TY - JOUR
T1 - An "anti-Gleason" phenomenon and simultaneous measurements in classical mechanics
AU - Entov, Michael
AU - Polterovich, Leonid
AU - Zapolsky, Frol
N1 - 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.
PY - 2007/8
Y1 - 2007/8
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=34548694783&partnerID=8YFLogxK
U2 - 10.1007/s10701-007-9158-0
DO - 10.1007/s10701-007-9158-0
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AN - SCOPUS:34548694783
SN - 0015-9018
VL - 37
SP - 1306
EP - 1316
JO - Foundations of Physics
JF - Foundations of Physics
IS - 8
ER -