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On Incompatible Descriptions of Systems Across Scales of Granularity

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Quantum Interaction (QI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9535))

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Abstract

The scientific description of any system depends on the target properties of that description. A detailed, fine-grained account of all individual constituents of a system differs from that of properties at larger scales of granularity, up to the system as a whole. All these level-specific descriptions can be compatible or incompatible with one another. This contribution addresses a particular pair of descriptions of complex dynamical systems: their Liouville dynamics, treating each constituent separately in a conventional state space, and their information dynamics, based on partitions of that state space. The relation between them can be formulated as a commutation relation, in which the commutator quantifies the degree of their incompatibility.

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Notes

  1. 1.

    Epistemic states are actually defined as distributions over measurable sets from a \(\sigma \)-algebra in measure theory (beim Graben and Atmanspacher 2006). For a simplified exposition, which captures the very basic ideas, set-theoretical concepts are sufficient (cf. beim Graben and Atmanspacher 2009).

  2. 2.

    The notion of an extended measurement refers to a series of measurements extending over time t.

  3. 3.

    \(H_{KS} > 0\) is only sufficient because time operators T also exist for mixing systems. Precise conditions under which T exists have been first formulated by Misra (1978), shortly after two pioneering papers by Tjøstheim (1976) and Gustafson and Misra (1976). For a later account see Suchanecki and Antoniou (2003).

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Authors and Affiliations

  1. Collegium Helveticum, University and ETH Zürich, Zürich, Switzerland

    Harald Atmanspacher & Peter beim Graben

  2. Institute of Linguistics, Humboldt University Berlin, Berlin, Germany

    Harald Atmanspacher & Peter beim Graben

Authors
  1. Harald Atmanspacher
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  2. Peter beim Graben
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Correspondence to Harald Atmanspacher .

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Editors and Affiliations

  1. ETH Zurich, Zurich, Switzerland

    Harald Atmanspacher

  2. University of Freiburg, Freiburg, Germany

    Thomas Filk

  3. City University London, London, United Kingdom

    Emmanuel Pothos

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Atmanspacher, H., beim Graben, P. (2016). On Incompatible Descriptions of Systems Across Scales of Granularity. In: Atmanspacher, H., Filk, T., Pothos, E. (eds) Quantum Interaction. QI 2015. Lecture Notes in Computer Science(), vol 9535. Springer, Cham. https://doi.org/10.1007/978-3-319-28675-4_9

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  • DOI: https://doi.org/10.1007/978-3-319-28675-4_9

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