Abstract
Paul Busch argued that the positive operator (valued) measure, a generalization of the standard quantum observable, enables a consistent notion of unsharp reality based on a quantifiable degree of reality whereby systems can possess generalized properties jointly, whereas related sharp properties cannot be so possessed (Busch and Jaeger in Found Phys 40:1341, 2010). Here, the work leading up to the formalization of this notion to which he made great contributions is reviewed and explicated in relation to Heisenberg’s notions of potentiality and actuality. The notion of unsharp reality is then extended further by the introduction of a distinction between actual and actualizable elements of reality based on these mathematical innovations.
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Notes
From here forward, we will also call such representatives “properties,” as a matter of shorthand.
It should be noted here that this move does not render the unsharp-reality approach and modal approach in the usual sense of that term, in that the move does not require the postulation of an addition sort of system state beyond the quantum state and, a forteriori, no additional definite states of properties as in modal approaches to quantum mechanics. Indeed, the unsharpness central to the approach taken here is understood as a denial of such definite property values.
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Jaeger, G. Quantum Unsharpness, Potentiality, and Reality. Found Phys 49, 663–676 (2019). https://doi.org/10.1007/s10701-019-00273-z
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DOI: https://doi.org/10.1007/s10701-019-00273-z