Measurement theory in classical mechanics

Abstract

Measurement theory in classical mechanics is investigated in the formulation of classical mechanics by Koopman and von Neumann (KvN), using Hilbert space. It is shown that the classical and the quantum measurements give different "relative interpretations" of the measurement state and the recording state of the measurement device. The uncertainty relation in classical mechanics is also derived.

arXiv comment22 pages, accepted version for publication in PTEP

References in corpus (8)

• Quantum Games and Quantum Strategies
• Decoherence, Chaos, and the Second Law
• Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement
• Operational Dynamic Modeling Transcending Quantum and Classical Mechanics
• On Koopman-von Neumann Waves
• On Koopman-von Neumann Waves II
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Cited by in corpus (3)

• The Schwinger action principle for classical systems
• Quantization of Nambu Brackets from Operator Formalism in Classical Mechanics
• Incompatible observables in classical physics: A closer look at measurement in Hamiltonian mechanics