Unsharp Quantum Reality

P. Busch, G. Jaeger

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)1341-1367
Number of pages26
JournalFoundations of Physics
Issue number9-10
Publication statusPublished - Oct 2010

Bibliographical note

© 2010 Springer Verlag. This is an author produced version of a paper published in FOUNDATIONS OF PHYSICS. Uploaded in accordance with the publisher's self archiving policy.


  • Unsharp observable
  • Unsharp property
  • Fuzzy value
  • Probability
  • Quantum indeterminacy
  • Potentiality
  • Unsharp reality
  • Degree of reality
  • Element of reality
  • Quantum measurement

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