Foundations of Physics

, Volume 37, Issue 8, pp 1306–1316 | Cite as

An “Anti-Gleason” Phenomenon and Simultaneous Measurements in Classical Mechanics

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Abstract

We report on an “anti-Gleason” phenomenon in classical mechanics: in contrast with the quantum case, the algebra of classical observables can carry a non-linear quasi-state, a monotone functional which is linear on all subspaces generated by Poisson-commuting functions. We present an example of such a quasi-state in the case when the phase space is the 2-sphere. This example lies in the intersection of two seemingly remote mathematical theories—symplectic topology and the theory of topological quasi-states. We use this quasi-state to estimate the error of the simultaneous measurement of non-commuting Hamiltonians.

Keywords

Symplectic Manifold Find Phys Uniform Norm Fuzzy Sphere Quantum Observable 
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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Michael Entov
    • 1
  • Leonid Polterovich
    • 2
  • Frol Zapolsky
    • 2
  1. 1.Department of MathematicsTechnionHaifaIsrael
  2. 2.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael

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