Talk:Counterfactual definiteness

Ambiguity

I think the article is ambiguous, and the examples misleading. CFD in this article is related too much to quantum mechanics while this should also be understood independently. For example (I'm not sure), "CDF implies that all values in nature are definite whether they are measured or not. To assume that something unmeasured is definite is counterfactual." Correct me please.Mastertek (talk) 03:59, 25 October 2011 (UTC)

Clarification

You know, I've yet to see a single comprehensible explanation of why it is that Bell's theorem assumes CFD, nor why many-worlds violates it. For that matter, I've only ever seen one good explanation of Bell's theorem and unfortunately it discusses neither CFD, nor many-worlds. http://www.mathpages.com/rr/rrtoc.htm (sections 9.5-9.8)

Kevin Aylward:

According to Leslie Ballentine, Professor at Simon Fraser University, and writer of the text book "Quantum Mechanics, A Modern Development" ISBN981-02-4105-4., Bell's theorem dosnt.

He explains in the above book that, firstly, EPR, *derives* CFD, not assumes it. Second, he points out that H. Strap dispenses with CFD, and still shows that QM violates locality.

Subsequently, other have argued that he still assumes CFD implicitly, however, H. P. Stap further answers these criticisms, but the debate is ongoing e.g http://adsabs.harvard.edu/abs/2004quant.ph..4121S, probably till the end of time.

Eberhard showed that CFD and locality lead to Bell's theorem while Arthur Fine showed that any theory conforming to Bell's theorem has a local hidden variable model which implies that it must satisfy CFD. Thus locality and CFD are in fact equivalent to Bell's theorem. Kuratowski's Ghost (talk) 22:42, 4 August 2008 (UTC)

I, too, have trouble seeing how many-worlds violates CFD. The Elitzur-Vaidman bomb-testing problem is an ideal (and experimentally proven) example of CFD, and (at least in my admittedly uneducated mind) it's quite easy to reconcile that experiment with many-worlds. The many-world interpretation of what happens when the photon winds up at the "C" detector is that, in an "alternate universe", the photon took the other path at the first half-silvered mirror, hit the bomb causing it to explode and thus preventing it from completing its trek. If it couldn't complete its trek, it couldn't interfere with the photon from *our* universe (like it does when the bomb is a dud) and so "our" photon winds up hitting detector C unimpeded. The way I see it, CFD not only doesn't violate many-worlds--it actually strongly implies it.

Furthermore, given that 1994 implementation of the bomb experiment actually proved that macroscopic CFD phenomena exist and the fact that the many-worlds interpretation is still very popular, I would say this is evidence that the two ideas are not at odds--if they were, many-worlds would have fallen out of favor given the concrete evidence supporting CFD. --Lode Runner 20:26, 3 October 2007 (UTC)

The bomb-testing problem doesn't determine an answer to a counterfactual question, the bomb detector is present, the bomb detector performs factual measurements, there is nothing counterfactual here in the CFD sense, the whole bomb detector methodology relies on the factual measurement the bomb detector performs. Kuratowski's Ghost (talk) 23:03, 4 August 2008 (UTC)

CFD, Bell's Thorem, and Locality

The last statement on this page says: "Abandoning CFD allows one to claim that violation of Bell's inequalities does not necessarily imply a violation of the locality principle." That's not true. There is always nonlocal correlation (the point of Bell's Inequality) in the experimental setup. Bell's Theorem says more about locality than it does CFD, thus GLOBAL hidden variable theories like Bohmian mechanics. I'm deleting that statement as "abandoning CFD" does not in any way allow for an accounting of the correlation between the detectors seen in experiments testing Bell's Theorem. Eluusive —Preceding undated comment added 00:10, 10 June 2009 (UTC).

Locality vs CFD

The line: "Bell's Theorem actually proves that every quantum theory must violate either locality or CFD." may be meaningful to people who understand the subject matter, but nothing in the article makes it clear why it matters if CFD is violated.Janus Shadowsong | contribs 20:39, 25 October 2010 (UTC)

Additionally, the "either" in the sentence should be dropped -- there is nothing stopping quantum theory from violating locality and CFD. — Preceding unsigned comment added by 65.123.216.4 (talk) 23:55, 2 January 2012 (UTC)

Accuracy

The article erroneously states the Heisenberg Uncertainty Principle (HUP). The article says that HUP implies that you cannot measure both the position and momentum of an electron. In fact, HUP has nothing to say about individual electrons. You can only derive the result if you use repeated measurements, so it relates either simultaneous measurement of many electrons or repeated measurement of the same electron (or a mixture of both). There is a well-known thought experiment for this (I first heard it in a physics lecture in 1976). Prepare a beam of electrons of known momentum, you can make this as precise as you like. The more precise the more spread out the beam will be (HUP). Measure the position of one electron in the beam, you can make this as precise as you like too. You have now measured the position and momentum to arbitrary precision. Of course, the electron subsequently will have neither. — Preceding unsigned comment added by Jschlesinger (talk • contribs) 21:52, 20 November 2011 (UTC)

Jschlesinger (talk) 09:34, 21 February 2017 (UTC) Jschlesinger (talk) 09:34, 21 February 2017 (UTC)

Macroscopic analogy or example

The following is a really stupid analogy! It really has no connection to physics: blocking photon (potential) waves in one arm of an interferometer gives us 'unmeasured' knowledge of the photon received in the other arm. This article is unworthy of Wikipedia.

 "To use a macroscopic analogy, an interpretation which rejects counterfactual definiteness views measuring the position as akin to asking where in a room a person is located, while measuring the momentum is akin to asking whether the person's lap is empty or has something on it. If the person's position has changed by making him or her stand rather than sit, then that person has no lap and neither the statement "the person's lap is empty" nor "there is something on the person's lap" is true. Any statistical calculation based on values where the person is standing at some place in the room and simultaneously has a lap as if sitting would be meaningless."  — Preceding unsigned comment added by Chrisman62 (talk • contribs) 03:18, 14 August 2015 (UTC) 

I respectfully suggest that the article use a different macroscopic example or analogy.

The example in the first section, "the return of an airborne ball to the Earth", is more about trust in the future validity of the laws of physics, in the sense of the problem of induction - whereas to my uneducated mind the issue of counterfactual (in)definiteness concerns "the road not taken", and therefore applies even to events entirely in the past.

Consider this macroscopic thought experiment.

Your phone is across the room so that you cannot see its display. It rings. You contemplate whether you will get up to answer it. You decide to let the call go. When you go to look at your phone after you have missed the call, the caller ID reads a certain number. If you had decided to get up to answer the phone while it was still ringing, would the number on the caller ID necessarily have been the same, or only with some probability?

In a counterfactually definite view of the universe, the answer is yes definitely, I guess on the assumption that since we have no information on the identity of the caller, we have no reason to believe it will be different in one case or another.

In a counterfactually indefinite view of the universe, the answer is no not necessarily, I guess on the assumption that since we have no information on the identity of the caller, it could be anything in any case.

Seems to me the definite view imposes a sort of "artificial symmetry" on the universe that does not really exist, and the more "maximum entropy"-like indefinite view is more realistic.

Michael Redman bornforthesummer@gmail.com — Preceding unsigned comment added by 50.112.18.160 (talk) 10:39, 3 May 2012 (UTC)

Badly written

This article is an incredibly badly written impenetrable wall of text, and I say that as a physicist. A jumbled up mess of half-explanations, terms for which isn't explained why they are called that (and that includes the subject) and misleading and inappropriate examples. I think if a layperson would start reading this, his eyes would glaze over near the end of the first sentence or so. — Preceding unsigned comment added by 82.139.81.0 (talk) 07:12, 9 May 2012 (UTC)

... and incorrect

The definition of CFD in the article does not coincide with the meaning the term has in the modern literature on Bell's theorem, interpretation of QM, and so on. The article also lacks decent modern references. I corrected the text but did not yet support this with references. Richard Gill (talk) 17:05, 5 June 2012 (UTC). I am inclined to agree with you and so have removed the "does not mean counter to the fact" since CFD does mean this more generally. I don't know what else I can do without a better referenced definition.William.winkworth (talk) 13:37, 13 May 2018 (UTC)

Macroscopic application

If counterfactual definiteness is a concept that arose from the analysis of experiments such as EPR, I wonder if we can make a macroscopic analogy that would make sense. I like that example about the caller's telephone number mentioned above, but I see one problem with it, which I'll explain: Counterfactual defineteness seems to apply to a variable which is "complementary" to the one that has been measured. Being the fact that in the macroscopic world ( which is governed by classical mechanics ) we don't have complementary variables, I don't think we can find a suitable set of variables to make an analogy. Well, perhaps we could think of some example where measurement of one variable spoils the other, but that would not say much about the state of this other variable before measurement was made. If on the other hand, we "defined" counterfactual definiteness, as applying to any measurement or observation which has not been made (without any reference to a complementary variable), then the meaning of this expresion would certainly apply to the macroscopic world. Of course we could suggest changing the meaning of this expression and extending it as I just mentioned, but the purpose of Wikipedia is to describe the meaning of words and expresions as they are currently used and not to introduce new ideas. It would be interesting to look at how this expression has been used in different published articles and specially to see who was the first to use it. Doing a quick search I found an article by Vaidman (http://www.tau.ac.il/~vaidman/lvhp/m105.pdf) But Vaidman talks about "counterfactuals" only and not together with "definiteness" Somewere else, I found "counterfactual definiteness" considered to be equivalent to "realism". I think these things may not be the same. Alexepascual (talk) 23:07, 25 July 2012 (UTC)

Wrong example of Counterfactual measurement in Mach-Zehnder interferometer

The explanation is simple, also classical. In 4a/b the photons are not detected because of destructive interfering of both waves from the upper and lower branch. In 4 c/d the new mirror blocks the wave from the lower path, so no destructive interfering anymore, so photons can be detected again in A. Nothing counterfactual about that. DParlevliet (talk) 22:17, 21 February 2014 (UTC)

Vague to the point of being meaningless

I just had a look back through the history of this article. It is amazing that it has been around for years without getting straightened out. Maybe part of the problem is the paucity of academic articles available to us.

There is a field in logic that deals with "counterfactual conditionals," and logicians sometimes have trouble dealing with them. How does one evaluate the truth value of an implication or other compound sentence formed by using one or more logical connectives? Conditionals always make beginning logic students at least a bit confused. Why are some sentences true, e.g., "If George Washington went to Siberia, then Washington D.C. is the present capital of the United States"? It's a poor example to give to somebody in Logic 101. Better would be, "If I gave you a penny, then I gave you a dollar." Supposing that I never gave you a penny, but I gave you a dollar, I would not have been lying when I said what I said. I only said what would happen if I gave you a penny. I never said what I would do if I did not give you a penny.

Counterfactual conditionals are also "if...then..." sentences, but they seem odd because they say things such as,

If the experiment had run one more time, then a photon would have contributed to the fourth interference fringe on the left and made it have an even 100 members rather than 99.

The most interesting thing about that sentence is perhaps that it cannot be disproven. Not only that, but experimenters can't just turn the apparatus back on and pump out one more photon. Setting up the initial circumstances happens only once. When you start again you get another set of initial circumstances. You try to prepare everything exactly the same way, but even in multiple runs of one apparatus (e.g., running multiple photons through one at a time) there are sources of experimental error such as a truck running into the loading dock and shaking the whole building. It's an act of faith to say that the apparatus stays absolutely constant for the length of x runs of such an apparatus. (That's one good reason for doing lots of runs on an experiment.)

In the original experiment proposed by Einstein, the one that suggested entanglement, two masses were linked together so that at least three points were in contact for some time and then somehow a slight force between them sent them onto diverging trajectories. Einstein argued that he could learn both the position and momentum of the leftmost mass, despite what Bohr claimed, because he could measure the position of the leftmost mass and then take advantage of the fact that the positions and momentums of both masses were interrelated by their having a joint position and joint momentum before they were nudged apart. So he would just measure the momentum of the rightmost mass and do his arithmetic. That idea assumed that the left and right masses each had a definite mass and a definite momentum to start with. Not even Schrödinger liked the idea that interfering with one did something that messed up the measurements on the other.

Einstein wanted to be able to say, "I measured the momentum and got one definite result. In doing so I messed up the possibility of getting a measure of the original position of the mass. If I had measured the position instead, then I would have gotten the true position of the mass and I would have messed up the possibility of getting a clean measurement of the momentum. Messing up measurements doesn't mean that there was nothing there to be measured in the first place. There was a definite momentum and a definite position. The fact that quantum mechanics can't deal with this situation indicates an incompleteness of your system. And, anyway, I can get from mass B what I messed up getting from A. It is absolutely impossible that my measuring A did anything to mess up my measurement of B." Of course not everybody agreed with Einstein.

Before getting a clear insight into what the experimenters and/or theoreticians are saying, it is a little difficult to sort out how this whole business will apply to Bell inequalities. It is at least clear that he calculates the probabilities for various outcomes on the assumptions of those who believe in hidden variables. Those hidden variables would take part in propositions such as, "If we were able to access these hidden variables, then we would be able to give deterministic predictions pertaining to the laboratory subjects." In that word "were," we get the counterfactual conditional characteristic of this sentence.

So far I have studied two documents cited. The first one was badly written in the sense that I had to guess what the guy was trying to say. The second was quite long and filled with detail. It was written for people who had already been involved in discussing counterfactual definitenes for some time and at some depth. Does anybody have a favorite?P0M (talk) 05:12, 28 February 2014 (UTC)

I just found one quotation that may help unsnarl this thing:

Rossella Lupacchini….illustrates by means of a simple Mach-Zehnder interferometer the occurrence in this interpretation of counterfactual effects, i.e., physical effects brought about by things that might have happened, although they did not happen.

The Foundations of Quantum Mechanics… Edited by Claudio Garola, Arcangelo Rossi, p. 16

Could that be all that the interferometer device is supposed to illustrate? Something like, "If a photon had gone by the southern route it would have 'learned' that the way was blocked, so, somehow, going only by the northern route it knew that the southern route was blocked and there could not be any interference, so when it came to the final beam splitter..." It did what? Why is only one path traced out there? 50% of the photons are going to be reflected and 50% are going to pass through, no?

Is the d part of this diagram meant to indicate a single event in which a photon emerges where it would never have emerged if the southern route had not been blocked? I guess that must be it. If that is what is going on, then note that whether there is an element of counterfactuality in this situation or not depends on what model, what conceptual scheme, an interpreter imposes on the universe. If it is one that says that photons are either waves or particles, and that as they interact with the first beam-splitter they necessarily "decide" to be either a wave or a particle, then there is a paradox. Let's say that the photon hits the first beam-splitter and says, "I am a wave." It goes both ways until it hits the mirror M and starts to bounce to the ground. It is simultaneously going by the northern route and it would have done as it did in (a) and bounced over to detector B. But it doesn't see its other half coming so it orders itself retroactively to exit the first beam-splitter as a particle. Meanwhile, the wave on the southern half somehow knows that it is not going to meet its other half by heading south at the new mirror M, so it retroactively (how else) tells itself not to become a wave, a little loop in time takes place, and it comes out of the first beam splitter as a particle. Or perhaps it "originally" came out of the beam-splitter as a particle. Since we've altered time, of course it came out of the beam-splitter as a particle. So it either goes by the southern route and shows up wherever the mirror M directs in onto, or it goes the northern route and ends up at A or at B. Since we are telling the tale of one photon that ended up at detector A, we will just look at what a photon has to do to "decide" that it can go through the beam-splitter and enter detector A. It has to know that it isn't going to meet itself coming by the southern path. How does it know that? Well, were it to have (counterfactually) gone by the southern route it would have found that out.

At some point, maybe it was among the Copenhagen group that assembled around Bohr, people started talking as though a photon is either a wave or else it is a particle. This bifurcation took hold even though everybody knew that "wave" and "particle" are words that apply to macro-world phenomena. If it is either one or else the other, then the experiment gives the proper setting for an impossibility, a photon that shows up as a particle and does not display any signs of wave behavior such as interfering with itself, a photon that has a clear which-way to its travels, a photon that as a particle travelled and could only have travelled as a single thing by a single path in a single trip, and a photon that could have had no interaction with the new mirror on the southern route. Yet it acted as though it were in full "knowledge" or "experience" of the southern path. In other words, there had to have been "physical effects brought about by things that might have happened, although they did not happen."

Somebody who holds another interpretation, say the one that claims that photons in flight are superpositions of wave and particle characteristics, will say that the photon went down both paths, and the probabilities for showing up somewhere are shown in (c), and the fact that this particular photon showed up at detector A was just what you should expect, over a long series of runs of the experiment, 25% of the time. P0M (talk) 08:47, 28 February 2014 (UTC)

The main body of the article is a mishmash of speculative philosophical babble, original research written in the form of an essay, and a tiny smidgen of decent physics. Stapp pretty much originated the debate on counterfactual definiteness, but his work has been heavily criticized. I'd be expecting to see references to Zeilinger, Kwiat, Aharonov, Vaidman etc.

The diagram illustrates a variant of the well-established Elitzur–Vaidman bomb tester. If one adjusts the interferometer so that 100% of the photons emerge at B, then detection of a single photon at A tells you that something has disturbed the experimental setup without you needing to know anything more about the system. Fig. d shows the disturbing influence as being a mirror M having been introduced into the southern path. The photon emerges from A without having interacted with M (i.e. there was no exchange of energy between that particular photon and M). The photon has been involved in an interaction-free measurement. That's all there is to the paradox, without the philosophical babble. Stigmatella aurantiaca (talk) 10:00, 28 February 2014 (UTC)

It's not clear to me why the photon could not emerge from the second beam splitter and be detected at B. Just removing that detector would mean that a photon could show up on the wall. But if the bomb is a dud, the photon would show up there because there is no possibility of its showing up in the bomb fuse. I guess that means that researchers only keep bombs in cases where a photon is detected at A. So half of the good bombs that don't blow up are kept. I guess they could run anything that survived and went into the B pile back through the mill. So they would end up with 1/4 + 1/8 +... With 3 going through during the first testing they would only keep 1/16 of the good bombs.

The makers of the bomb tester would have to have very good quality control with regard to the device that delivers only one photon.

Imagine that they have a stockpile of these bombs somewhere. They must be kept in total darkness. A thief in the darkness of the night manages to get into the warehouse holding all the bombs. He strikes a match to see what's in there. The match is later found, virtually unburned, under the dead body of the thief. ;-)

What is the counterfactual aspect of the bomb experiment? "If the photon that tested this bomb had been detected by the bomb trigger, then the bomb would have blown up!"?

I have the feeling that there is something more substantial to the proper subject matter of this article. Counterfactual statements are pretty tame. Counterfactual definiteness is serious business if it forms an inconsistent part of the Bell arguments. P0M (talk) 18:03, 28 February 2014 (UTC)

Useful link

I have found one link that leads to an actual article. It is long and detailed, but at least it is serious and has some connection with real physics issues. I have added it to the bottom of the list. P0M (talk) 18:46, 28 February 2014 (UTC)

Quite a bit of disagreement, it seems, between different authors. Figuring out current consensus will be a bit difficult. Stigmatella aurantiaca (talk) 08:24, 1 March 2014 (UTC)

One good thing is that one of the principle authors contributes to physics articles on Wikipedia. He has his own website (http://www.phys.tue.nl/ktn/Wim/muynck.htm) and his own take or interpretation of quantum mechannics.

I think the term itself is a potent source of trouble. It is murky enough that it is easy to think that, e.g., there is a special kind of definiteness that is not subject to expression as a matter of fact. If that sounds nutty, that is what I was trying for. Sometimes it is assumed to be a sort of code word for realism, for a belief in hidden variables, or in other words for beliefs such as that electrons simultaneously have real positions and real momenta.

A couple of sources indicate that the Bell Inequalities are subject to criticism for themselves depending on assuming that there are some real values that would have been discovered had people bothered to investigate or if people had not messed up the possibility of doing those observations by making other observations. (The detective rushes into the middle of a crime scene to be able to catch sight of the fleeing murderer, but in the process he obscures the footprints left by the felon.) I remember seeing a reference to one paper that claimed to demonstrate 'how little the Bell arguments actually depended on counterfactual definiteness.' So it sounds like there really is something to be explicated for the general audience if all the highly qualified and pre-defended arguments can be clarified.P0M (talk) 23:13, 1 March 2014 (UTC)

Counterfactuals in the laboratory and in logic

Assuming that the counterfactual definiteness business has something to do with counterfactual conditions and also with Bell Inequalities that deal with what would happen if researchers had not done something, I'll summarize what I know about the logical side of things. Maybe it will help us all look for useful materials, or otherwise define what we are looking for in a better way.

Researchers do some experiments in which momentum is detected and then they take further measurements in each run of the experiment to try to look at position. Perhaps they prepare photons identically, measure them for momentum using the identical physical operations, and then catch the photons on a distant detection screen. It may turn out that the photons land all over the place. Now some other researcher comes along after the fact and says, "If you hadn't measured Momentum then you could always measure and even predict Position." I'll symbolize that statement as: ¬M → P

M P | M → P | ¬M  P |  ¬M → P  Logical predictions:

1 1 |   1   | 0  1  |    1    (R does measure momentum and does get position) (1) XXX

1 0 |   0   | 0  0  |    1    (R does measure momentum and does fail to get position) (2) lab: as expected

0 1 |   1   | 1  1  |    1    (R does not measure momentum and does get position) (3) lab: as expected

0 0 |   1   | 1  0  |    0    (R does not measure momentum and does not get position) (4) lab: as expected.

However, the predictions are wrong, so we can't accept the last researcher's position. (1) is logically true according to the premise offered by the last researcher, but it must fail in the laboratory. It fails because while if... then... statements are treated as logically true when the "if" part is false but the "then" part is true, logicians just mean that if something doesn't happen for the reason stated in the logical reason, but happens for some other reason, that doesn't make the original argument a lie. Saying "You'll die if you drink that poison," does not become false simply because you die of a heart attack instead. But in the physics lab case the individual was asserting that giving up measuring momentum was necessary and sufficient to getting good position readings, but we've kept the momentum measurements and logic says we could get position measurements. What logic "means" is that there is no reason why the position measurements should not be available somehow or "once in a while," but what happens in the physics lab shows that getting a good position measurement after the same photon was tested for momentum would be a very dicey thing indeed. (2) is true logically and it also is true in the physics lab. (To do the logic carefully, we should have supplied something like, "For all x runs of an experiment, if you don't measure Momentum then you can always measure position.") (3) is a good prediction in the lab. (Occasionally there will be experimental error, so the "for all x" part would be too optimistic.) (4) says that if the researchers do not measure momentum and they also do not get good position readings, then there is proof that the logical argument is wrong. The lab is going to support the theory offered because they aren't going to find this evidence.

The physics problem is more like a situation in which someone who has embezzled money claims: "If you hadn't caught me, then I would have replaced the money the next day." We cannot test the alternative offered. The best we could hope to do would be to recreate the original "experiment" and wait one additional day to see if the second accountant replaced the stolen money. The two parts are, strangely, true, if by "true" you mean "not falsified." Like an untested theory, we can't prove that that man would not have replaced the money, and we can't know that "in another universe" the investigators would not have waited a couple of days. So the whole thing stands in the real of "not yet falsified."

I think that anybody familiar with the twists and turns of contrafactual conditionals would have avoided just the word "contrafactual" unless they actually wanted to jump into this particular briar patch.

If they did mean to use this word in all its social context, then the accompanying lesson must be that whenever you start talking about alternate pasts, or "what would have happened if only you hadn't let the cat out" situations, you risk getting into a lot of unintended complications.

So what was happening with Bell researches that brought in assertions about what might have been? Anything? If Bell said something like, "If they had not measured the position, then they could have gotten a good measurement of momentum," are people possibly objecting, "How do you know?" Is Bell then saying, "Because that's what always happens in the lab?" That would be my guess from reading between the lines of some of the things I've seen thusfar. But at this point it is just a guess. P0M (talk) 23:13, 1 March 2014 (UTC)

I did a reality check on contrafactual conditionals and it is even worse than I remembered. The philosophers can't agree on how to handle them. P0M (talk) 02:45, 2 March 2014 (UTC)

The way forward

It has become clear to me that this article must have been written to fill out a "red link" in the article on Bell Inequalities. So we need to look at articles on Bell Inequalities that mention "counterfactual."

One of them gives a good clue about how researchers are using "counterfactual."

As the Bell’s inequalities are derived within LR [local realism], counterfactual reasoning is acceptable and no additional hypotheses are necessary to derive the eq.13. But, there is still the problem of assigning values to the counterfactual terms. In order to solve this problem, a “possible world” must be defined to ensure logical consistency [7]. There is no mystery in this situation, but simply lack of information. Let see an example of everyday life: let suppose that when I go to the pub and find my friend Alice there, the result of measuring the variable A ≡ “I find Alice in the pub” is 1, and 0 when I do not find her there. After many visits to the pub, I measure the expectation value 〈A〉=0.3. Now, let consider the question: “what is the expectation value of A when I don’t go to the pub?” If it is assumed that Alice and the pub have a well defined existence even when I do not go there (roughly speaking, if Realism is assumed), the expectation value of A is some well defined number, say, q. But, the value of q cannot be known with the information available at this point. More information is needed, regarding the behavior of Alice and the properties of the pub when I am not observing them (i.e.: a “possible world” must be defined) to assign a numerical value to q.

Once a possible world is defined, the counterfactual terms can be calculated. Depending on the possible world chosen, the eq.1 is retrieved, or not [6]. The important point here is that the definition of a possible world unavoidably involves one assumption additional to LR. This weakens the consequences of the violation of the Bell’s inequalities reported in the experiments, for the violation can be interpreted as a refutation of the additional hypothesis, not necessarily of LR. Note that this weakening does not arise from an experimental imperfection (as in the case of the loopholes [1]). The setup is assumed ideally perfect. The weakening arises from the fact that real measurements are performed during time, and that it is impossible to measure with two different angle settings at the same time. For, time is a magnitude that takes any given value only once.

These quotations are taken from: "On the meaning of an additional hypothesis in the Bell’s inequalities." Alejandro A. Hnilo. http://arxiv.org/pdf/1402.6177%E2%80%8E

A useful secondary source says:

Finally, one subtle assumption of the Bell inequalities is counterfactual definiteness. The derivation refers to several objective properties that cannot all be measured for any given particle, since the act of taking the measurement changes the state. Under local realism the difficulty is readily overcome, so long as we can assume that the source is stable, producing the same statistical distribution of states for all the subexperiments. If this assumption is felt to be unjustifiable, though, one can argue that Bell's inequality is unproven. In the Everett many-worlds interpretation, the assumption of counterfactual definiteness is abandoned, this interpretation assuming that the universe branches into many different observers, each of whom measures a different observation.

http://www.quantiki.org/wiki/Bell%27s_theorem

Here is the basic problem, as I conceive of it from the sources I've read. Sorry, but at this point I can't prove any conclusions.

A major finding of quantum mechanics is:

For all particle_x measurements, accurate measurement_x of position means that accurate measurement_x of momentum is impossible.

For all particle_x measurements, accurate measurement_x of momentum means that accurate measurement_x of position is impossible.

For any particle_x measurement of a given quantum characteristic, EPR claim that the particle_x of the covariant condition would fall within range A.

For any particle_x measurement of a given quantum characteristic, Bell claims that the particle_x of the covariant condition would fall within range B where B > A.

However, particle_x having been measured for, e.g., position, it is impossible to know any true value for the momentum of particle_x. So it is impossible on the basis of empirical measurements to know the value of B.

Is it, nevertheless, possible to know an accurate range of values for B after investigating a wide range of cases?

It's too late at night to dig out specifics on Bell inequalities. Does this much look right?P0M (talk) 08:02, 2 March 2014 (UTC)

P.S. See Greene, The Fabric of the Cosmos, p. 107ff, for an example of how a quantum view of possible outcomes differs from a classical view. Running through all of the logical possibilities based on two sets of premises leads to different ranges of possible values. P0M (talk) 08:22, 2 March 2014 (UTC)

Greene on Bell

Here is something I wrote for an earlier discussion:

I don't have a lot of time right now to go through The Fabric of the Cosmos and pick up the points that Brian Greene makes. Basically he says that something happens and that what happens is very hard to reconcile with any attempt that tries to limit the reasons for some changes to physical processes that proceed at the speed of light. For right now, let me show you the chart that results when you follow through his argument/analogy about correlations. His way is the reverse of what Tercer says, as I have remarked before. I think this difference is a function of the way the experiments are set up, not due to any error on Greene's part.

He sets up (starting on page 107) the following analogy or thought experiment. There are two "boxes" linked to receptors for two sets of entangled particles. Each box gives a measurement of three different characteristics of the incoming particles by opening doors (labeled G(rey), W(hite), and B(lack) in the chart below). Opening each door gives a different measurement, and the measurements are reported in terms of red and blue lights (labeled r and b). If the two boxes give the same response (color) when a door on each is opened, then that is counted as "+1", and if one shows red and the other shows blue, then that result is counted as "-1."

Look at the second and third lines in the chart below (Preset and Match). If the boxes are pre-programmed (i.e., if the experiment is controlled by hidden variables) then when the G doors of the two boxes are opened, both see blue, if G is opened on one box and W is opened on the other box then blue is seen, when G is opened on one box and B is opened on the other box, then blue is seen on one and red is seen on the other (so no match). So if you go through and look at all possible connections, you win 55% of the time.

What he concludes is that if you are measuring pairs (canonical conjugates) of phenomena in the same system of entangled particles, pure chance will let you "win the shell game" 55% of the time if there are hidden variables, but that Copenhagen quantum mechanics, if true, means that you can only win 50% of the time. Here is a picture of his two "boxes" and the chart I made:

Two boxes, one on Earth and one far away

	G-W-B	Choose	Choose	Choose	Choose	Choose	Choose	Choose	Choose	Choose	SUM
Preset	b-b-r	G-G	G-W	G-B	W-G	W-W	W-B	B-G	B-W	B-B
Match?		+1	+1	-1	+1	+1	-1	-1	-1	+1	55%
Preset	b-r-b	G-G	G-W	G-B	W-G	W-W	W-B	B-G	B-W	B-B
Match		+1	-1	+1	-1	+1	-1	+1	-1	+1	55%
Preset	b-r-r	G-G	G-W	G-B	W-G	W-W	W-B	B-G	B-W	B-B
Match		+1	-1	-1	-1	+1	+1	-1	+1	+1	55%
Preset	r-b-b	G-G	G-W	G-B	W-G	W-W	W-B	B-G	B-W	B-B
Match		+1	-1	-1	-1	+1	+1	-1	+1	+1	55%
Preset	r-b-r	G-G	G-W	G-B	W-G	W-W	W-B	B-G	B-W	B-B
Match		+1	-1	+1	-1	+1	-1	+1	-1	+1	55%
Preset	r-r-b	G-G	G-W	G-B	W-G	W-W	W-B	B-G	B-W	B-B
Match		+1	+1	-1	+1	+1	-1	-1	-1	+1	55%

If Bell is right, i.e., if there are no "gotcha" factors that will mess up his analysis, then experiments would either show a true 50% figure when QM predicts 50%, or not. If not, then QM is missing some factor of reality and is incomplete.

End of copied material.

The reference to Tercer above was, I think, because most examples show quantum mechanical range of variables greater than classical mechanics range of variables, but the way Greene has set up his example it is classical physics that would provide a larger range (i.e. 55% rather than 50%).

If I'm following the general argument correctly, then we should be looking at the empirical basis for the results that Bell predicts. I think people are claiming that he is depending on an argument that says that the "machine" always kicks out the same range of answers regardless of any other factors, so the results cited to establish Greene's inequalities should be reliable even though they are not empirical measures that pertain to the same photons or whatever quantum entities were being empirically measured. They are probably right, but is there any real problem with doing so? Technically it is "counterfactual" if I say it rains ten days this year on Xero Island but I haven't actually set out measuring devices and monitored them this year and am instead depending on weather records taken over the last 100 years that show that rain days have a maximum of 10.9 and a minimum of 10.0. If somebody's weather prediction says it ought to have rained on 100 days this year, do I have to interview the last resident of Xero Island to feel justified in questioning the new climate model? How much statistical information on weather and climate do I need before I can be reasonably assured that 100 days a year indicates a problem with the theory that predicts it? P0M (talk) 09:08, 2 March 2014 (UTC)

We know why classical reasoning comes up with 55%. We just worked that out on the chart above. Bell comes along and says, "55% is wrong. It should be 50%."

"Sez who?!"

"Quantum mechanics says it is 50%."

"Theory says. Theory says. Did you measure it? Of course you didn't because it is impossible to do so, as quantum mechanics itself says."

"True, but we've done a gazillion tests of quantum mechanics and they all show that this is the way nature works. I'll concede that if you look at an individual photon you can see almost anything. But we are not talking about a small sample here. This is a large sample, and something would have to be seriously wrong with quantum mechanics if the results came out to anything but 50%. You, on the other hand, predict 55% forever and always, and that clearly is not what is happening."

How far off from what the major papers are claiming is this scenario? I doubt that Greene could be wrong, but I don't recall him discussing contrafactuality.P0M (talk) 09:22, 2 March 2014 (UTC)

Greenstein and Zajonc, chapter 5, gives a complete treatment, math included. However they do not touch explicitly on counterfactuality. P0M (talk) 18:27, 2 March 2014 (UTC)

useful to Google for:

counterfactual "Mach-Zehnder interferometer"

There are many references. The main idea seems to be that "had the bomb been 'measured' it would have exploded, but it wasn't 'measured' and yet we know what would have happened, so we can salvage this bomb." P0M (talk) 18:59, 2 March 2014 (UTC)

From there we presumably go to: "Can, e.g., the angular momentum of a photon be known without measuring it? Yes, if we measure the angular momentum of its entangled twin. Does that mean that if we measure the angular position of the first photon then we can likewise know the angular position of the photon whose spin we just measured?" P0M (talk) 19:20, 2 March 2014 (UTC)

Draft for discussion

I think I am beginning to see what is going on with "counterfactual definiteness." Here is a revised draft of the lede of the article. Tell me if I've got anything wrong.

Counterfactual definiteness is a term used in discussions of physics calculations. The adjective "counterfactual" is also involved in physics discussions. The word "counterfactual" does not mean "characterized by being opposed to fact." Instead, it is used to characterize values that could have been measured but, for one reason or another, were not. Counterfactual measurements are measurements derived by means other than direct observation, such as by calculation on the basis of well-substantiated theory. If one knows an equation that permits deriving reliably expected values from a list of inputs to the physical system under investigation, then one has "counterfactual definiteness."

Some examples of counterfactuality produce effects that have immediate and observable consequences in the macro world. One such example is the Elitzur-Vaidman quantum bomb inspector. See the illustration for details.

Counterfactual measurement in quantum mechanics. "If the photon had not appeared in the "Good Bomb" detector where would it have been detected?" The Elitzuer-Vaidman bomb tester depends on a counterfactual measurement possibility in quantum mechanics. A photon can appear in the "Good Bomb" detector providing that there is a detector of photons in the fuse of the bomb in the test box. The Mach-Zehnder interferometer is adjusted so that no photons are absorbed by the detector at the position marked "Good Bomb." With nothing in the test box, a single photon emitted by the laser at the lower left corner will travel by both paths. The wave-functions that emerge in the detector at the position marked "Good Bomb" will be 180° out of phase, will cancel each other out, and so no photons will be detected there and the "Good Bomb" indicator will not light. The wave-functions that emerge in the detector for "Dud" will be exactly in phase and a photon will be detected, causing the "Dud" indicator to light. When placed in the test box, a bomb with no photon receptor in its fuse will make the interferometer behave just the way it does when there is nothing in the box. So the "Dud" indicator will light appropriately. When a bomb with a good fuse is placed in the test box, then half of the time the wave-function will allow the single photon to show up in the bomb fuse, and the bomb will explode. The other half of the time the other copy of the wave-function will travel by the lower path. When it encounters the second beam-splitter it will be divided once more. Half of the time it will light up the "Good Bomb" indicator, and half the time it will falsely light up the "Dud" indicator. So all of the duds must be run through the apparatus until all the good bombs have either exploded or have been identified by having the "Good Bomb" indicator light up.

It is easy to demonstrate the meaning, and even the efficacy, of counterfactualy definite states in such situations as the Mach-Zehnder interferometer being used as a detector of bombs that are not duds. Something that is (half of the time at least) not measured can nevertheless provide knowledge of its presence that is useful for diagnosing the suspect bomb fuses. The experiment (presumably minus the explosives) has been successfully tested in the laboratory. The models used to understand the behavior of single photons in such an interferometer have been shown adequate to predict what precentage of functioning bombs would be exploded, and what percentage could be recovered from the total accumulation of suspect bombs by repeatedly winnowing the pile until no more bombs ever exploded. The consequence of quantum mechanics theory that disturbed Einstein was that entities that had once been joined (e.g., by remaining in mutual contact at a minimum of three points for some measurable period of time) would continue to behave in some ways like a single entity after they had become separated. The issue was conceived at that time, and continues to be conceived by most researchers, as a matter of locality, i.e., in the model of the universe offered by classical physics it is impossible that entities separated in space-time can effect each other (except by intermediating field forces such as gravity, magnetic fields, etc.) so theoretical consequences drawn from quantum mechanics indicating that measurement of one entangled object could give give related information about an object it is entangled with even across great distances offended Einstein's sense of how the universe works. That knowledge would be "counterfactual" in the sense that the conjugate state of the entangled twin is known without any empirical measurement having been made.

Those who hold similar points of view to Einstein's are naturally interested in preserving locality, i.e., in accounting for the effects of entanglement by means other than implying that some kind of interaction occurs instantaneously across great distances. One prominent attempt to remove the challenge to locality was originated by Einstein and his group. It has come to be called dependence on hidden variables.

For decades no decisive argument could be offered for or against the explanations drawing on hidden variables. Then John Bell established a mathematical proof to show that there could be no hidden variables that would account for the statistical results of the quantum experiments being considered. Bells work, called the "Bell Inequalities," were taken to disprove the idea of hidden variables and to reinforce the explanations involving non-locality.

Comments on the draft

The above should make it fairly clear what "counterfactual definiteness" is, and the next step would be to explain the relevance of this source of indeterminacy to the question of why correlations seem to occur in entanglement investigations, the fact that only "locality" has been considered as a possible answer to why strange entanglement phenomena occur, etc.P0M (talk) 03:35, 8 March 2014 (UTC)

I've added to the text above, and changed the diagram so that people who have been looking at the other schematics I've done won't have to turn diagrams upside down in their heads to compare things. The de Muynck DeGaere and Martens article is very helpful in figuring out what the discussions are all about, but it is challenging to follow because it brings in reference to a great many interpretations of quantum mechanics and how each would try to argue from the same set of facts. P0M (talk) 07:39, 9 March 2014 (UTC)

I think I've taken this about as far as possible. I need comments soon. If I see no objections within a couple of days I will start to merge this material with what is in the present article. (I've tried to incorporate the useful parts already, but some parts are more in the way of contentions, and they may have their value too.) P0M (talk) 18:57, 9 March 2014 (UTC)

I think Counterfactual definiteness is more philosophy then science. According the description of the article and Bradford about everything is counterfactual. The average reader (anyway me) will not understand what is special about that (or perhaps it is not special at all). I think it needs simple examples to show what Counterfactual definiteness is and what is scientifically special. The bomb is just standard double slit wave explanation. DParlevliet (talk) 08:14, 10 March 2014 (UTC)

Classical physics has no concept of photon, no way of talking about a single quantum of energy. A classical wave is a disturbance, as if of a medium (usually called the aether). A wave, when split by a barrier, goes on both sides of the barrier and impacts the "shore" (i.e., two detectors on one side and the bomb fuse on the other side), and the impacts are proportional to how much of the wave goes on either side of the barrier. In the bomb experiment, every time a light turned on light would be detected both by a regular detector and by the bomb. The same amount of incoming wave energy would be divided in the same proportion every time. If the energy received were less than that needed to set the bomb off on the first trial then the same amount of energy would hit the bomb the next time with the same results. If the energy received were enough to set off the bomb on one test, then it would be enough to set off any bomb that was functional on the first or on any run of the test apparatus. The result would be that all bombs would be tested as duds or that all good bombs would be set off by the testing apparatus.

The purpose of the article is not to announce personal opinions as non-physicists about how the universe works. The purpose of the article is to summarize and explain what the experts in the field have worked out or are still working on. Dr. de Muynck is a university professor who spent his whole professional life in this field, and even though he has retired from teaching he is still active in the field. The paper that he and his colleagues wrote should have enough material to keep anybody busy for many hours to understand completely. It appeared in a peer-reviewed journal. Other physicists, equally qualified, have written other articles and books that try to make clear and well grounded conclusions in a field that is fraught with difficulties. There is no way that you or I should push their sincere efforts aside.

Bradford certainly does not say that "everything is counterfactual." Please be responsible when you attribute conclusions to other people.P0M (talk) 17:00, 10 March 2014 (UTC)

I don't object your article. I just don't understand it. But it is probably useful for those who are interrested. But so many text to explain such a simple example is somewhat overdone, for me. DParlevliet (talk) 22:52, 10 March 2014 (UTC)

I tried to look, but it is difficult to me to understand so long and informal text (sorry, this is probably a drawback of being a mathematician). Anyway, my understanding of counterfactual definiteness can be found here, if you like. Boris Tsirelson (talk) 06:48, 11 March 2014 (UTC)

Your text is a lot clearer and more useful than anything else I have found. I presume that counterfactual definiteness is possible in classical thermodynamics even though it is a model that does not attempt to treat of "microscopic particles." There only has to be reasonable grounds for affirming that repeating the experiment but, e.g., raising the temperature x degrees centigrde, one could expect to get definite and reliable results.P0M (talk) 18:08, 11 March 2014 (UTC)

Thank you for the compliment!

Yes, in classical thermodynamics; and everywhere in classical physics. I do not know whether there exists "quantum thermodynamics", but quantum statistical physics surely exists, and CFD should be possible there, except maybe some fine points. Really, as far as I know, CFD is not possible only in presence of entanglement on the observable level. Indeed, we know that existence of atoms, and the discreteness of the set of possible atoms, is purely quantum effect. And we all consist of atoms. In this sense we all contain entanglement. But usually it is hidden deeply inside. For this reason CFD was unproblematic in the classical physics (of large systems of atoms). ONLY when quantum entanglement becomes explicitly observable, CFD becomes problematic. Boris Tsirelson (talk) 20:27, 11 March 2014 (UTC)

Could you clarify? This is the point that has blocked me for some time. People declare that Bell is in trouble because of dependence on CFD, for instance, but they don't really say at what point. One can observe quantum entanglement, in a sense, when doing experiments, such as you describe in your article referenced above, that produce higher rates of matching than can be accounted for on the basis of classical physics, hidden variables, etc. The higher rates found in the lab are observations, not work done by filling in data tables on the basis of theory. I have seen discussions about what rates of matching might be present in the absence of an observer under different assumptions about the impact the observer could be having on the measurements observed. (These observations could all be in accord with classical conditions pertinent to observation. ) So if somebody compares classical projections including different ways of estimating statistical results with the results that are actually seen in the lab, then there would be different degrees of mismatch between classical and quantum predictions. However, I can't see how that kind of thing would cast doubt on the Bell equations, so I suspect that I must have the whole thing wrong. P0M (talk) 20:54, 11 March 2014 (UTC)

I did not see what these (strange?) people wrote. But I do not understand "Bell is in trouble because of dependence on CFD". Bell inequalities are derived in several assumptions. The point is to prove that at least one of them is wrong. Yes, CFD is one of them. So, what is the trouble? If someone is not inclined to believe in CFD from the beginning, then this man has no reason to be bothered with entanglement. The same for someone not inclined to believe that information never propagates faster than light. And so on (according to the list of classical premises). Bell theorem is intended for people that are very much inclined to keep alive ALL fundamental features of the world-view of the classical physics. For others, "Bell is in trouble" in the sense that they are not interested in his theorem. Boris Tsirelson (talk) 06:35, 12 March 2014 (UTC)

And what is the CFD in the used "Bomb" example above? DParlevliet (talk) 08:07, 12 March 2014 (UTC)

Since the article was written by a mathematician/physicist it is easily possible that I missed the point(s). To be fair, I was coming into the middle of the movie when I read that article. It seemed to be part of a series of discussions, most of which had already been well hashed over by the concerned researchers. I thought that the main point was to put up an argument in favor of some variety of realism or quasi-realism that Einstein would have been happy with. One way to do that would be to defend the idea of hidden variables or to find something that would provide exact "reasons" for why quantum particles do what they do instead of just having calculations for the probabilities of their doing various things.

Maybe I am misunderstanding what you just wrote. However, you did say: if "Bell inequalities are derived in [= based on?] several assumptions. The point is to prove that at least one of them is wrong. Yes, CFD is one of them." When you say what the point is, I am not sure whose point this is. Are you expressing Bell's intention? Somehow I don't think so. I'll proceed on the assumption that it was the point being hammered at by the opposition to Bell, so maybe I'll go completely wrong. If I am going to go completely wrong, then skip the rest of what I say below.

If there is no really valid way to calculate or otherwise obtain the counterfactual data (and for that to be true Bell must have overlooked something major I suppose) then one of the assumptions that the Bell inequalities are based on is shot down. If Bell thought he had a valid theoretical test that could be performed in the laboratory, but at least one of his premises was wrong, then his whole attempt to disprove hidden variables would be in question.

That result would not make me happy, but it would make some other people happy. There actually were two articles involved in the "CFD is to blame" argument, together over 50 pages or so, and in so much detail and talk about different interpretations that I find it difficult to relocate some passages that I remember reading. I think there was an assertion, similar to yours, that there are several assumptions, one of them being CFD, and another being non-locality, that Bell based himself on to try to prove that what appears to be entanglement cannot be explained on the basis of hidden variables or on any idea that says that, e.g., when two masses have been in contact on at least 3 points for some measurable time and are subsequently separated then by examining one you can learn the position or the momentum of the other because the two had their respective positions and momenta from the time they separated. The article wanted to argue that the reasoning by which Bell tried to show the hidden variables people wrong was flawed because of his assumptions and that the phenomena advertised as entanglement were not due to our everyday ideas about locality being wrong, but due to some defect in Bell's use of CFD. Probably I have just failed to understand these articles properly. Now it is too near to dawn to think clearly. P0M (talk) 08:46, 12 March 2014 (UTC)

"Are you expressing Bell's intention? Somehow I don't think so." — Surely I do. I do not know why do you doubt it. Let me quote my text (that you've found useful).

'A combination of empirical facts, observed or only hypothetical, incompatible with the conjunction of three fundamental assumptions about nature, called "counterfactual definiteness", "relativistic local causality" and "no-conspiracy" (see below), but compatible with the conjunction of the last two of them ("relativistic local causality" and "no-conspiracy").' (I call it "empirical entanglement"; probably this is my neologism, but we may use it for now.)

Quantum physics predicts "that the empirical entanglement must occur in appropriate physical experiments".

This is what Bell theorem says.

Yes, you may say Bell uses hidden variables rather than CDF. Yes; but these two languages are equivalent (at least, when discussing Bell theorem).

Thus, I really insists that one of equivalent formulations of Bell theorem is: ASSUMING the three fundamental assumptions (above) we can DERIVE an inequality (on observable results) that, according to the quantum theory, must be VIOLATED in an appropriate experiment.

Ultimately, Bell theorem states: If the relevant prediction of the quantum theory is true then the empirical entanglement exists in the nature.

Boris Tsirelson (talk) 10:19, 12 March 2014 (UTC)

.

But wait; I can say it better. More clearly.

I quote my text again:

The simplest example of empirical entanglement is presented here. First, its idea is explained informally.

Alice and Bob pretend that they know a 2×2 matrix

${\begin{pmatrix}a&b\\c&d\end{pmatrix}}$

consisting of numbers 0 and 1 only, satisfying four conditions:

$a=b,c=d,a=c,$ but $b\neq d.$

Surely they lie; these four conditions are evidently incompatible. Nevertheless Alice commits herself to show on request any row of the matrix, and Bob commits himself to show on request any column. We expect the lie to manifest itself on the intersection of the row and the column (not always but sometimes). However, Alice and Bob promise to always agree on the intersection!

Assume in addition that Alice and Bob are widely separated and the local causality applies.

Question 1: is it logically possible that Alice and Bob fulfill their promise?

Question 2: are you able to instruct Alice and Bob, how to fulfill it?

Please think, until you answer "no" to Question 2, and to Question 1 there are two answers: "no" if CDF is a logical necessity (some people believe that it is), but "yes" if CDF is not a logical necessity (some people believe that it is not);

and in addition, understand that the same holds if you replace CFD with existence of hidden variables.

Boris Tsirelson (talk) 11:24, 12 March 2014 (UTC)

Is it permitted to "write" a superposition of 0 and 1 in each cell of the matrix? I saw this question already on your website,

What?? This question on my site? Surely you are joking, mister Moran! Alice and Bob did not learn physics. --Boris

No. I meant I saw the question on how to work with such a matrix.P0M (talk) 00:29, 14 March 2014 (UTC)

and it is of course easy to see that in the classical mode of operation, whichever way you try to fill out the matrix, it doesn't work. I spent a few hours last night experimenting in my virtual laboratory, and without electrocuting myself. However, I have yet to figure out a way to make Alice and Bob ready to take out the great casino with ever-increasing chips in their hands. To me is seems that in a classical world if Alice were only required to call out the values of her row, and Bob were only required to call out the values of his column, then in 2/12 of the possible cases they could have results that would neither announce anything that makes b = d but also announces only cases in which a = b = c. For instance:

Alice reports a = 0 & b = 0 Bob reports a = 0 & c = 0

Alice reports a = 1 & b = 1 Bob reports a = 1 & c = 1

That's almost 17% assuming that Bob is not required to report that his values break the c = d requirement. If he could get away with not reporting that his b and d values are equal, then he could make the results appear to be 1/3. It is only by not calling attention to data that is available for investigation if any judge cares to go into the matter that there can be anything but complete failure. But the numbers may be useful in comparison with what I think may happen if Alice and Bob each own a couple of coins that are entangled, forming a web of sorts between them. In some cases they can do much better than 0 and not break any of the rules of the game:

If when asked, Alice generates a & b or c & d, and Bob generates a & c or b & d,

Alice reports a = 0 & b = 0 Bob reports a = 0 & c = 0

Alice reports a = 1 & b = 1 Bob reports a = 1 & c = 1

Alice reports c = 0 & d = 0 Bob reports a = 0 & c = 0

Alice reports c = 1 & d = 1 Bob reports a = 1 & c = 1

That's 4 out of 16 cases for 25%. None of them violate the requirement that b ≠ d. If Bob avoids generating b & d measurements, then he can get 4 out of 8 for 50%.

Perhaps that's not what you have been aiming at. P0M (talk) 20:09, 13 March 2014 (UTC)

I bother, do you take into account that Alice must show on request the requested row? Either requested to show the first row (a,b), or alternatively, the second row (c,d). And Bob - the requested column. But this is one-time game. Alice will not answer a second question. Nor Bob. Boris Tsirelson (talk) 20:46, 13 March 2014 (UTC)

I considered all possibilities of what could be asked of Alice and what could be asked of Bob to complete the interrogation. If, for instance, Alice is asked for numbers for c and d, tosses her coins, and comes up with 1 and 0, then if the entanglement is such that Bob must get the same 1 and 0, and the inquisitor asks him for b and d, the answers will be inconsistent with the demand that c = d. Three times out of four the demand that a = b = c = d, and that b ≠ d will not be met. Assuming an equal distribution of "must shows," 1 in 4 is the best results I can produce. Sorry, but I must leave the virtual world for an hour or two. P0M (talk) 22:30, 13 March 2014 (UTC)

You set the problem up. I'm not sure where you are going with it. I suspect that I will be unable to get the correct answer to the problem. But I am curious enough to spend some time on it.P0M (talk) 00:08, 14 March 2014 (UTC)

Ah. The moran (sic) has made some progress. I have discovered how to make Alice and Bill always fail. But this is no fairytale, and no way in sight to make straw turn into gold. P0M (talk) 00:29, 14 March 2014 (UTC)

But now I see that further work in that direction only makes another way to make Alice and Bill always fail.P0M (talk) 02:04, 14 March 2014 (UTC)

You are right: "1 in 4 is the best results I can produce", and in fact, it is the best result compatible with CFD (which is not so difficult to see). The next step should be, to understand that if CFD is not assumed then it is logically possible to reach 100% success. (If in trouble, see my Citizendium text for a hint.) Boris Tsirelson (talk) 06:32, 14 March 2014 (UTC)

"y = f(x). Existence of this function f is called "counterfactual definiteness"". I mentioned above that about everything (classical) is CFD. So that is right? My confusion was that the bomb example suggested that CFD is a strange effect in QM, but your explanation is that the absence of CFD is a strange QM effect. DParlevliet (talk) 08:57, 13 March 2014 (UTC)

Sure. The absence of CFD is a strange QM effect. As well as the absence of local realism, etc. Boris Tsirelson (talk) 09:57, 13 March 2014 (UTC)

Thanks, now I understand. In the "bom" experiment a photon detected in A = dud bomb, so that is CFD. There should be an example where CFD is absent. DParlevliet (talk) 10:07, 13 March 2014 (UTC)

Ah, it seems I understand why the confusion. In the quantum universe, the way from the past to the future is (generally) not a single history but a bunch of (alternative) histories. "Quantum possibility is more than classical possibility but less than classical reality". Yes; but CFD is another thing. Boris Tsirelson (talk) 10:09, 13 March 2014 (UTC)

So is the bomb CFD (as mentioned in the article) or not? And why? DParlevliet (talk) 11:56, 13 March 2014 (UTC)

Assume CFD. Think about the (counterfactual) result of the (unperformed) experiment: photon counting in the beginning of the blue path and also in the beginning of the red path. There are two cases: count in blue path only, or count in red path only. In the latter case the bomb explodes (unless a dud). In the former case the photon should exit to "dud" or "good" detectors with probabilities 1/2, 1/2 (irrespective of the bomb). Thus, we never get sure that now we have a good bomb. But we do! Therefore CFD must fail.

Really, this is an intuition, not a proof of failure of CFD. The best proof we can have is that violation of Bell inequality falsifies at least one of three assumptions; one of these is CFD; others are "relativistic local causality" and "no-conspiracy". Some people prefer to conclude that relativistic local causality fails. Others, that "no-conspiracy" fails. I prefer to conclude that CFD fails. But this is an opinion, not proof. Boris Tsirelson (talk) 12:55, 13 March 2014 (UTC)

And more simple: suppose the black box contains only a 50% mirror. The input is a photon the output can be a photon or no photon. So no CFD? DParlevliet (talk) 13:21, 13 March 2014 (UTC)

Too simple. A mirror consists of (a lot of) atoms, in thermal motion. They can work as a (quite good) source of pseudorandomness. Maybe the output is a function of (the input and) this (pseudo-random) internal state. Then CFD holds. Boris Tsirelson (talk) 14:34, 13 March 2014 (UTC)

Mmm... then the bomb experiment as an black box without looking inside. Input is the bomb, output the green "good bomb" detector. If this detector detects a photon, the input is 100% sure a good bomb. Of course the bomb can explode or detector "dud" detects the photon, but that depends on 50% reflection mirrors, which hold CFD. DParlevliet (talk) 14:53, 13 March 2014 (UTC)

First, the mirror does not really "hold CFD". Rather, in a too simple situation the violation of CFD remains implicit (and so we see no reason to abandon CFD). Every electron in every atom violates CFD each picosecond (just ask yourself, on which side of the nucleus is the electron situated now... the atom will be ionized immediately if you'll know... also if you do not know but the nature knows... but it is not); but this remains implicit for us. The entanglement between the blue and red paths makes CFD violation explicit for us. Boris Tsirelson (talk) 18:58, 13 March 2014 (UTC)

I thought that according QM positions of atoms or electrons can by definition not be determined, so not-CFD. But anyway, the detection by the detectors can be calculated with wave's formula. So y = f(x) is known, with sine and cosine. 100% sure. All is in the black box without knowing what is in there, and an exact formula which predicts with a certain output what the input was. That looks quite CFD. DParlevliet (talk) 21:38, 13 March 2014 (UTC)

Wow! Did you forget that QM formulas give probabilities, not outcomes? According to QM, the choice of one of the possible outcomes (according to these probabilities) comes "from thin air", not caused by anything, absolutely random; this is CFD violation; but one could hope (and was hoping before Bell) that a future better theory will give the same probabilities while satisfying CFD. Boris Tsirelson (talk) 06:23, 14 March 2014 (UTC)

But in the (new) article I now see the bomb experiment being used as an example of CFD. DParlevliet (talk) 11:07, 15 March 2014 (UTC)

Indeed. It does not make me happy. And moreover... see the (new) section below. Boris Tsirelson (talk) 16:21, 15 March 2014 (UTC)

@Tsirel
When you said: the "Bell inequalities are derived in several assumptions. The point is to prove that at least one of them is wrong. Yes, CFD is one of them," I had the wrong idea of what you meant by "derived in." I thought you meant "derived on the basis of" or "derived from" and by "several assumptions" I thought you might mean several proposed axioms. It was difficult for me to imagine that Bell would create a deductive system based on axioms that he chose himself, and then try to prove that one of his proposed axioms was wrong. The result of such an exercise would be only the self-defeat of a would-be theorist. The word "derived" threw me off.

No, sorry; just the opposite. You had the absolutely right idea of what I meant by "derived in." Not at all "the self-defeat of a would-be theorist", since a lot of people, including Einstein and myself (sorry for such non-modest pairing) agree that "his proposed axioms" are the fundamental principles of the world-view of classical physics, and crash of any one of them would be (or "is"), well, if not a tragedy then at least a dramatical revolution, considerably harder than Einstein's relativity of space-time. Boris Tsirelson (talk) 06:33, 16 March 2014 (UTC)

Blessed are they who sojourned here

In this world's fateful hours-

For they were summoned by the angels

As guests to a great feast;

They witnessed spectacles majestic,

Were brought into the inner circle,

And, while there, drank immortal life

From heav'n's own chalice!

Tutchev, translated from Russian

.

I observe with mixed feelings that now Bell theorem starts to interest wide circles of people, and often these people are so far from physics that the horror and the greatness of the greatest scientific revolution means just nothing to them; just a stupid fuss with stupid assumptions and their stupid implications. I do not know whether there exists a source intended to explain the situation to these. Sources assume implicitly that the reader shares with physicists at least the most fundamental features of their world-view. A problem... Maybe Feynman's "character..." should be treated as a prerequisite for interested non-physicists. Boris Tsirelson (talk) 07:00, 16 March 2014 (UTC)

You may have answered my question while I was formulating it in my mind. I can see the deep importance of the three axiomatic statements. They do not form the entirety of what would be a view of the core of modern physics. So my question is whether anyone has given a coherent synthesis of the most fundamental concepts, the ones on which everything else depends. There is an element of discipline in putting ideas together in a formal presentation. That discipline can pay off by providing a stable foundation and serving as the basis for useful elaborations and applications.P0M (talk) 07:56, 16 March 2014 (UTC)

"They do not form the entirety of what would be a view of the core of modern physics" — No, why "modern"? Classical. Modern (namely, quantum) physics conflicts with (at least one) of these.

O.K. I should have said two of them and the denial of the third, but as individual observations about the universe standing by themselves they do not tell the person who is not in daily contact with the world of practicing physicists how or why "his proposed axioms are the fundamental principles of the world-view of classical physics," nor do they give much of a clue as to how the list when reduced to two principles forms something revolutionary in human thought.

No, physics is not axiomatic. Probably hopeless. But see Hilbert's sixth problem.

Of course it is not axiomatic. On the other hand, there are some ideas that one has to accept just to work out the consequences of theory and experiments the way practicing physicists do. So it would make sense to me to work out clearly what insights are important and central and concentrate on educating people about them. To do so in an economical way it would seem important to have a clear understanding of how they fit together and then to convey a clear understanding to others.

There was just no point in formulating "the entirety of what would be a view of the core of classical physics" before the Bohr–Einstein debates. Then, some critical fragment was elucidated in EPR paper. But only Bell theorem was the reason to formulate those that are its assumptions. This is probably the only (semi)axiomatic approach to a physical problem. Indeed, Bell theorem remains unprecedent, unique in its kind. Boris Tsirelson (talk) 08:54, 16 March 2014 (UTC)

My impression is that real progress in science began to be made when researchers started not with the earth at the center of the universe but with balls rolling down inclined planes. They went from the concrete to the abstract. Finally we have gathered enough by inductive reasoning to start integrating things, and as the integration carries upward toward the most general we begin to find out that some of the useful rules of thumb used in the beginning to good effect now have to be given up. Now the discussion about things like counterfactual definiteness gets carried out in journal articles where often it is so much an "in" thing that unexplained acronyms are used with abandon. I suspect that grad students in physics pick these things up by osmosis.

Maybe there needs to be a single article on the three: local reality, no conspiracy, and counterfactual definiteness.

I did, on Citizendium. There, an editor is a verified expert, and may say: "I know what I am writing". Here an editor is just someone, and has to collect truth from reliable sources. I do not criticize this system, it must be like that. But it makes it impossible to use here my article therefrom. By the way, I do not think you may cite my Citizendium article here (as you did); not a reliable source. Maybe all written there can be sourced (contrary to your phrase "I am pretty sure that nobody has"); but I am lazy to seek; sorry. Boris Tsirelson (talk) 12:38, 16 March 2014 (UTC)

It looks to me like you have an idea that is very important. I am pretty sure that nobody has put things together before, at least not in writing. All of the pieces could be assembled into a single article on Wikipedia and it could probably be done without getting the article deleted. However, declaring that the three pieces fit together to make a revolution or a paradigm shift will hit the problem that it is original research. In this case the solution is to get your ideas published in a peer-reviewed journal. Meanwhile, you could try telling me how to fix the following paragraph, or tell me it is all wrong and better to go away. P0M (talk) 17:36, 16 March 2014 (UTC)

Oops! It is nearly impossible to me to imagine how you can interpret my words. Not only my presentation of Bell theorem does not constitute "a revolution or a paradigm shift", but also the (quite famous) Bell theorem does not. The quantum theory does. Neither Bell nor me could not imagine such immodesty. I could not published that in a jornal just for that reason: only on the wikipedia slang that can be called "original research" (by synthesis); for a journal, it is all absolutely clear to experts. My effort was pedagogical, not scientific. Basically, all that is already contained in our article Bell's theorem (did you look there?). Only in somewhat different form, with different emphasis, and slightly different terminology. Boris Tsirelson (talk) 18:38, 16 March 2014 (UTC)

The Bell inequalities are relationships calculated on the basis of three axiomatic characteristics of classical physics: counter-factual definiteness, relativistic local causality, and "no conspiracy." Bell demonstrates that classical physics conforms itself to these three requirements, and that, given these requirements, certain predictions are confined within bounds expressed by the Bell inequalities. Bell has expressed the limits of what, under a classical physics picture of the world, can be delivered. His ultimate goal, however, is to further demonstrate predictions based on quantum mechanics that go beyond the reach of, or "violate," the classical limits to what can be successfully predicted.P0M (talk) 17:36, 16 March 2014 (UTC)

Sorry if the above is a little long-winded, but I am trying to get the right way to say things so that people unfamiliar with the realities encountered in the physics lab will not get carried away upon taking something the wrong way.P0M (talk) 22:36, 15 March 2014 (UTC)

About this paragraph I am somewhat reluctant since anyway it does not solve the problem that the article is (in my opinion) not quite on CFD. But if you insists... Specifically, your language (scientific I mean, not English, of course) sounds somewhat nonnative (and no wonder: you came from very different culture). "relationships calculated"? Rather, bounds (or inequalities) proved (or derived). "three axiomatic characteristics of classical physics"? Sounds somewhat unusual. "Bell demonstrates that classical physics conforms itself to these three requirements"? No, he did not bother to. He took it for granted, since it was not new; it was discussed a lot since 1935 (EPR). Also, Bell did not use CFD; he used hidden variables; now it is understood to be equivalent. "given these requirements, certain predictions are confined within bounds"? Predictions of which theory? Well, of every theory that obeys these requirements. "classical limits to what can be successfully predicted"? Successfully? Who is meant to be successful, and in which project? And after all, we already has a (much more expertly written) article about Bell inequalities; why explain the same here? Boris Tsirelson (talk) 19:00, 16 March 2014 (UTC)

Thanks. I am not concerned to apply the paragraph. I am just trying to clarify some of the points in earlier discussion.P0M (talk) 19:47, 16 March 2014 (UTC)

Is this really an article about counterfactual definiteness?

As for me, it is not. It is rather an article on counterfactuality, a rather vague wide scope idea. Counterfactual definiteness is another story! It is a crisp, well-defined assumption about the nature. Or do I stick to an obsolete terminology? If so, I am sorry. Otherwise, these two quite different notions should be discussed separately. Either in separate articles, or in separate sections of a single article. See also Counterfactual (disambiguation), Elitzur–Vaidman bomb tester, and "Unperformed experiments have no results". Boris Tsirelson (talk) 16:19, 15 March 2014 (UTC)

I agree. One of the major problems with trying to sort through what other people have said about the subject is the way people use the term. I will make a division of sections in the article. P0M (talk) 17:11, 15 March 2014 (UTC)

I think that putting in a separate section for "counterfactuality" of whatever it should be called is not a good solution. For one thing, there is just enough similarity to confuse beginning students. On top of that, I do not know of any other examples to put into such an article.

Other people were involved before I came along. So let me see whether anybody objects to what is now the top part of the article. I think it is written clearly enough that there are not ambiguities that could make some agree to what is said without realizing I meant something else. As for the bomb tester, after looking at the availability of other Wikipedia articles that describe it, I think it should go. I will wait for any further discussion before deleting it. P0M (talk) 18:02, 15 March 2014 (UTC)

The assertions in the section on main theoretical considerations are mostly lacking in citations. If anyone knows of useful papers to cite, please help make this part better. P0M (talk) 17:58, 15 March 2014 (UTC)

The content in "main theoretical considerations" seems to have come from User:Kuratowski's Ghost. I haven't found published sources to back up what he has written. P0M (talk) 19:18, 15 March 2014 (UTC)

I've gone back over the history of that part of the article. One of the unsourced statements goes all of the way back to the stub from which this article started. If nobody will supply citations then I will delete unsourced material and replace it with what I can find citations to support.

I am not inclined to spend time on merging the bomb detector into the article about it, so I will delete it. The materials will still be available in the history of this article.P0M (talk) 19:53, 16 March 2014 (UTC)

Removed sentence about locality

If physics gives up locality, that amounts to admitting the possibility of sudden "magical" intervention in human affairs from unknown and possibly unknowable sources of action.

I removed the above sentence for two reasons. First, it was in the wrong place; locality was treated earlier in the section. Second, the reference to magic and unknowable things is somewhat over-the-top; the debate actually occurs between more down-to-earth alternatives, such as: the heat equation with infinite propagation speed, the incompressible Euler equation with a global equation for pressure fields; various well-defined mathematical theories where determinism fails, such as Markov processes or evolution equations that are not well-posed with respect to initial conditions.

178.38.122.45 (talk) 12:12, 10 April 2015 (UTC)

I agree. Boris Tsirelson (talk) 13:03, 10 April 2015 (UTC)

Rather old-fashioned account

The account as it was before I made a couple of edits just now was very, very old-fashioned. Referring to Stap is going back to pre-history. Counterfactual definiteness is an uncontroversial property of classical physics. We can, in classical physics, talk about what would happen to the tea in my tea-cup if the moon were suddenly removed. Surely it would effect the gravitational pull on that body of fluid, and it would start to change shape and move towards a slightly different position, even if only a tiny bit. Just because the “measurement” is impossible does not mean that we cannot do calculations with it. Quantum mechanics does not *forbid* certain simultaneous measurements. It just disdains from talking about them. For practical purposes, that is no problem, since nobody can imagine how such a measurement could be performed. The story about disturbances is a classical, intuitive, attempt to rationalise the situation. It makes students feel comfortable with the situation. Richard Gill (talk) 15:03, 15 April 2022 (UTC)

The usual measurement postulates actually forbids certain simultaneous measurements. Perarve (talk) 08:52, 16 April 2022 (UTC)

I know. But we are talking about a competing framework, local realism, which does not have a “ban” on measuring several things at the same time. And anyway, counterfactual definiteness is not about what measurements can be done or not done in the real world. It’s about a mathematical framework which merely includes “what would have been seen, had the measurement been a different one”. Your objection is the standard objection of quantum physicists since Bell first published his work. It shows a deep misunderstanding of Bell’s purpose. Of course, if you are completely happy with QM, then Bell’s theorem is completely uninteresting. It’s just some totally irrelevant mathematics, if no use whatsoever to practicing physicists. Richard Gill (talk) 09:17, 16 April 2022 (UTC)