Editing Counterfactual definiteness (section)

==Theoretical considerations==
An [[interpretation of quantum mechanics]] can be said to involve the use of counterfactual definiteness if it includes in the mathematical modelling outcomes of measurements that are counterfactual; in particular, those that are excluded according to quantum mechanics by the fact that quantum mechanics does not contain a description of simultaneous measurement of conjugate pairs of properties.<ref>[[Henry P Stapp]] ''S-matrix interpretation of quantum-theory'' Physical Review D Vol 3 #6 1303 (1971)
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For example, the [[uncertainty principle]] states that one cannot simultaneously know, with arbitrarily high precision, both the position and [[momentum]] of a particle.<ref>Yakir Aharonov et al., "Revisiting Hardy's Paradox: Counterfactual Statements, Real Measurements, Entanglement and Weak Values, p. 1, says, "For example, according to Heisenberg’s uncertainty relations, an absolutely precise measurement of position reduces the uncertainty in position to zero Δx = 0 but produces an infinite uncertainty in momentum Δp = ∞." See https://arxiv.org/abs/quant-ph/0104062v1 arXiv:quant-ph/0104062v1</ref> Suppose one measures the position of a particle. This act destroys any information about its momentum. Is it then possible to talk about the outcome that one would have obtained if one had measured its momentum instead of its position? In terms of mathematical formalism, is such a counterfactual momentum measurement to be included, together with the factual position measurement, in the statistical population of possible outcomes describing the particle? If the position were found to be '''r<sub>0</sub>''' then in an interpretation that permits counterfactual definiteness, the statistical population describing position and momentum would contain all pairs ('''r<sub>0</sub>''','''p''') for every possible momentum value '''p''', whereas an interpretation that rejects counterfactual values completely would only have the pair ('''r<sub>0</sub>''',⊥) where [[⊥]] (called "up tack" or "eet") denotes an undefined value.<ref>Yakir Aharonov, et al, "Revisiting Hardy's Paradox: Counterfactual Statements, Real Measurements, Entanglement and Weak Values," p.1 says, "The main argument against counterfactual statements is that if we actually perform measurements to test them, we disturb the system significantly, and in such disturbed conditions no paradoxes arise."</ref> 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.<ref>Inge S. Helland, "A new foundation of quantum mechanics," p. 3.</ref>

The dependability of counterfactually definite values is a basic assumption, which, together with "time asymmetry" and "local causality" led to the [[Bell inequalities]]. Bell showed that the results of experiments intended to test the idea of [[Hidden variable theory|hidden variable]]s would  be predicted to fall within certain limits based on all three of these assumptions, which are considered principles fundamental to classical physics, but that the results found within those limits would be inconsistent with the predictions of quantum mechanical theory. Experiments have shown that quantum mechanical results predictably exceed those classical limits. Calculating expectations based on Bell's work implies that for quantum physics the assumption of "local realism" must be abandoned.<ref>Yakir Aharonov, et al, "Revisiting Hardy's Paradox: Counterfactual Statements, Real Measurements, Entanglement and Weak Values," says, "In 1964 Bell published a proof that any deterministic hidden variable theory that reproduces the quantum mechanical statistics must be nonlocal (in a precise sense of non-locality there in defined), Subsequently, Bell' s theorem has been generalized to cover stochastic hidden variable theories. Commenting on Bell' s earlier paper. Stapp (1971) suggests that the proof rests on the assumption of "counterfactual definiteness" : essentially the assumption that subjunctive conditionals of the form: " If measurement M had been performed, result R would have been obtained" always have a definite truth value (even for measurements that were not carried out because incompatible measurements were being made) and that the quantum mechanical statistics are the probabilities of such conditionals." p. 1 arXiv:quant-ph/0104062v1</ref> [[Bell's theorem]] proves that every type of quantum theory must necessarily violate [[locality principle|locality]] ''or'' reject the possibility of extending the mathematical description with outcomes of measurements which were not actually made.<ref>[[David Z Albert]], ''Bohm's Alternative to Quantum Mechanics'' Scientific American (May 1994)</ref><ref name=Cramer1986 />

Counterfactual definiteness is present in any interpretation of quantum mechanics that allows quantum mechanical measurement outcomes to be seen as deterministic functions of a system's state or of the state of the combined system and measurement apparatus. Cramer's (1986) [[transactional interpretation]] does not make that interpretation.<ref name=Cramer1986>{{cite journal | last=Cramer | first=John G. |author-link=John G. Cramer| title=The transactional interpretation of quantum mechanics | journal=Reviews of Modern Physics | publisher=American Physical Society (APS) | volume=58 | issue=3 | date=1986-07-01 | issn=0034-6861 | doi=10.1103/revmodphys.58.647 | pages=647–687| bibcode=1986RvMP...58..647C }}</ref>