Is action at a distance possible as envisaged by the EPR Paradox.

[JesseM]

So then your answer is that the left hand side of Bell's equation (2) is conditional with respect to (a,b) but marginal with respect to λ. And that outcome dependence between A and B exists when conditioned only on (a,b) but does not exist when conditioned on λ.

Yes.

So then the expression P(AB|a,b) will accurately reflect what the probability Bell is calculating in equation (2) on the LHS? Yes or no.

Yes.

And according to the chain rule of probability theory, the following expression is also true according to Bell's equation (2).

P(AB|a,b) = P(A|a,b)P(A|a,b,B)

Yes or no.

No, but if you meant to write P(AB|a,b) = P(B|a,b)P(A|a,b,B) then yes. This would actually be derived from the chain rule plus a few substitutions...the chain rule of probability would tell us this:

P(A,B,a,b)=P(A|B,a,b)P(B|a,b)P(a|b)P(b)

And from the definition of conditional probability we know P(a|b)*P(b)=P(a,b), and P(A,B,a,b)=P(AB|a,b)*P(a,b), so substitute these in the above equation, divide both sides by P(a,b) and we get P(AB|a,b)=P(A|B,a,b)P(B|a,b).

 

[JesseM]

but that doesn't mean that it's assumed that correlations in measurements of the two particles can be explained by local hidden variables given to them by the source.

I agree. The relationship between the two particles isn't, strictly speaking, a 'local' hidden variable. It's a parameter that emerges, and is only relevant, in the joint context. It doesn't determine individual measurement probabilities.

But are you saying that this relationship is completely explained by some parameters that each particle got at the moment they were created at a common location by the source (like each starting out with the same 'polarization vector'), and where the parameter for each particle is itself a local variable that's carried around by the particle as it travels, either unchanging (like if each particle's own polarization vector continues to point in the same direction as the particle travels, at least until the particle is measured by a polarizer) or changing in a way that isn't causally affected by anything outside the particle's past light cone? If so this would be a local hidden variables explanation for the relationship between the particles.

And yet, isn't Bell's (2) requiring that the joint probability be modeled as the product of the two individual probabilities?

Only when conditioned on the hidden variables. In other words, P(AB|λ) is equal to the product of the two individual probabilities P(A|λ)*P(B|λ), but P(AB) is not equal to the product of the two individual probabilities P(A)*P(B). Do you understand the distinction?

If by "a locally produced relationship" you mean local hidden variables, then no, the fact that the statistics violate Bell's inequalities show that this cannot be the explanation.

I agree, per above. But the root cause of the relationship can be assumed to be a local common source.

I think you misunderstand, if the "root cause of the relationship" can be explained in terms of correlated local hidden variables assigned to each particle by the source, then is exactly what a "local hidden variables explanation" means, and this sort of explanation is ruled out if the statistics violate Bell's inequality.

The local hidden variable in any trial is the randomly varying (from trial to trial) polarization angle that, presumably, would, if known, allow precise predictions of individual results.

Can you explain how the "polarization angle" would interact with the detector angle to give the results? I've asked you this before and you haven't answered my question. Suppose the particle's polarization angle were 90 degrees while the detector angle was set to 60 degrees...what would this imply about the results? Would it mean the probability the particle passes through the detector is cos²(90-60), for example?

And it's suggested that the attribution of, and subsequent projection along, a 'principle' axis given a qualitative result at one end or the other is compatible with the assumptions of locality and predetermination (albeit not separable) regarding the jointly measured underlying parameter.

"suggested" by who? You? It certainly isn't suggested by orthodox QM or by anyone who agrees with Bell's analysis.

Why does the cos^2 theta rule following the attribution of the principle axis wrt a detection attribute work? Because the local hidden variable (as differentiated from the global parameter) can be any polarization angle. There are three vectors involved, call them, V1, V2, and V3, an optical vector and two unit vectors. They can be ordered in any way. One, the optical vector, is undetermined but assumed to be continuous between the two unit vectors.

I don't understand, what do these vectors represent physically in the problem? Is the optical vector supposed to be the hidden polarization angle, and the unit vectors are the angles of the two detectors? If not, what?

So, it seems logical to me, and compatible with the idea that everything is evolving according to the principle of locality, that the joint detection rate would be described by the cos^2 of the angular difference between the two unit vectors. As, I've said before, it's just accepted optics. And, because it's accepted optics, this is why the qm treatment for these types of setups is evaluated using Malus Law. I don't think that Bell's analysis rules this out, but rather that it's saying something about how this situation can be modeled.

Again, if you're just saying that each particle received the same "polarization vector" when they were created by the source, and that the polarization vectors are local properties of the particles that travel along with them and determine their response to the detectors, then this is definitely ruled out by Bell's analysis.

The equation (2) was based on the assumption of causal independence between the two particles (i.e measuring one does not affect the other), which was expressed as a condition saying they're statistically independent conditioned on the hidden variables L ...

I agree. The equation says that the two particles (ie., the sets of detection attributes denoted by A and B) are statistically independent.

No it doesn't. P(AB) can be different than P(A)P(B), meaning that they are statistically dependent in their probabilities when not conditioned on the hidden variables λ. For example, if A and B represent measurement results when both detectors are set to the same angle (say, 60 degrees), then if we know B, that automatically tells us the value of A with probability 1. Do you disagree?

It would really help if you would answer my question from post 781:

Do you agree it's possible to have a situation where P(AB) is not equal to P(A)*P(B), and yet P(AB|λ)=P(A|λ)*P(B|λ)? (and that this situation was exactly the type considered by Bell?) In this situation do you think there is a single correct answer to whether A and B are "statistically independent" or not? If so, what is that answer?

Can you address this please?

... but the equation is consistent with the idea that P(AB) can be different from P(A)*P(B).

Not sure what you mean.

Do you understand that if P(AB)=P(A)*P(B), that means A and B are statistically independent in their marginal probabilities (i.e. probabilities not conditioned on another variable like λ)? If so, my point is that if P(AB) is different from P(A)*P(B), that models a situation where A and B are statistically dependent in their marginal probabilities, equivalent to saying that P(A|B) is different from P(A) (i.e. learning the outcome B causes you to modify your estimate of the probability of A). Bell's equation certainly allows for this--it had better do so, because he was trying to explain the perfect correlation (the highest degree of statistical dependence possible) between A and B when both detectors were set to the same angle.

 

[DrChinese]

But you are drawing the wrong conclusion. EPR did not say Bell's a, b, c must be simultaneous elements of reality. So I do not see which EPR assertion is claimed to be wrong here?

Yes, EPR says this. Of course they do not say a, b and c. Bell said that.

What EPR gives is a definition of an element of reality. By that definition, any angle setting measuring particle spin qualifies as an element of reality because it can be predicted with certainty. They then discuss whether 2 or more such elements of reality stand if they cannot be predicted with certainty simultaneously. They assert that such requirement is unreasonable. You are then left with the EPR definition of realism being that any observable which can be predicted with certainly maps to an element of reality.

That would include Bell's a, b and c, which qualify as elements of reality.

 

[DrChinese]

Put this way I have to agree. The operational definition of realism as provided by EPR is fatally flawed beyond any reasonable doubt. I see this as an indication that observables are not non-degenerate. As such, the observables likely do, in a sense, lack a reality independent of the measurement. I don't see the generalization of this as a refutation of realism in general, nor that determinism is refuted. Though this, and other considerations, indicates that if elements of reality exist they are not directly accessible empirically and also most likely transfinite.

You could be correct, to a certain degree it is in fact a function of your definition of reality. I choose to believe that observables of a particle do not have simultaneous reality in the EPR sense of being elements of reality. In other words, I believe their reality is a function of the act of observation.

 

[DrChinese]

Another thing is that as in any real experiment you don't have perfect result. So if you say that every single (4-fold coincidence) detection confirms QM and contradicts LR then in experiment we have situation like that:
"The experimental results in (f) are in agreement with the QM predictions (d) while in conflict with LR (e), with a visibility of 0.789+-0.012."
That means we have 90 detections out of every 100 that without any doubt confirm QM and 10 detections that without any doubt confirm LR.

That of course is not very serious interpretation of experimental results.

Hmmm, I am not sure how you get this because that is quite different than the actual conclusion. Visibility means the number that are detected. So that is 78.9% +/-1.2%. The actual result was a value of 4.433+/-0.032. This was greater than the Local Realistic max of 4 by 76 standard deviations.

So, no this was not a contest where 90% of events say one thing, and 10% say the opposite. 76 SD is overwhelming. 5 SD was enough for the 1982 Aspect experiment.

 

[DevilsAvocado]

P(A,B,a,b)=P(A|B,a,b)P(B|a,b)P(a|b)P(b)

JesseM, you are PF Science Advisor with +6,000 posts, I beg you to read https://www.physicsforums.com/showthread.php?p=2766674#post2766674" to get information about the source for billschnieder’s search for "knowledge and clarity".

Also read the following posts between billschnieder and me, and you will see beyond any doubt that the one and only source for billschnieder’s reasoning is Crackpot Kracklauer.

It may look like billschnieder is here to learn more about professional mainstream science, while billschnieder and Crackpot Kracklauer are in fact trying to dismiss Bell’s Theorem by cranky argumentation around the notation in Bell (2).

This is the cranky "truth", that you are currently engaged in:

http://arxiv.org/abs/quant-ph/0602080"
Authors: A. F. Kracklauer
...
IX. CONCLUSIONS
...
And, once it is clear that Bell Inequalities cannot be derived using BAYES’ formula, the issue of nonlocality is rendered moot. This, in turn, resolves one conflict between two fundamental theories of modern physics—a conflict that on the face of it has the character typical of small, technical misunderstandings. This is only reinforced by the observation that there is no empirical evidence for nonlocality; that which has been taken as such, is in fact just an interpretation imposed indirectly on statistics derived from non kinematic data, but as argued herein, incorrectly.

I sincerely hope you realize the madness in continuing this kind of discussion, spread out all over PF.

 

[my_wan]

You could be correct, to a certain degree it is in fact a function of your definition of reality. I choose to believe that observables of a particle do not have simultaneous reality in the EPR sense of being elements of reality. In other words, I believe their reality is a function of the act of observation.

Put this way I can respect such a position. I'm accustomed to thinking of observables as degenerate, since even before my teens or any notion of what QM was. The reasoning very closely followed your argument on the unobservability of independent variables I like to quote. I didn't know about the correspondence between statistical mechanics and classical thermodynamics at the time either, but the same basic reasoning was embedded in my thinking.

I'll give up what notions I must, but my feeling is that, in some sense, defining what ideas must go requires a comparison to various notions of realism, not just the one operationally defined by EPR. Much like what inspired Bell to derive his inequality. However, I must admit science has made astounding progress without it, and the crackpots that want to claim QM is not science are easy to lose patients with. That's enough to prove my feelings about it are not strictly true, but I still think comparing different notions of realism has value, even if only to define exactly where and how they break. I guess you could call it a minimalist approach to weirdness.

 

[DrChinese]

I have started a new thread in Independent Research:

https://www.physicsforums.com/showthread.php?t=408231

This is on another subject off-topic to this thread. I wanted to invite my friends here to come over and give me your thoughts on a paper I have written on a proposed experiment. Thanks!

 

[billschnieder]

No, but if you meant to write P(AB|a,b) = P(B|a,b)P(A|a,b,B) then yes.

That is what I meant, thanks for spotting the typo.

So then according to Bell, the P on the LHS ie equivalent to P(AB|a,b) in standard notation, where as we have agreed before a and b are place-holders for a specific value of the "random variables" a and b.

Now on age 405 of Bell's paper, just after equation (12) he writes the following:

P in (2) can not be less than -1. It can reach -1 at a = b, only when when
A(a,λ) = -B(b,λ)

How can a probability reach -1? Clearly then, according to Bell, P can not be a probability, since probabilities are only defined from 0 to 1. Do you agree? Yes or no?

 

[JesseM]

How can a probability reach -1? Clearly then, according to Bell, P can not be a probability, since probabilities are only defined from 0 to 1. Do you agree? Yes or no?

OK, this is another minor quibble, the left side is actually an expectation value. I noted earlier in post #790 that A and B in (2) were just written as functions rather than probabilities:

I suppose I should point out that strictly speaking, in equation (2) Bell actually assumes the measurement outcomes are determined with probability 1 by the value of λ, so instead of writing P(A|a,λ) he just writes A(a,λ)

I neglected to note there that he allows the function A(a,λ) (and likewise B(b,λ)) to take values +1 or -1 depending on the measurement result (+1 for spin-up when measured with setting a and -1 for spin-down when measured with setting a, for example). So the notation P(a,b) on the left side of the equation is the expectation value for the product of A and B, which would be equivalent to a weighted sum of four different probabilities: P(A=+1, B=+1|ab)*(+1*+1) + P(A=+1, B=-1|ab)*(+1*-1) + P(A=-1, B=+1|ab)*(-1*+1) + P(A=-1, B=-1|ab)*(-1*-1)

This can be simplified to [P(A=+1, B=+1|ab) + P(A=-1, B=-1|ab)] - [P(A=+1, B=-1|ab) + P(A=-1, B=+1|ab)], and if you wish to do the substitution P(AB|a,b) = P(B|a,b)P(A|a,b,B), then it becomes:

[P(B=+1|a,b)P(A=+1|a,b,B=+1) + P(B=-1|a,b)P(A=-1|a,b,B=-1)] -
[(P(B=-1|a,b)P(A=+1|a,b,B=-1) + P(B=+1|a,b)P(A=-1|a,b,B=+1)]

 

[DrChinese]

So then according to Bell, the P on the LHS ie equivalent to P(AB|a,b) in standard notation, where as we have agreed before a and b are place-holders for a specific value of the "random variables" a and b.

I thought you guys were using a, b as measurement settings, not hidden variables. Where/when did you switch to this notation? Lambda represents the hidden variables.

 

[JesseM]

I thought you guys were using a, b as measurement settings, not hidden variables. Where/when did you switch to this notation? Lambda represents the hidden variables.

I'm still using them to mean measurement settings--perhaps Bill is too, and just called them "random variables" because it's assumed the measurement settings are to be chosen randomly by the two experimenters on each trial.

 

[RUTA]

Sorry, I haven't been able to keep up with this thread. I'm out of town this week and without access to his papers, but a couple of people have asked me to explain where Kracklauer is mistaken.

Again, my last exchange with him was some years ago concerning one of his published papers. In that paper I pointed out to him that his statistics assumed information concerning the detector settings at all sites was available at all sites. He confirmed this was correct. I told him that there is no mystery if this is true (and sent him a quote from Mermin to this effect, since I'm not an authority). I told him that experimentalists understand that this would have to be avoided and change polarizer settings at very high frequencies so that information concerning settings at remote sites is not available prior to recording relevant outcomes. He said I didn't know what I was talking about, so I sent him a quote from one of Aspect's papers making this same claim and never heard from him again.

That's all I know about Kracklauer.

I may not be able to tend to PF in the immediate future because I'm teaching, doing research and preparing for a conference in July. I'll get back to you after my summer research students and class are finished :-)

 

[billschnieder]

OK, this is another minor quibble, the left side is actually an expectation value. I noted earlier in post #790 that A and B in (2) were just written as functions rather than probabilities

I neglected to note there that he allows the function A(a,λ) (and likewise B(b,λ)) to take values +1 or -1 depending on the measurement result (+1 for spin-up when measured with setting a and -1 for spin-down when measured with setting a, for example). So the notation P(a,b) on the left side of the equation is the expectation value for the product of A and B, which would be equivalent to a weighted sum of four different probabilities: P(A=+1, B=+1|ab)*(+1*+1) + P(A=+1, B=-1|ab)*(+1*-1) + P(A=-1, B=+1|ab)*(-1*+1) + P(A=-1, B=-1|ab)*(-1*-1)

There now appears to be two different meanings ascribed to what Bell is doing in equation (2), which I asked you earlier several times:
1) Bell is marginalizing with respect to λ.
2) Bell is calculating an expectation value for the probability P(AB|ab)
Which one is it? I see only a single integral and no summation, and you need one for each if you are doing both.

 

[JesseM]

There now appears to be two different meanings ascribed to what Bell is doing in equation (2), which I asked you earlier several times:
1) Bell is marginalizing with respect to λ.
2) Bell is calculating an expectation value for the probability P(AB|ab)
Which one is it? I see only a single integral and no summation, and you need one for each if you are doing both.

Yes, I didn't notice before that the left side of (2) was an expectation value rather than a straight probability. But it's not quite an expectation value for P(AB|ab) as you suggest, it's actually an expectation value for A*B, which is equivalent to a sum over all possible combinations of values for A and B of the quantity A*B*P(AB|a,b). Remember, though, Bell is assuming that the value of A and B is completely determined by the values of a, b, and λ. So, the integral on the right of (2) is exactly equivalent to the following weighted sum of four integrals:

$$(+1)*(+1)\int P(A=+1, B=+1|a,b,\lambda)P(\lambda)\,d\lambda$$ +
$$(+1)*(-1)\int P(A=+1, B=-1|a,b,\lambda)P(\lambda)\,d\lambda$$ +
$$(-1)*(+1)\int P(A=-1, B=+1|a,b,\lambda)P(\lambda)\,d\lambda$$ +
$$(-1)*(-1)\int P(A=+1, B=+1|a,b,\lambda)P(\lambda)\,d\lambda$$

The reason this works is because for any given value of λ, say λ=λ_i, three of the probabilities in the four integrals above will be equal to zero, while the other probability will be equal to 1. So by splitting up the single integral into the four above, you aren't overcounting or undercounting A*B*P(λ) for any specific value of λ, you're counting it exactly once. This is easier to see if you suppose λ can only take a discrete set of values from 0 to N, so the integral on the right side of (2) can be replaced by the sum $$\sum_{i=0}^N A(a,\lambda_i)*B(b,\lambda_i)*P(\lambda_i)$$. Then if a,b,λ completely determine the values of A and B (which each take one of two values +1 or -1), that means the four-term sum (+1)*(+1)*P(A=+1,B=+1|a,b,λ_i) + (+1)*(-1)*P(A=+1,B=-1|a,b,λ_i) + (-1)*(+1)*P(A=-1,B=+1|a,b,λ_i) + (-1)*(-1)*P(A=-1,B=-1|a,b,λ_i) will always be equal to A(a,λ_i)B(b,λ_i) for each specific value of λ_i [for example, if a,b,λ_i determine that A=+1 and B=-1, then (+1)*(+1)*P(A=+1,B=+1|a,b,λ_i) + (+1)*(-1)*P(A=+1,B=-1|a,b,λ_i) + (-1)*(+1)*P(A=-1,B=+1|a,b,λ_i) + (-1)*(-1)*P(A=-1,B=-1|a,b,λ_i) = (+1)*(+1)*0 + (+1)*(-1)*1 + (-1)*(+1)*0 + (-1)*(-1)*0 = (+1)*(-1) = A(a,λ_i)B(b,λ_i)]. So, if we substitute the four-term sum in for the individual term A(a,λ_i)B(b,λ_i) in the sum over all possible values of λ I wrote above, we get:

$$\sum_{i=0}^N [(+1)*(+1)*P(A=+1,B=+1|a,b,\lambda_i)\,+\,(+1)*(-1)*P(A=+1,B=-1|a,b,\lambda_i)$$$$+ \,(-1)*(+1)*P(A=-1,B=+1|a,b,\lambda_i)\,+\,(-1)*(-1)*P(A=-1,B=-1|a,b,\lambda_i)]*P(\lambda_i)$$

Which can be split up into the following four sums:

$$\sum_{i=0}^N (+1)*(+1)*P(A=+1,B=+1|a,b,\lambda_i)*P(\lambda_i)$$ +
$$\sum_{i=0}^N (+1)*(-1)*P(A=+1,B=-1|a,b,\lambda_i)*P(\lambda_i)$$ +
$$\sum_{i=0}^N (-1)*(+1)*P(A=-1,B=+1|a,b,\lambda_i)*P(\lambda_i)$$ +
$$\sum_{i=0}^N (-1)*(-1)*P(A=-1,B=-1|a,b,\lambda_i)*P(\lambda_i)$$

...which is just the discrete version of the four integrals I wrote before.

So, the left side is an expectation value which can be broken up into a weighted sum of four probabilities of the form P(AB|ab), and the right side can be broken up into a weighted sum of four integrals or sums over all possible values of λ of terms of the form P(AB|a,b,λ). For example, on the left side one of the four weighted probabilities is (+1)*(-1)*P(A=+1,B=-1|ab), and on the right side one of the four weighted integrals is $$(+1)*(-1)\int P(A=+1, B=-1|a,b,\lambda)P(\lambda)\,d\lambda$$. So if you take the marginalization equation $$P(A=+1,B=-1|a,b) = \int P(A=+1, B=-1|a,b,\lambda)P(\lambda)\,d\lambda$$ and then multiply both sides by A*B=(+1)*(-1) and add this equation to three other marginalization equations where both sides have been multiplied by the corresponding value of A*B, you get something mathematically equivalent to equation (2) in Bell's proof.

 

[billschnieder]

But it's not quite an expectation value for P(AB|ab) as you suggest, it's actually an expectation value for A*B, which is equivalent to a sum over all possible combinations of values for A and B of the quantity A*B*P(AB|a,b)...

One unanswered question and a few comments:
This "thing" which Bell calculates in equation (2), which you now say is an expectation value and from my initial glimpse of your explanation, it appears to be. Is the equation as it stands indicating that the numerical value represents what is obtained by measuring a specific pair of settings (ai, bi) a large number of times, or is it indicating that expectation value is what will be obtained my measuring a large number of different pairs of angles (ai,bi)? Or do you think the two are equivalent.

As a follow up of the above, in order to understand what you understand the expected value to mean: If I perform a survey in which respondents answer either ("yes") or ("no") and I know that both outcomes are equally likely, what would you say the expectation value of the survey result?

 

[JesseM]

One unanswered question and a few comments:
This "thing" which Bell calculates in equation (2), which you now say is an expectation value and from my initial glimpse of your explanation, it appears to be. Is the equation as it stands indicating that the numerical value represents what is obtained by measuring a specific pair of settings (ai, bi) a large number of times, or is it indicating that expectation value is what will be obtained my measuring a large number of different pairs of angles (ai,bi)? Or do you think the two are equivalent.

The first, I think he's calculating the expectation value for some specific pair of settings. If he wanted to talk about the expectation value for a variety of different a_i's I think he'd need to have a sum over different values of i in there.

As a follow up of the above, in order to understand what you understand the expected value to mean: If I perform a survey in which respondents answer either ("yes") or ("no") and I know that both outcomes are equally likely, what would you say the expectation value of the survey result?

You have to assign a number to each possibility to have an expectation value. For instance, if you let yes=1 and no=2, then if they're equally likely the expectation value is 1.5, but if you let yes=-1 and no=-1, the expectation value is 0. In Bell's case he's doing something like "result of particle's measurement is spin-up"=+1 and "result of particle's measurement is spin-down"=-1.

 

[billschnieder]

The first, I think he's calculating the expectation value for some specific pair of settings. If he wanted to talk about the expectation value for a variety of different a_i's I think he'd need to have a sum over different values of i in there.

The first, I think he's calculating the expectation value for some specific pair of settings. If he wanted to talk about the expectation value for a variety of different a_i's I think he'd need to have a sum over different values of i in there.

So then, let us consider a specific pair of settings (a, b), and presume that we have calculated an expectation value from equation (2) of Bell's paper, say E(a,b). From what you have explained above, there is going to be a specific probability distribution P(λi) over which E(a,b) was obtained, since the corresponding P(AB|ab) which you obtained your E(a,b) from, was obtained by marginalizing over a specific P(λi) . Do you agree?

Fast forward to then to the resulting CHSH inequality
|E(a,b) + E(a,b') + E(a',b) - E(a',b')| <= 2

In your opinion then, is the P(λi) the same for each of the above terms, or do you believe it doesn't matter.

 

[JesseM]

So then, let us consider a specific pair of settings (a, b), and presume that we have calculated an expectation value from equation (2) of Bell's paper, say E(a,b). From what you have explained above, there is going to be a specific probability distribution P(λi) over which E(a,b) was obtained, since the corresponding P(AB|ab) which you obtained your E(a,b) from, was obtained by marginalizing over a specific P(λi) . Do you agree?

If we wanted to calculate a precise expectation value, yes we'd need a specific probability distribution on the hidden variables, as well as knowledge of what value of A and B went with each possible value of λ. However, the inequalities he derives would apply to any specific choice of probability distribution in a local realist universe.

Fast forward to then to the resulting CHSH inequality
|E(a,b) + E(a,b') + E(a',b) - E(a',b')| <= 2

In your opinion then, is the P(λi) the same for each of the above terms, or do you believe it doesn't matter.

The same probability distribution should apply to each of the four terms, but the inequality should hold regardless of the specific probability distribution (assuming the universe is a local realist one and the specific experimental conditions assumed in the derivation apply).

 

[billschnieder]

The same probability distribution should apply to each of the four terms, but the inequality should hold regardless of the specific probability distribution (assuming the universe is a local realist one and the specific experimental conditions assumed in the derivation apply).

So then, if it was found that it is possible in a local realist universe for P(λi) to be different for at least one of the terms in the inequality, above, then the inequality will not apply to those situations where P(λi) is not the same. In other words, the inequalities above are limited to only those cases for which a uniform P(λi) can be guaranteed between all terms within the inequality. Do you disagree?

Do you believe, P(λi) is always uniform between all the terms in the inequality, when calculating from data acquired in Aspect-type experiments?

 

[JesseM]

So then, if it was found that it is possible in a local realist universe for P(λi) to be different for at least one of the terms in the inequality, above, then the inequality will not apply to those situations where P(λi) is not the same.

When you suggest the possibility that P(λi) could be "different for at least one of the terms in the inequality", that would imply that P(λi) depends on the choice of detector settings, since each expectation value is defined relative to a particular combination of detector settings. Am I understanding correctly, or are you talking about something else?

If I am understanding you right, note that it's generally accepted that one of the assumptions needed in Bell's theorem is something called the "no-conspiracy assumption", which says the decisions about detector settings should not be correlated with the values of the hidden variables. For example, this page on EPR/Bell says:

Assumption 4. The choices between the measurement setups in the left and right wings are entirely autonomous, that is, they are independent of each other and of the assumed elements of reality that determine the measurement outcomes.

Otherwise the following conspiracy is possible: something in the world pre-determines which measurement will be performed and what will be the outcome. We assume however that there is no such a conspiracy in our world.

And later on the same page:

a. Conspiracy
There is an easy resolution of the EPR/Bell paradox, if we allow the conspiracy that was prohibited by Assumption 4 (Brans 1988; Szabó 1995). It is hard to believe, however, that the “free” decisions of the laboratory assistants in the left and right wings depend on the value of the hidden variable which also determines the spins of the two particles.

Likewise the fairly rigorous-looking derivation Minimal assumption derivation of a Bell-type inequality mentions this assumption on p. 6:

D. No conspiracy

The events of type $$C^{+-}_{ii}$$ are not supposed to be influenced by the measuring operations Li and Rj . One reason for this assumption is that the measurement operations can be chosen arbitrarily before the particles enter the magnetic field of the Stern-Gerlach magnets and that an event of type $$C^{+-}_{ii}$$ is assumed to happen before the particles arrive at the magnets. Therefore a causal influence of the measurement operations on events of type $$C^{+-}_{ii}$$ would be tantamount to backward causation. Also an inverse statement is supposed to hold: The event types $$C^{+-}_{ii}$$ are assumed not to be causally relevant for the measurement operations. This is meant to rule out some kind of “cosmic conspiracy” that whenever an event of type $$C^{+-}_{ii}$$ is instantiated, the experimenter would be “forced” to use certain measurement operations. This causal independence between $$C^{+-}_{ii}$$ and the measurement operations is assumed to imply the corresponding statistical independence. The same is assumed to hold also for conjunctions of common cause event types. We refer to this condition as no conspiracy (NO-CONS).

So, I agree the inequality can only be assumed to hold if the choice of detector settings and the value of the hidden variables are statistically independent (which means the probability distribution P(λi) does not change depending on the detector settings), but this is explicitly included as an assumption in the more rigorous modern derivations. If you dispute that a "conspiracy" of the type being ruled out here would in fact have some very physically implausible features so that it's reasonable to rule it out, I can give you some more detailed arguments for why it's so implausible.

 

[billschnieder]

You are wondering off now, JesseM. Try not to pre-empt the discussion. The question I asked should have a straightforward answer. The reason why P(λi) might be different shouldn't affect the answer you give to my question. If you believe P(λi) will be different when a conspiracy is involved, then you should have no problem admitting that Bell's inequalities do not apply to situations in which there is conspiracy.

Here it is again:

So then, if it was found that it is possible in a local realist universe for P(λi) to be different for at least one of the terms in the inequality, above, then the inequality will not apply to those situations where P(λi) is not the same. In other words, the inequalities above are limited to only those cases for which a uniform P(λi) can be guaranteed between all terms within the inequality. Do you disagree?

Do you believe P(λi) can different between the terms in a locally causal universe if and only if conspiracy is involved?

 

[JesseM]

You are wondering off now, JesseM. Try not to pre-empt the discussion.

You are acting like a bully, Bill. You don't have dictatorial control over the terms of "the discussion", we are both allowed to contribute whatever we think is relevant. If you want to be a dictator who gets to tell me what I am and am not allowed to discuss, what questions from you I must answer, but who refuses to address topics/questions I think are relevant if you don't immediately spot the relevance yourself, I'm not going to participate in that sort of game.

The reason why P(λi) might be different shouldn't affect the answer you give to my question.

True, but for anyone following along it may still help their understanding of the physical meaning of what we're talking about to point out that the only way P(λi) could be different for the four expectation values would be if there are different probability distributions for different combinations of detector settings. We can show this with pure math, no physical reasoning whatsoever. After all, as I explained in post #855, E(a,b) for some specific pair of detector settings a and b is just defined as (sum over all possible values of A and B) of A*B*P(AB|a,b), or equivalently the same sum but for A*B*P(A,B,a,b)/P(a,b). And we can marginalize P(A,B,a,b) over λ by setting it equal to $$\int P(A,B,\lambda,a,b)\,d\lambda$$, which by the chain rule of probability is equal to $$\int P(A,B|\lambda,a,b)P(\lambda|a,b)P(a|b)P(b)\,d\lambda$$, and P(a|b)P(b) = P(a,b) so this reduces to $$\int P(A,B|\lambda,a,b)P(\lambda|a,b)P(a,b)\,d\lambda$$. So, (sum over all possible values of A and B) of A*B*P(A,B,a,b)/P(a,b) is equal to (sum over all possible values of A and B) of (A*B/P(a,b))*$$\int P(A,B|\lambda,a,b)P(\lambda|a,b)P(a,b)\,d\lambda$$, and dividing out P(a,b) gives (sum over all possible values of A and B) of $$A*B\int P(A,B|\lambda,a,b)P(\lambda|a,b)\,d\lambda$$. This looks just like the sum of four integrals in #855 which I said was equivalent to the right side of equation (2) in Bell's paper, except with P(λ|a,b) substituted in for P(λ). Along the same lines, if you wanted to calculate the expectation value for a different pair of settings like a' and b', (sum over all possible values of A and B) of $$A*B\int P(A,B|\lambda,a',b')P(\lambda|a',b')\,d\lambda$$. So, if there was a different P(λ) for each version of equation (2) calculating the expectation value for each possible pair of detector settings, just using pure math we can see that the only way this could happen was if P(λ|a,b) for one pair of detector settings is different than P(λ|a',b') for a different pair of detector settings.

If you believe P(λi) will be different when a conspiracy is involved, then you should have no problem admitting that Bell's inequalities do not apply to situations in which there is conspiracy.

Didn't I already "admit" that in my last post? Read again:

So, I agree the inequality can only be assumed to hold if the choice of detector settings and the value of the hidden variables are statistically independent (which means the probability distribution P(λi) does not change depending on the detector settings)

Do you believe P(λi) can different between the terms if and only if conspiracy is involved?

Yes, since "conspiracy" is just defined as P(λ|a,b) being different from P(λ). I showed above using pure math (no physics) that P(λ) can be different between the integrals Bell uses to calculate expectation values only if P(λ|a,b) is different from P(λ), i.e if there is a "conspiracy".

 

[billschnieder]

You are acting like a bully, Bill. You don't have dictatorial control over the terms of "the discussion"

I haven't twisted your arm to force you to comply with my requests. All I am trying to do is have a focused discussion, which apparently is very very difficult for you to do. You have been cooperating until now, why the sudden change of heart. I ask you a simple question to which you either agree or disagree, and you go back and pull already settled issues, raise new issues, with tons of equations into the response as if you want to drown the the real issue. I understand you like to write a lot and you have every right, but for once could you please make an effort to just stick to the point?

So then, I will assume that the last few posts did not happen, and I will consider that the responses moving forward are as follows:

So then, if it was found that it is possible in a local realist universe for P(λi) to be different for at least one of the terms in the inequality, above, then the inequality will not apply to those situations where P(λi) is not the same. In other words, the inequalities above are limited to only those cases for which a uniform P(λi) can be guaranteed between all terms within the inequality. Do you disagree?

... I agree ...

Do you believe P(λi) can different between the terms if and only if conspiracy is involved?

Yes ...

See how short and to the point this would have been. You would have saved yourself all the typing effort, and to boot, we don't have to start a new rabbit trail about the meaning of "conspiracy"! Your answer presented as precisely above would already have incorporated your view about what "conspiracy" means, but the fact that it is precise enables use to continue the discussion on topic. But if you now define conspiracy in a manner that I don't agree with, I will be forced to challenge it because if I don't it may appear as though I agree with that definition, then we end up 20 posts later, discussing whose definition of "conspiracy" is correct, having left the original topic. The more you write, the more things need to be challenged in your posts and the more off-topic the discussions will get. This is why I insist that the discussion be focused. I hope you will recognize and respect this, otherwise there is no point continuing this discussion.

 

[JesseM]

I haven't twisted your arm to force you to comply with my requests.

The only way a person can "twist someone's arm" over the internet is by adopting a demanding or aggressive tone whenever the other person doesn't comply with their requests, and that's exactly what you've done.

All I am trying to do is have a focused discussion, which apparently is very very difficult for you to do. You have been cooperating until now, why the sudden change of heart. I ask you a simple question to which you either agree or disagree, and you go back and pull already settled issues, raise new issues, with tons of equations into the response as if you want to drown the the real issue.

Again, I bring these things up because I want anyone else reading the discussion to understand exactly what various conditions entail. I have answered your questions, and you are perfectly free to ignore the extra points I make if they don't seem relevant to you, so there is absolutely no need for you to berate me and imply I am trying to obscure the issue just because I don't confine myself to the shortest possible answers. Like I said, it just seems like bullying for the sake of bullying, unless you can give a practical rationale for why including some extra points in a post that already answers all the questions you asked is going to prevent you from developing whatever point you intend to make.

So then, I will assume that the last few posts did not happen, and I will consider that the responses moving forward are as follows:

So then, if it was found that it is possible in a local realist universe for P(λi) to be different for at least one of the terms in the inequality, above, then the inequality will not apply to those situations where P(λi) is not the same. In other words, the inequalities above are limited to only those cases for which a uniform P(λi) can be guaranteed between all terms within the inequality. Do you disagree?

... I agree ...

Do you believe P(λi) can different between the terms if and only if conspiracy is involved?

Yes ...

See how short and to the point this would have been. You would have saved yourself all the typing effort, and to boot, we don't have to start a new rabbit trail about the meaning of "conspiracy"!

There is no "rabbit trail" about the meaning, it's a technical term with a single well-defined meaning in the context of a discussion of assumptions needed in deriving Bell inequalities. "Conspiracy" in this context is defined in terms of P(λ) being different from P(λ|ab) (i.e. a statistical dependence between hidden variables and measurement state), I was just pointing out that this official definition is actually equivalent to your own comment about P(λ) being different for different expectation values, but it's not instantly obvious that they're equivalent, so for pedagogical reasons I was explaining why (again, even if this explanation is not interesting to you it may be helpful for others reading).

And speaking of "short and to the point", there's no need for you to elaborately berate me about how much time I could have saved or how you will "assume that the last few posts did not happen", you could just quote the part of the posts that are relevant to you and respond to that.

Your answer presented as precisely above would already have incorporated your view about what "conspiracy" means, but the fact that it is precise enables use to continue the discussion on topic.

But as I said, it wouldn't have made clear how the standard definition relates to the fact that P(λ) can only differ for different expectation values if a "conspiracy is involved" (which is not the standard way of defining it).

But if you now define conspiracy in a manner that I don't agree with, I will be forced to challenge it because if I don't it may appear as though I agree with that definition, then we end up 20 posts later, discussing whose definition of "conspiracy" is correct, having left the original topic.

There would be no need for an extended debate about the meaning of a technical term like "conspiracy", a condition that can be expressed as a simple equation, any more than there would about other technical terms that can be expressed in terms of equations like "energy" or "force". Our debate about "probability" was because we weren't debating the purely mathematical aspects (like the fact that the sum of probabilities of all possible outcomes must always be 1, and individual probabilities can never be negative), but were debating philosophical interpretations of the meaning of the mathematical symbols and how they apply to the real world.

The more you write, the more things need to be challenged in your posts and the more off-topic the discussions will get. This is why I insist that the discussion be focused. I hope you will recognize and respect this, otherwise there is no point continuing this discussion.

I don't recognize that the hypothetical you mention actually applies to this discussion. In fact you didn't need to challenge anything in my definition of the no-conspiracy assumption, so going on about how I need to keep it short is completely gratuitous here. In other situations where you have challenged me on less straightforward mathematical issues, I would say that the debates were central to the main issues we were disagreeing about, like how the frequentist definition of a "population" of hypothetical experiments shows why an Aspect-type experiment will naturally be a "fair sample", something you were continually asserting it wouldn't be unless we precisely controlled for the values of all hidden variables (just bringing this up as an example, the actual debate on this point can continue on the other thread).

 

[billschnieder]

Well JesseM,
Thank you then for your cooperation so far, and I won't bother you again. Unfortunately I can not continue the discussion like this when you are unable to stay on topic. Despite my complaints, you continue in like manner as if though secretly hope I will abandon the discussion. So you get your wish. Anyone else following the discussion who is interested in finding out where I was going with the line of questioning is welcome to PM me.

 

[JesseM]

Despite my complaints, you continue in like manner as if though secretly hope I will abandon the discussion. So you get your wish.

It's not my wish that the discussion stop, it's just that you haven't provided any practical justification for why I should change my posting style (as I already pointed out, I did answer all your questions so nothing is stopping you from just responding to the parts of my posts that are relevant to your argument and ignoring the rest), and your requests amount to little more than "shut up and answer exactly the way I tell you to, not the way you want to" (and the tone of your requests is only marginally more civil than that). Again it pretty much just seems like bullying to me, and while I'm happy to continue the discussion in a civil and adult manner, I'm not going to cede total control over my own posting style just because you bark orders at me.

 

[ThomasT]

Could you please show me one title, link, or paper-id?

One? There's a bunch, and they're legit. As ajw1 pointed out, you're the one who provided the links in the first place. (thanks again) You might consider clicking on the links to some of the papers and actually reading them.

--- snip ---

... Crackpot Kracklauer is just too much, and I will never back off from this, never.

What is it? Do you have some personal history with this guy or something?

Supporting Crackpot Kracklauer must be against all and everything in Physics Forums Global Guidelines ...

You've presented what so far seems to be a groundless personal attack on a physicist who's got some interesting papers (several in peer reviewed journals), the conclusions of which are, apparently, contrary to certain views which, apparently, you've emotionally bonded with. So, who's the crackpot deviating from the PF guidelines?

Now, DA, I'm not saying you're a crackpot, in fact my understanding is that you've gotten into the Bell-EPR stuff relatively recently. This was the case, at one time or another, for everyone (including Zeilinger, DrC, Kracklauer, RUTA, JesseM, and even Einstein and Bell) who's been interested in the implications of a certain, call it 'realistic', view of how theories of quantum experimental phenomena might be formulated. These considerations involve semantics, logic and physics. What I ask of you is that you not attack anyone as a 'crackpot' until you fully understand everything involved in their particular view. This will take some time. As DrC might confirm, I've revisited this topic several times, have changed my approach (my way of thinking about it) several times, and I'm still not sure that I fully understand everything involved. So, please, don't be so quick to dismiss someone as a 'crackpot' unless and until you fully understand exactly what it is that they're saying. And, when you do fully understand the arguments involved, then I think that you will just deal with the arguments.
I hope that you stay interested in this and continue to learn, as I hope to do.

In connection with this, I think it's important that I learn as much about OPDC as I can. That's my next agenda, and so after my next few posts in this thread I won't be contributing to it.

 

[ThomasT]

DrC, thanks for your elaboration on your 'requirement' for candidate local realistic models of entanglement. I still don't understand what you're saying. I think the best thing to do is to start a new thread on this. Which I will do tonight.

 

[ThomasT]

JesseM, thanks for your thoughtful post #842. I don't want to nitpick (but I will be thinking about the questions you've posed). I want you to understand why I don't understand why some people present Bell's theorem as implying that nature is nonlocal. I look at the experimental setups involved and I see a local optical 'explanation' for the observed correlations. I've talked to maybe two dozen working experimental physicists about this and they agree.

As far as the form of Bell's (2) is concerned, it represents the experimental situation in a factorable form, which means that it reduces to an expression that the data sets A and B are independent. Is this how you see it?

Should I start a new thread on this?

 

[ThomasT]

... his statistics assumes that knowledge of detector settings is available at both detection sites.

This 'global' knowledge is available via the data processing and analysis. Isn't it?

I wrote him a detailed email explaining that experiments change polarization settings at very high frequencies precisely so info about Alice's detector settings is not available to Bob and vice versa.

While it's true that the settings are changed rapidly and randomly, it's also true that for any given time-matched pair of detection attributes there's an associated pair of polarizer settings. The statistics associated with any given run would include all of that. "Wouldn't they?

I've only just glanced at the paper so far. If you can point out where his error appears, that would be appreciated.

Sorry, I haven't been able to keep up with this thread. I'm out of town this week and without access to his papers, but a couple of people have asked me to explain where Kracklauer is mistaken.

Again, my last exchange with him was some years ago concerning one of his published papers. In that paper I pointed out to him that his statistics assumed information concerning the detector settings at all sites was available at all sites. He confirmed this was correct. I told him that there is no mystery if this is true (and sent him a quote from Mermin to this effect, since I'm not an authority). I told him that experimentalists understand that this would have to be avoided and change polarizer settings at very high frequencies so that information concerning settings at remote sites is not available prior to recording relevant outcomes. He said I didn't know what I was talking about, so I sent him a quote from one of Aspect's papers making this same claim and never heard from him again.

That's all I know about Kracklauer.

I may not be able to tend to PF in the immediate future because I'm teaching, doing research and preparing for a conference in July. I'll get back to you after my summer research students and class are finished :-)

Please reply to my specific questions.

You stated that Kracklauer's "statistics assumed information concerning the detector settings at all sites was available at all sites." Isn't it true that at the conclusion of a run this info is available ... to the global observer, the experimenter? So, I'm suggesting that maybe Kracklauer's objection to your criticism was valid.

As I've asked, if you can point out the specific error in Kracklauer's analysis, then that woud be appreciated.

 

[JesseM]

JesseM, thanks for your thoughtful post #842. I don't want to nitpick (but I will be thinking about the questions you've posed). I want you to understand why I don't understand why some people present Bell's theorem as implying that nature is nonlocal. I look at the experimental setups involved and I see a local optical 'explanation' for the observed correlations. I've talked to maybe two dozen working experimental physicists about this and they agree.

Well, can you present your local optical explanation in detail, either here or on a new thread? You'll need to present it in enough quantitative detail that we can calculate what measurement outcome will occur (or what the probability is for different outcomes) given knowledge of a detector settings and the local hidden variables at the location of the measurement (like the 'polarization vector' of the particle being measured, if that's your hidden variable).

As far as the form of Bell's (2) is concerned, it represents the experimental situation in a factorable form, which means that it reduces to an expression that the data sets A and B are independent. Is this how you see it?

No, A and B are not independent in their marginal probabilities (which determine the actual observed frequencies of different measurement outcomes), only in their probabilities conditioned on λ. I've asked whether you understand the distinction a bunch of times and you never answer. If you'd like to see a numerical example where there's a statistical dependence in marginal probabilities but not when conditioned on some other variable I could easily provide it.

 

[RUTA]

Please reply to my specific questions.

You stated that Kracklauer's "statistics assumed information concerning the detector settings at all sites was available at all sites." Isn't it true that at the conclusion of a run this info is available ... to the global observer, the experimenter? So, I'm suggesting that maybe Kracklauer's objection to your criticism was valid.

As I've asked, if you can point out the specific error in Kracklauer's analysis, then that woud be appreciated.

That the information is available AFTER the fact doesn't bear on a possible CAUSE for the correlations. The point is that the detector setting at site A is NOT available to site B BEFORE the detection event occurs at site B. If this information is available prior to detection, the correlations in the outcomes can be orchestrated to violate Bell's inequality. No one disputes this fact -- you have to keep the outcome at each site dependent ONLY upon information AT THAT SITE to have the conundrum about their correlations.

Thus, there are generally two ways to account for EPR-Bell correlations. 1) The detection events are separable and you have superluminal exchange of information. 2) The detection events are not separable, e.g., the spin of the entangled electrons is not a property of each electron. The first property is often called "locality" and the second property "realism."

Kracklauer's statistics simply assumed detector setting information was available at each site prior to detection outcomes. When I discussed this with him at a conference, he was adamant that the outcome at each site was contingent upon outcomes and settings at other sites so the "proper" statistics had to contain this fact. His whole argument was that we needed to use the "proper" statistics and the mystery would disappear. His "proper" statistics just assume global knowledge of detector settings. But, unless he has a proposal for how this information is available, he has done nothing to resolve the mystery. How is this information available? FTL signals or nonseparability? Or both? What is the mechanism? All he had was a statistical counterpart to the mystery, although it could be published if no one else had pointed this out. But, nothing was "resolved."

 

[DevilsAvocado]

One? There's a bunch, and they're legit. As ajw1 pointed out, you're the one who provided the links in the first place. (thanks again) You might consider clicking on the links to some of the papers and actually reading them.

Here’s http://arxiv.org/find/all/1/all:+Kracklauer/0/1/0/all/0/1" of Crackpot Kracklauer’s 21 papers on arXiv.org. Where is the "bunch" of peer reviewed papers? These two are peer reviewed before 2000:

And the only one peer reviewed after 2000, is this one:

These 2 mumbling pages of a rebuttal of http://en.wikipedia.org/wiki/David_Mermin" , and this was his last paper that made it thru a scientific journal.

(Note that http://www.springer.com/physics/journal/10701" , which resulted in the takeover of Gerard ‘t Hooft as Editor-in-Chief in 2007.)

What is it? Do you have some personal history with this guy or something?

The question is why you risk all your credibility for a 100% crackpot as A. F. Kracklauer? Didn’t you watch the http://video.google.com/videoplay?docid=-1112934842741515675" ? Crackpot Kracklauer thinks QM mainstream physics are wrong! And we are not talking a little 'disagreement' around Bell (2) – everything is wrong according to Crackpot Kracklauer!

A completely lost "independent researcher" with a crazy homepage at freehosting.com, and you are supporting this guy!? Why??

I know you dislike nonlocality very much, and are fighting to find a "solution". But don’t you think this is a 'little' too "far out"? This man has a mental problem:

A. F. Kracklauer - Non-loco Physics
"Loco'' (Spanish for 'crazy'). Contemporary Physics is vexed by some really "loco'' ideas, with nonlocality and asymmetric aging leading the list.
...
A second motivation is sociological. Some see a mutual interplay between fundamental science and the development of civilization. If this notion is accepted, then physics, as a social enterprise, has some responsibility to support those things making positive contributions to civilization by being the exemplar of rationality, contrary to the current fashion of spewing forth ever new and more exotic pop-psycho-sci-fi contrivances, i.e., loco ideas.

Convinced yet? No? How about this 'excellent' paper by Crackpot Kracklauer?


(Edit: Crackpot Kracklauer’s fancy host freehosting.com doesn’t allow direct linking to PDF, use http://www.google.com/search?hl=en&...ing.com/ws01.pdf&aq=f&aqi=&aql=&oq=&gs_rfai=" instead.)

http://www.nonloco-physics.000freehosting.com/ws01.pdf"
ABSTRACT. Of the various “complimentarities” or “dualities” evident in Quantum Mechanics (QM), among the most vexing is that afflicting the character of a ‘wave function,’ which at once is to be something ontological because it diffracts at material boundaries, and something epistemological because it carries only probabilistic information. Herein a description of a paradigm, a conceptual model of physical effects, will be presented, that, perhaps, can provide an understanding of this schizophrenic nature of wave functions. It is based on Stochastic Electrodynamics (SED), a candidate theory to elucidate the mysteries of QM. The fundamental assumption underlying SED is the supposed existence of a certain sort of random, electromagnetic background, the nature of which, it is hoped, will ultimately account for the behavior of atomic scale entities as described usually by QM.
In addition, the interplay of this paradigm with Bell’s ‘no-go’ theorem for local, realistic extentions of QM will be analyzed.

Have you ever heard of the "SCHIZOPHRENIC NATURE of wave functions" before?


Still not convinced? How about this?

(Edit: Crackpot Kracklauer’s fancy host freehosting.com doesn’t allow direct linking to PDF, use http://www.google.com/search?hl=en&....pdf&btnG=Search&aq=f&aqi=&aql=&oq=&gs_rfai=" instead.)

http://www.nonloco-physics.000freehosting.com/abort.pdf"
Does quantum mechanics have anything to do with abortion? Something, maybe. Quantum mechanics is the theory that encodes the mathematical patterns involved in the chemical bond. The chemical bond, in turn, writ big, or rather, writ oft, is the tool for assembling DNA, the crucial stuff of living matter. So, as the non plus ultra of life, the quantum mechanical chemical bond, may well have some relevance to abortion too, as an event affecting life.

When did you last hear a "scientist" speculate around quantum mechanics and ABORTION?

As I said – this is the worst crackpot I have ever seen, and I think you should make it very clear that you are not backing up this man and his totally crazy ideas. This is not science.

So, who's the crackpot deviating from the PF guidelines?

I think you owe me an apology.

 

[my_wan]

As I said – this is the worst crackpot I have ever seen,...

There's worse, much worse...