A Quantum View of “Free Existence” as Entangled Indeterminacy

Dale Jacquette

Thierry Paul

Cristian Mariani, Robert Michels, Giuliano Torrengo

It has been argued that quantum mechanics forces us to accept the existence of metaphysical, mind-independent indeterminacy. In this paper, we provide an interpretation of the indeterminacy involved in the quantum phenomena in terms of a view that we call Plural Metaphysical Supervaluationism. According to it, quantum indeterminacy is captured in terms of an irreducibly plural relation between the actual world and various misrepresentations of it.

C. Robert Mesle

Maurice A. de Gosson

The notion of polarity between sets, well-known from convex geometry, is a geometric version of the Fourier transform. We exploit this analogy to propose a new simple definition of quantum indeterminacy, using what we call "hbar-polar quantum pairs", which can be viewed as pairs of position-momentum indeterminacy with minimum spread. The existence of such pairs is guaranteed by the usual uncertainty principle, but is at the same time more general. We use recent advances in symplectic topology to show that this quantum indeterminacy can be measured using a particular symplectic capacity related to action and which reduces to area in the case of one degree of freedom. We show in addition that polar quantum pairs are closely related to Hardy's uncertainty principle about the localization of a function and its Fourier transform.