An "anti-Gleason" phenomenon and simultaneous measurements in classical mechanics

Michael Entov, Leonid Polterovich, Frol Zapolsky

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1306-1316
Number of pages11
JournalFoundations of Physics
Issue number8
StatePublished - Aug 2007
Externally publishedYes

Bibliographical note

Funding Information:
M. Entov partially supported by E. and J. Bishop Research Fund and by the Israel Science Foundation grant # 881/06. L. Polterovich partially supported by the Israel Science Foundation grant # 11/03.

ASJC Scopus subject areas

  • General Physics and Astronomy


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