The following specific comments raised my brows:
gill1109 wrote:By “realism” I mean counterfactual definiteness, which is a property classical mathematical physical models tend to have: they allow us to define, alongside of the outcomes of the experiments actually performed, also outcomes of experiments which could have been performed instead. Deterministic models have this property. Also non-deterministic, as long as any randomness is local.
gill1109 wrote:Bell’s modelling of the EPR-B experiment, with functions A(a, lambda) and B(b, lambda), allows one to define outcomes of all possible spin measurements alongside of the measurements actually done. This model has the property of counterfactual definiteness. It is “local” because Bob’s measurement choice does not effect Alice’s outcome.
I think a discussion about the meaning of Counterfactual Definiteness (CFD) is badly needed. Like many other concepts such as "randomness", "locality", "realism". etc, the concept of "counterfactual definiteness" (CFD) has been bastardized by many in the quantum foundations community. One of the reasons nobody understands QM is because the meanings of words are free for all. It's the wild-wild west and don't even get me started about "virtual" particles.
A careful look at CFD will reveal that it does not mean what most people in the Bell community mistakenly think it means. First, let us start with a few definitions:
Realism: Realism means objects have properties independently of measurements. It does not mean measurements can't create some new properties, it only means something exists even if it is not being measured (cf. the moon exists even if nobody is looking).
Counterfactual: Counterfactual means contrary to actuality. Say Alice must make one measurement, for which she must pick one of two settings {x, y}. After the measurement, the actual setting is the one she picked and the counterfactual setting is the one she did not pick.
Counterfactual Definiteness: Now consider conditional statements of the form if Alice picks x she will obtain result -1. Although written out as a sentence, these types of statements are equivalent to statements of the form . These are statements made before the measurement -- a prediction of what will happen if the conditions are met. Such statements are not limited to any specific type of model (local, classical or quantum). Every model/theory that makes predictions, makes conditional statements similar to this before any experiments are performed. CFD only comes into the discussion when discussing the situation after the measurement has been made. Say Alice actually picked "y" instead of "x". In this case, "x" is the counterfactual setting. Counterfactual definiteness simply means the prediction made before the measurement remains valid even after the measurement has been made. In other words, it is still the case that had Alice picked "x", she would have obtained the -1 result. This is the meaning of CFD.
A little bit of common-sense will reveal that CFD is universally applicable in logic, and even QM makes use of CFD all the time. The truth value of conditional statements like "if X then Y", is not affected if the antecedent is false.
A prime example of the use of CFD in QM from Bell's paper is the following:
Consider a pair of spin one-half particles formed somehow in the singlet spin state and moving freely in opposite
directions. Measurements can be made, say by Stern-Gerlach magnets, on selected components of the
Spins and , If measurement Of the component , where is some unit vector, yields the value
+ 1 then, according to quantum mechanics, measurement of must yield the value -1 and vice versa.
In other words, Bell says, according to QM . This is a prediction (a conditional statement). Counterfactual definiteness simply means that the prediction is definite (still valid, not changed), even if Alice and Bob actually measured at settings instead of . QM says it must be so.
Therefore those who claim that CFD does not apply to QM are sorely mistaken. I'll leave it as an exercise for the reader to demonstrate from Bell's quote above how "realism" is used in QM. Another exercise for the astute reader, expand Bell's equation 14b using conditional statements, and see if you can figure out the logical contradiction [hint: viewtopic.php?f=6&t=292].