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In wikipedia article one can read that:

In current theory, post-1972, various interpretations (i.e. theories) of quantum mechanics violate different aspects of Local Realism. But some interpretations only violate aspects of a related principle, known as counterfactual definiteness.[5] [bolded by myself]

Could you please help me understand the subject by explaining to me concept of counterfactual definiteness? It is stated that

In quantum mechanics, counterfactual definiteness (CFD) is the ability to speak meaningfully of the definiteness of the results of measurements that have not been performed (i.e. the ability to assume the existence of objects, and properties of objects, even when they have not been measured).

How can there exist values for each measurement (realism) but one cannot "speak meaningfully of definiteness of the results (...)" (violation of counterfactual definiteness)?

Let us use example of throwing a coin (not real world coin, but coin violating or not violating realism, locality, counterfactual definiteness and such as we please).

With local realism I can (with enough information and computation) state with certainity that result will be for example tails. Is that correct?

With realism (without local realism) I can only say (knowing the forces I used throwing the coin etc.) that there is let's say 75% chance of getting tails and 25% of getting heads. The outcome doesn't deppend on fact of my observation and that alone is realism. Is that correct?

How does counterfactual definiteness apply to that?

Please - explain to me these three concepts (realism, local realism, counterfactual definiteness) and relations between them).

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    The first quote is misleading, local realism implies counterfactual definiteness: if there are "elements of reality" they will determine even the outcomes of measurements precluded from being performed. The converse is false, a theory might fix counterfactual outcomes without admitting any "elements of reality" to do it. Bell's proof of his inequalities goes through with just counterfactual definiteness assumed. The difference between realism and local realism has nothing to do with probabilities and certainty, the former allows faster than light causation and the latter doesn't. – Conifold Dec 1 '16 at 20:36
  • Thank you for response! "a theory might fix counterfactual outcomes without admitting any "elements of reality" to do it" could you please elaborate on that? – PrzemysławP Dec 1 '16 at 23:37
  • It can have a calculational procedure for counterfactual outcomes, for example, without postulating any "elements of reality" that pre-exist to determine them. I suspect that in such a case people would be inclined to make up some "elements of reality", and add them to the theory anyway, because we are wired to think that way. – Conifold Dec 2 '16 at 0:15
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    Realism usually means a lot more than "result is independent of your mind". Quantum mechanical outcomes are perfectly independent of your mind on statistical interpretations, but Einstein complained that they lack realism. To him "realism" apparently meant populating the world with entities, expected to behave according to some classical intuitions ("God doesn't roll dice", etc.), which were supposed to "explain" or "justify" the calculations. – Conifold Dec 2 '16 at 0:51
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    General meaning of "realism" is highly obscure and controversial, and it does not amount to "mind independence", Wikipedia notwithstanding, it is best to avoid the word. Fortunately we do not need to know what it "means in physics", only what Einstein meant by it in the context of QM, and he was more specific. So was Bell because he needed an assumption he could use in his proof rather than the vacuous "nature exists independently of man's mind". – Conifold Dec 2 '16 at 1:31
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In the context of quantum mechanics, the violation of counterfactual definiteness (CFD) means that the laws of standard logic, or standard probability calculus, will be violated if you consider other measurements that the one you performed on the system, and the results that could have occurred (and their probabilities).

The coin toss example is not very appropriate to understand this because there's only one property to be measured. Here's another example. In an experiment, you have two people going out of a room from different opposite doors. They cannot communicate once outside the room. Two experimenters wait for them outside and ask them only one question each, either question A or question B. The people can answer either yes or no. Imagine you run the same experiment several times, and get the following results:

  • When both persons are asked A, at least one of them answers yes
  • When one person is asked A and the other B, if the first answers yes, then the other answers yes too
  • When both persons are asked B, sometimes, they both answer no

Here is how standard logic is violated. Imagine you asked B to both persons and get two "no". Then from rule 2 you can infer: if I had asked A to one or the other, they would have answered "no" (otherwise rule 2 would be violated). Then you infer that if you had asked A to both of them, they would have answered "no". But then, rule 1 is violated...

How can you solve the problem? Obviously you cannot assume that the two persons prepared their response in advance, unless they already knew what questions will be asked. There's no way to prepare answers in advance and respect the three rules (at least one would be prepared to answer "yes" to A, the other "yes" to B, and your would violate rule 3).

You can assume that they communicate by telepathy: they tell each other what question they're being asked. But this violate locality.

If you do not want to violate locality, the only solution is to assume that there's no sense to ask "what would have happened if we'd asked different questions". This is CFD violation.

Now this solution is a bit bizarre, because you can only attribute a definite state to the persons (their dispositions to answer in certain ways) relatively to a set of questions. In the case of quantum mechanics, you can only attribute definite properties to particles relatively to what will be measured on them. This is a mark of contextuality. So this kind of solution is not truly realist.

CFD can be considered a criteria for realism. All this indicates that you have to drop either locality or realism. Either particles "communicate"at a distance, or their previous state is relative to what is measured.

(I did not mention another solution which is the many world interpretation: there, properties are contextual because they are relative to a branch. CFD is violated because measurement results are indefinite: all possibilities occur in different branches. Arguably this is still a realist solution).

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