Unsharp Quantum Reality

TL;DR

This paper explores how positive operator measures extend the concept of quantum observables to include unsharp properties, providing a consistent framework for joint properties and a potentiality-based interpretation of quantum probability.

Contribution

It introduces a unified view of unsharp reality using POMs, linking potentiality to actualization and offering a single-case interpretation of quantum probability.

Findings

Unsharp properties are represented as elements of unsharp reality.

Potentiality acts as a causal agency evolving over time.

Quantum probability is interpreted as a degree of reality.

Abstract

The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it an adequate concept of joint properties. A sharp or unsharp property manifests itself as an element of sharp or unsharp reality by its tendency to become actual or to actualize a specific measurement outcome. This actualization tendency - or potentiality - of a property is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way.