## Final Report Summary - QUANTDISPOSITION (Philosophy of quantum mechanics and the metaphysics of dispositional properties)

The central part of the project “Philosophy of quantum mechanics and the metaphysics of dispositional properties” was an attempt to develop and apply the notion of quantum dispositional properties in order to analyse some metaphysical consequences of quantum theory, in particular its non-local character. Although it is commonly accepted that quantum mechanics indeed implies the existence of non-local, instantaneous causal influences between spatially separated objects, the nature of these influences is still open to debate. The most radical view is that the quantum principles admit the possibility of a physical influence between the selection of a physical observable for measurement in one region, and the physical state in another, space-like separated region. Arguments in favour of the existence of such strongly non-local interactions have been proposed and developed by H.P. Stapp in a series of publications. In the preliminary stage of the project, Stapp’s recent argument has been scrutinised. The conclusion of this analysis is that the argument requires stronger premises than those Stapp explicitly admits. One such premise may be Einstein’s criterion of reality, stating that if the outcome of a possible measurement can be predicted with certainty, then the system possesses a categorical property corresponding to this outcome. It turns out that this criterion can be rephrased in terms of quantum dispositions that reveal particular outcomes upon measurement. Seen in this perspective, the problem of non-locality in quantum mechanics can be expressed in the question of how to explain the fact that the choice of measurement settings in one system can instantaneously create a quantum disposition of another, distant system.

The notion of quantum dispositions has been further clarified. Generally, two types of quantum dispositions should be distinguished: value dispositions (deterministic and probabilistic dispositions to reveal particular values upon measurements) and dynamic dispositions (dispositions to evolve into certain future states as a result of interactions with the environment). The project was focused primarily on the value dispositions and on one particular conceptual problem which they give rise to. An argument has been presented to the effect that the characterisation of value dispositions leads to circularity when coupled with the standard quantum-mechanical characteristic of measurements. It has been showed that the circularity problem can be avoided in the case of probabilistic dispositions thanks to the theorem proved by P. Mittelstaedt which establishes that the postulate called “the probability reproducibility condition” can be derived from the probability-free “calibration” postulate. However, the problem remains for deterministic dispositions, i.e. dispositions associated with eigenstates. Several suggestions of how to avoid the problem have been proposed, but they require further investigations into the role the notion of measurement plays in quantum mechanics.

The notion of quantum dispositions has been further clarified. Generally, two types of quantum dispositions should be distinguished: value dispositions (deterministic and probabilistic dispositions to reveal particular values upon measurements) and dynamic dispositions (dispositions to evolve into certain future states as a result of interactions with the environment). The project was focused primarily on the value dispositions and on one particular conceptual problem which they give rise to. An argument has been presented to the effect that the characterisation of value dispositions leads to circularity when coupled with the standard quantum-mechanical characteristic of measurements. It has been showed that the circularity problem can be avoided in the case of probabilistic dispositions thanks to the theorem proved by P. Mittelstaedt which establishes that the postulate called “the probability reproducibility condition” can be derived from the probability-free “calibration” postulate. However, the problem remains for deterministic dispositions, i.e. dispositions associated with eigenstates. Several suggestions of how to avoid the problem have been proposed, but they require further investigations into the role the notion of measurement plays in quantum mechanics.