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.
|Number of pages||11|
|Journal||Foundations of Physics|
|State||Published - Aug 2007|
Bibliographical noteFunding 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
- Physics and Astronomy (all)