Counterfactual definiteness
In quantum mechanics, counterfactual definiteness is the ability to speak "meaningfully" of the definiteness of the results of measurements that have not been performed. The term "counterfactual definiteness" is used in discussions of physics calculations, especially those related to the phenomenon called quantum entanglement and those related to the Bell inequalities. In such discussions "meaningfully" means the ability to treat these unmeasured results on an equal footing with measured results in statistical calculations. It is this aspect of counterfactual definiteness that is of direct relevance to physics and mathematical models of physical systems and not philosophical concerns regarding the meaning of unmeasured results.
"Counterfactual" may appear in physics discussions as a noun. What is meant in this context is "a value that could have been measured but, for one reason or another, was not."
Overview
The subject of counterfactual definiteness receives attention in the study of quantum mechanics because it is argued that, when challenged by the findings of quantum mechanics, classical physics must give up its claim to one of three assumptions: locality, counterfactual definiteness, and no conspiracy.If physics gives up the claim to locality, it brings into question our ordinary ideas about causality and suggests that events may transpire at faster-than-light speeds.
If physics gives up the "no conspiracy" condition, it becomes possible for "nature to force experimenters to measure what she wants, and when she wants, hiding whatever she does not like physicists to see."
If physics rejects the possibility that, in all cases, there can be "counterfactual definiteness," then it rejects some features that humans are very much accustomed to regarding as enduring features of the universe.
"The elements of reality the EPR paper is talking about are nothing but what the property interpretation calls properties existing independently of the measurements. In each run of the experiment, there exist some elements of reality, the system has particular properties < #ai > which unambiguously determine the measurement outcome < ai >, given that the corresponding measurement a is performed."
Something else, something that may be called "counterfactuality," permits inferring effects that have immediate and observable consequences in the macro world even though there is no empirical knowledge of them. One such example is the Elitzur-Vaidman bomb tester. These phenomena are not directly germane to the subject under consideration here.
Theoretical considerations
An interpretation of quantum mechanics can be said to involve the use of counterfactual definiteness if it includes in the statistical population of measurement results any measurements that are counterfactual because they are excluded by the quantum mechanical impossibility of simultaneous measurement of conjugate pairs of properties.For example, the Heisenberg uncertainty principle states that one cannot simultaneously know, with arbitrarily high precision, both the position and momentum of a particle. 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 r0 then in an interpretation that permits counterfactual definiteness, the statistical population describing position and momentum would contain all pairs for every possible momentum value p, whereas an interpretation that rejects counterfactual values completely would only have the pair where ⊥ denotes an undefined value. 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.
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 variables would be predicted to fall within certain limits based on all three of these assumptions, which are considered principles fundamental to classic 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. In Bell's derivation it is explicitly assumed that every possible measurement, even if not performed, can be included in statistical calculations. The calculation involves averaging over sets of outcomes that cannot all be simultaneously factual—if some are assumed to be factual outcomes of an experiment others have to be assumed counterfactual. Bell's theorem proves that every type of quantum theory must necessarily violate locality or reject the possibility of reliable measurements of the counterfactual and definite kind.
Counterfactual definiteness is present in any interpretation of quantum mechanics that regards quantum mechanical measurements to be objective descriptions of a system's state, but which fails to take into account that not all such objective descriptions can be simultaneously revealed by measurements. Cramer's transactional interpretation is an example of such an interpretation.
Examples of interpretations rejecting counterfactual definiteness
Copenhagen interpretation
The traditional Copenhagen interpretation of Quantum Mechanics rejects counterfactual definiteness as it does not ascribe any value at all to a measurement that was not performed. When measurements are performed, values result, but these are not considered to be revelations of pre-existing values. In the words of Asher Peres "unperformed experiments have no results".Many Worlds
The Many Worlds interpretation rejects counterfactual definiteness in a different sense; instead of not assigning a value to measurements that were not performed, it ascribes many values. When measurements are performed each of these values gets realized as the resulting value in a different world of a branching reality.Thus although unperformed experiments have values, they cannot be used in statistical calculations as one would the single value of a performed experiment. As Prof. Guy Blaylock of the University of Massachusetts Amherst puts it, "The many-worlds interpretation is not only counterfactually indefinite, it is factually indefinite as well."