new random numbers per run, so that the intial state of the pseudo RNG at the start of the n'th run doesn't depend on what happened in earlier runs).

I state that there is no difference between the basic situation and the situation with the cloned computers. For the same coin tosses, and the same initial random seeds of all the computers concerned, the final data and the final value of CHSH is precisely the same.

Note: I do not claim that it is impossible to simulate a clocked experiment.

I do claim that if you simulate a clocked experiment in a local realistic way, where each run always results in a binary outcome, one on each side of the experiment, and you do a lot of runs, while the settings are being chosen at random by fair coin tosses, then the chance is only very very small that the final CHSH result will be far above 2. I have proven theorems which state just how small the chance is, of any given deviation above 2. The bigger the deviation, the smaller the chance. The bigger N (the number of runs), the smaller the chance.

[minkwe]

I don't have anything to say about this particular thought experiment of yours, Minkwe. (So far, I don't think the experiment interesting. Also, I don't know where you are going. I don't know what you are trying to prove. I'm waiting to hear a punch-line or a question.)

Interesting. You are either not reading what I'm writing or you know very well what I'm talking about but for some reason don't want to engage. This despite the fact that you wrote a whole paper about a similar issue, in response to Accardi. Now for the umpteenth time I will state the claim which the above abstract thought experiment proves.

I claim that:

1) The CHSH can not be violated by anything if you are doing a correct mathematical calculation. Not even QM can violate the CHSH. The reason is because the terms in the CHSH represent a relationship between joint properties which can not be simultaneously measured (factual & counterfactual).

2) The claimed QM violation of the standard CHSH is not a valid calculation as far as QM is concerned since the full expression implies combining separate observations of non-commuting observables to obtain the joint measurement result. This is not allowed in QM. Classically, it is equivalent to the nonsensical calculation of performing algebra on functions with different domains.

3) Bell's inequalities (and the CHSH) are valid mathematical constructs. Unfortunately, they have little if any relationship to experiments because they use terms in the derivation which are unmeasurable (counterfactual outcomes).

4) The error which makes *Bell's theorem* false is the mistaken assumption that we can substitute measurement outcomes from a different set of particles for counterfactual outcomes on a single set of particles. It is this assumption that is false. In other words, Bell's inequalities (and the CHSH) are violated because we of the error of substituting actual outcomes from a different set of particles for counterfactual outcomes of a single set of particles.

The abstract thought experiment provides clear proof that for a locally realistic simulation, substituting measurement outcomes from a different set of particles for counterfactual outcomes on a single set of particles leads to violation even though using the counterfactual outcomes directly does not.

It also proves that you were wrong to assume that properties from disjoint samples can be used to make meaningful estimates about joint properties in a single sample. No doubt you do not want to do the simple modification (probably you have but don't want to share the results). Nor have you presented any counter arguments to any of the above points. In fact you have not even stated if you agree or disagree with any of them. You've simply ignored them. But they are all devastating to the point of view you are trying to propagate, so I would have expected that you would be interested in it.

[minkwe]

I'm assuming that the computer program is not using the memory loophole. It doesn't need to take account of past settings and outcomes when doing the work for the n'th run.

Just another "loophole" fantasy. Your statement above is equivalent to the assumption that: "Nature is not allowed to have detectors whose state at time t, influences their state at time t+1". Do you have any experimental evidence to back such a ridiculous assumption?

[gill1109]

I'm assuming that the computer program is not using the memory loophole. It doesn't need to take account of past settings and outcomes when doing the work for the n'th run.

Just another "loophole" fantasy. Your statement above is equivalent to the assumption that: "Nature is not allowed to have detectors whose state at time t, influences their state at time t+1". Do you have any experimental evidence to back such a ridiculous assumption?

Dear Minkwe

Please do not be so rude. Think before you write.

I am talking about a thought experiment pertaining to a particular class of simulation models. Your very own simulation model falls in this category. You are telling me that you think that the stuff you wrote in Python is totally ridiculous? That's funny.

Richard

[minkwe]

I'm assuming that the computer program is not using the memory loophole. It doesn't need to take account of past settings and outcomes when doing the work for the n'th run.

Just another "loophole" fantasy. Your statement above is equivalent to the assumption that: "Nature is not allowed to have detectors whose state at time t, influences their state at time t+1". Do you have any experimental evidence to back such a ridiculous assumption?

Dear Minkwe

Please do not be so rude. Think before you write.

I am talking about a thought experiment pertaining to a particular class of simulation models. Your very own simulation model falls in this category. You are telling me that you think that the stuff you wrote in Python is totally ridiculous? That's funny.

Richard

There is nothing rude in my post. You tell me, does it make any sense whatsoever to assume that "Nature is not allowed to have detectors whose state at time t, influences their state at time t+1". ???

My simulation makes no such assumption. I do not use such time influences in my simulation. That does not mean anybody else can not write one that uses it. You were stating a requirement that should apply to all simulations, which means you were making a statement about the way nature is not allowed to behave. I'm simply stating to you that it makes no sense.

BTW, forceful irrefutable arguments by your opponents are not personal attacks against you. Rather they are fatal attacks against your point of view. Sometimes it can be difficult to distinguish the two because they may feel the same, especially if you hold our points of view very personally.

[minkwe]

but the CHSH inequality is intended to be applied to four correlations computed on four different sets of particles.

This is blatantly false! If you start from 4 different sets of particles, you will not obtain the CHSH inequality. You will obtain 4 on the RHS. The CHSH can not be derived starting from 4 different sets of particles.

[FrediFizzx]

Yes, that is right. CHSH is for angle settings of the polarizers. a, a', b, b'. So two pairs of particles not 4 "sets" which I think would mean 4 pairs.

[minkwe]

The proof can be found in this paper by Accardi http://arxiv.org/pdf/quant-ph/0007005v2.pdf

Consider a single pair of particles. Assume that the pair of particles have outcomes at 4 angles a, b, a', b' and that those outcomes are definite even if we do not measure them. And those outcomes can only be one of (+1, -1). Then it follows that
ab + ab′ + a′b′ − a′b ≤ 2

We can verify by factorization:
a(b + b′) + a′(b′ − b) ≤ 2
As concerns the values (b′, b). There are 4 possibilities. We may have (+1, -1), (-1, +1), (-1, -1) or (+1, +1). For the first two cases, the first of the terms (b + b′), (b′ − b) will be 0 and the second will be 2 or -2. For the other two cases, the first of the terms (b + b′), (b′ − b) will be 2 or -2 and the second will be 0. Which means that the maximum or minimum of the expression will be determined by 2a' XOR -2a. However, a and a' can only have values (+1, -1) which proves that the expression ab + ab′ + a′b′ − a′b ≤ 2 as a valid inequality for any four values (a, b, a', b') from a single particle pair. This inequality can be extended from the individual cases to averages over multiple particles because the extrema of each term will not be affected by averaging over multiple sets of values with the same extrema, on the condition that all averages of paired-product terms are calculated from the exact same set of particles.

If different sets of particles are used to calculate averages, it is equivalent to using a different particle pair to calculate each paired product for the individual case. For this we would have a situation similar to

a1b1 + a2b2′ + a3′b3′ − a4′b4

Where the numbers represent the particle pair used. In this case we now have 8 different variables each that can have a value of (+1, -1). Let us verify what the upper bound is for this expression.

Each term, being independent from any other term is free to have it's own upper and lower bound. Since the values are each +1 and -1, those will be the upper and lower bound for each paired product. We will have a maximum of 4 if a1b1 = 1, a2b2' = 1, a3b3' = 1 and a4b4' = -1. This violates the original expression for a single set, and proves that the correct inequality is

a1b1 + a2b2′ + a3′b3′ − a4′b4 ≤ 4

This can be extended to averages similarly to the previous case.
Clearly the former expression and not this one is the CHSH. Clearly, the correct upper bound for using 4 different sets of particles for measuring the individual terms is 4 not 2.

Therefore Richard Gill is wrong. The reason for the violation as I have claimed already is:

The error which makes *Bell's theorem* false is the mistaken assumption that we can substitute measurement outcomes from a different set of particles for counterfactual outcomes on a single set of particles. It is this assumption that is false. In other words, Bell's inequalities (and the CHSH) are violated because of the error of substituting actual outcomes from a different set of particles for counterfactual outcomes of a single set of particles. (aka, using 4 different sets of particles when the inequality asks for just one)

The abstract thought experiment provides clear proof that for a locally realistic simulation, using 4 different sets of particles for counterfactual outcomes (as is done in EPR experiments) violates the inequality even though using the counterfactual outcomes directly (a single set of particles, as was assumed in the derivation of the CHSH) does not, using exactly the same simulation, not even a repeat.

Therefore the assumption that we can substitute measurement outcomes from a different set of particles for counterfactual outcomes on a single set of particles is False! And the claim that the CHSH is based on 4 different sets of particles is false! QED.

[gill1109]

The deterministic upper bound is 4. However when the N setting pairs which are actually chosen to be measured are indendently sampled with equal probability from the four possibilities a b; a b'; a' b; a' b' then on average, CHSH does not exceed 4.

[minkwe]

The deterministic upper bound is 4. However when the N setting pairs which are actually chosen to be measured are indendently sampled with equal probability from the four possibilities a b; a b'; a' b; a' b' then on average, CHSH does not exceed 4.

For 4 separate sets of particles, each of the averages <a1b1>, <a2b2'>, <a3'b3>, <a4'b4'> are independent from each other. Each of those terms has an upper bound of +1 and a lower bound of -1. Of course in any specific set, the averages can have any value between those two extremes but we are only interested in the extremes for deriving the inequality. Obviously then <a1b1> + <a2b2'> + <a3'b3> - <a4'b4'> must have an upper bound not less than 4, IF we have 4 different independent (aka disjoint) sets of particles. It does not matter how randomly or non-randomly you sample the 4 sets, so long as the 4 terms above are independent, the upper bound is clearly 4 not less, not more.

The only way the upper bound of expression the <a1b1> + <a2b2'> + <a3'b3> - <a4'b4'> measured from 4 sets of particles can be less than 4 is if we introduce dependencies between the sets of particles. To see this, notice that when the first three terms are each at their maximum of +1, to have an upper bound less than 4, the last term must not be at it's minimum of -1. If the last term is at -1, then the only way to have the upper bound less than 4 is by forcing at least one of the other 3 terms to not be at their maximum of +1. This way we have introduced a dependency between the separate sets of particles which should be independent, so that values in one set of particles now impose conditions on a separate set of particles. It is also clear that it is impossible for this expression to exceed 4 no matter how you sample the individual values, that is what is meant by "upper bound". This simple proof demonstrates that there must be a serious error in any proof claiming to demonstrate an upper bound of less than 4 for independent sets of particles (like those measured in EPR experiments). The two are mutually contradictory.

I emphasize "upper bound" many times to make it very clear that the averages can be any value between the extremes but can not exceed the extremes in either direction. This is why I have argued that the results from experiments and QM are being compared with the wrong inequality. The correct inequality should be <a1b1> + <a2b2'> + <a3'b3> - <a4'b4'> <= 4 (which is not the CHSH). I believe my proof above combined with the though experiment using my simulation I presented earlier provides more support for the argument that Bell's theorem is wrong.

[minkwe]

However when the N setting pairs which are actually chosen to be measured are indendently sampled with equal probability from the four possibilities a b; a b'; a' b; a' b' then ....

Although not really relevant for the argument in my previous post, I thought I should address one other point, a specific outcome of +1 or -1 is a result of, the particle hidden variables (say λ), the instrument hidden variables (say γ), the freely chosen setting α = (a b; a b'; a' b; a' b'). Therefore we can say each outcome is a function of three variables

f(α,λ,γ)

Of those, only α are known and controllable by experimentalists. Therefore only α can be truly randomly sampled (see .http://en.wikipedia.org/wiki/Bertrand_p ... robability) for why it is not possible to randomly sample a "hidden variable"). Therefore, although we may randomly sample, the angles α, it does not follow that we have randomly sampled the outcomes of the function f(α,λ,γ).

[gill1109]

I agree. Alice and Bob can randomly sample settings, or set them fixed to desired pre-set values. e.g. alpha = 0 degrees, beta = 30 degrees. The hidden variables in the source and in the detector can't be controlled by Alice and Bob. Nature samples them from Nature's probability distribution.

[Mikko]

The recommendations in the initial message still look good without any need of revision. However, different purposes impose different requirements that in some cases may conflict with my recommendations. In particular, use of files restricts the number of particle pairs. In addition, when the intent is to simulate a particular experiment, the most important consderation is to reproduce the experiment as accurately as possible; and, to a lesser extent, when simulating experiments of a particular type.

My intent was to make obvious that the simulated model is local and realistic (in some naive sense) and to prevent secret use of (at least known) loopholes, while avoiding other restrictions. So far my attempt looks reasonably good.

[gill1109]

The recommendations in the initial message still look good without any need of revision. However, different purposes impose different requirements that in some cases may conflict with my recommendations. In particular, use of files restricts the number of particle pairs. In addition, when the intent is to simulate a particular experiment, the most important consderation is to reproduce the experiment as accurately as possible; and, to a lesser extent, when simulating experiments of a particular type.

My intent was to make obvious that the simulated model is local and realistic (in some naive sense) and to prevent secret use of (at least known) loopholes, while avoiding other restrictions. So far my attempt looks reasonably good.

Indeed. A very nice codification of sensible recommendations.

[gill1109]

There is another way to ensure compliance of computer programs with locality, freedom, etc. Let's focus on what I call clocked experiments (synchronized; pulsed; discrete time; event-ready detectors; ...).

There is just one program. It simulates the source, two particles, and two detectors. We initialize it and save the initial state (the seed) of the pseudo RNG so that it can be reinitialized, and given the same inputs, would produce identical outputs.

We give it a setting chosen by Alice and a default ("empty") setting from Bob, meaning, Alice measures her particle, Bob does nothing. Now we reset and rerun, with same pseudo RNG seed, but with the roles reversed. Now we have obtained one outcome in each wing of the experiment, for just one pair of particles, one setting of Alice, and one setting of Bob.

Locality is enforced, not by the rules of separation of three programs, but by the procedure whereby we "interrogate" just one program!

We can now continue and get a second pair of outcomes for a second pair of settings, in the same way.

A continuous time experiment can be treated in the same way by dividing time into, say, microseconds. Alice and Bob supply the settings for one microsecond. Two runs of one program generate Alice's outcomes and Bob's outcomes, separately.