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No-Go Theorem for Modeling with Von Neumann Observables

Andrei Yu. Khrennikov

Springer eBooksJan 1, 20230 citations

Physics of Non-Observables

Paul K. Suh

Bulletin of the American Physical SocietyApr 17, 20070 citations

A No-Go Theorem for Nonlinear Canonical Quantization

Miroslav Engliš

We want to point out the following strengthening of the classical theorem of Groenewold and van Hove: There exists no mapping Op from polynomial observables on the phase space into linear operators on which would map Poisson brackets into commutators, the position and momentum observables p and q into the usual (Schrödinger) position and momentum operators, and would obey the von Neumann rule for and . The point is that neither linearity, nor continuity etc. of Op are assumed.

Communications in Theoretical PhysicsMar 15, 20023 citations

A No—Go Theorem for Nonlinear Canonical Quantization

MiroslayEnglis

We want to point out thc following strcngthcning of the classical theorem of Grocnewold and van Hove:There exists no ,napping Op from polynomial observables f (p, q) on the phase space R2n into linear operators on L2(Rn)which would map Poisson brackets into commutators, the position and momentum obscrvablcs p and q into the usual(Schrodinger) position and momentum operators, and would obey the yon Neumann rifle 0p(cfk) = c 0p(f)k for k = 1,2, 3and c R. The point is that neither linearity, nor continuity etc. of Op are assumed.We want to point out thc following strcngthcning of the classical theorem of Grocnewold and van Hove:There exists no ,napping Op from polynomial observables f (p, q) on the phase space R2n into linear operators on L2(Rn)which would map Poisson brackets into commutators, the position and momentum obscrvablcs p and q into the usual(Schrodinger) position and momentum operators, and would obey the yon Neumann rifle 0p(cfk) = c 0p(f)k for k = 1,2, 3and c R. The point is that neither linearity, nor continuity etc. of Op are assumed.

理论物理通讯：英文版Jan 1, 20020 citations

Physical Observables as Operators

K. Tamvakis

Undergraduate texts in physicsJan 1, 20190 citations

Comment on "Continuous simultaneous measurement of position and momentum of a particle"

Adélcio C. Oliveira

In a recent paper, [Gampel, F. and Gajda, M., Phys. Rev. A 107, 012420, (2023)], the authors claimed they are proposing a new model to explain the existence of classical trajectories in the quantum domain. The idea is based on simultaneous position and momentum measurements and a "jump Markov process". Consequently, they have interpreted the emergence of classical trajectories as sets of detection events. They successfully implemented the model for a free particle and for one under a harmonic potential. Here, we show that the continuous observation limit is a realization of a coherent semiclassical expansion; Also, as has already been demonstrated, the jump process is not necessary and is not observable. In other words, the collapse, as they propose, is a non-go theorem; even if it is real, it can not be measured under the needed assumptions to obtain Newtonian classical dynamics.In a recent paper, [Gampel, F. and Gajda, M., Phys. Rev. A 107, 012420, (2023)], the authors claimed they are proposing a new model to explain the existence of classical trajectories in the quantum domain. The idea is based on simultaneous position and momentum measurements and a "jump Markov process". Consequently, they have interpreted the emergence of classical trajectories as sets of detection events. They successfully implemented the model for a free particle and for one under a harmonic potential. Here, we show that the continuous observation limit is a realization of a coherent semiclassical expansion; Also, as has already been demonstrated, the jump process is not necessary and is not observable. In other words, the collapse, as they propose, is a non-go theorem; even if it is real, it can not be measured under the needed assumptions to obtain Newtonian classical dynamics.

arXiv:2311.06606Nov 11, 20230 citations

Observables have No Value: A no-go Theorem for Position and Momentum Observables

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