Foundations of Physics Letters

, Volume 14, Issue 2, pp 133–145 | Cite as

Quantaloids Describing Causation and Propagation of Physical Properties

  • Bob Coecke
  • David J. Moore
  • Isar Stubbe
Article

Abstract

A general principle of ‘causal duality’ for physical systems, lying at the base of representation theorems for both compound and evolving systems, is proved; formally it is encoded in a quantaloidal setting. Other particular examples of quantaloids and quantaloidal morphisms appear naturally within this setting; as in the case of causal duality, they originate from primitive physical reasonings on the lattices of properties of physical systems. Furthermore, an essentially dynamical operational foundation for studying physical systems is outlined; complementary as it is to the existing static operational foundation, it leads to the natural axiomatization of ‘causal duality’ in operational quantum logic.

causal duality property lattice Galois adjoint quantaloid 

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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • Bob Coecke
    • 1
  • David J. Moore
    • 2
  • Isar Stubbe
    • 3
  1. 1.Dept. of MathematicsFree University of BrusselsBrusselsBelgium
  2. 2.Dept. of Theoretical PhysicsUniversité de GenèveGenève 4Switzerland
  3. 3.Dépt. de MathématiquesUniversité Catholique de LouvainLouvain-la-NeuveBelgium

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