# Counterfactual definiteness

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In some interpretations of quantum mechanics, counterfactual definiteness (CFD) is the ability to speak meaningfully about the definiteness of the results of measurements, even if they were not performed. (i.e., the ability to assume the existence of objects and properties of objects even when they have not been measured). More rigorously an interpretation of quantum mechanics satisfies CFD if it includes in the statistical population of measurement results, those measurements which are counterfactual due to being excluded by quantum mechanical constraints on simultaneous measurement of certain pairs of properties. [1]

For example, by the Heisenberg uncertainty principle, one cannot simultaneously know the position and momentum of a particle. Suppose one measures the position: this act destroys any information about the momentum. The question then becomes: is it possible to talk about the outcome one would have received if one did measure the momentum instead of the 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 was found to be r0 then in an interpretation satisfying CFD, the statistical population describing position and momentum would contain all pairs (r0,p) for every possible momentum value p, whereas an interpretation that rejects counterfactual values completely would only have the pair (r0,⊥) where ⊥ denotes an undefined value.

Counterfactual definiteness is a basic assumption, which, together with locality, leads to Bell inequalities. In their derivation it is explicitly assumed that every possible measurement, even if not performed, can be included in statistical calculations. Bell's Theorem actually proves that every quantum theory must violate either locality or CFD.[2][3]

CFD is present in any interpretation of quantum mechanics that regards quantum mechanical measurements to be objective descriptions of a system's state independent of the measuring process. It is not present in interpretations such as the Copenhagen interpretation and its modern refinements which regard the measured values as resulting from both the system and the measuring apparatus without being defined in the absence of an interaction between the two.