Classical mechanics is not h=0 limit of quantum mechanics

Abstract

Both the set of quantum states and the set of classical states described by symplectic tomographic probability distributions (tomograms) are studied. It is shown that the sets have common part but there exist tomograms of classical states which are not admissible in quantum mechanics and vica versa, there exist tomograms of quantum states which are not admissible in classical mechanics. Role of different transformations of reference frames in phase space of classical and quantum systems (scaling and rotation) determining the admissibility of the tomograms as well as the role of quantum uncertainty relations is elucidated. Union of all admissible tomograms of both quantum and classical states is discussed in context of interaction of quantum and classical systems. Negative probabilities in classical mechanics and in quantum mechanics corresponding to the tomograms of classical states and quantum states are compared with properties of nonpositive and nonnegative density operators, respectively.

14 pages, to appear in Journal of Russian Laser Res.(Kluwer Pub.)

Cited by in corpus (14)

• Wigner phase space distribution as a wave function
• Quantum Tomography twenty years later
• Partial positive scaling transform: a separability criterion
• Four questions for quantum-classical hybrid theory
• Tomograms in the Quantum-Classical transition
• General linear dynamics - quantum, classical or hybrid
• Correlations in a system of classical--like coins simulating spin-1/2 states in the probability representation of quantum mechanics
• Proliferation of observables and measurement in quantum-classical hybrids
• A path integral for classical dynamics, entanglement, and Jaynes-Cummings model at the quantum-classical divide
• An analog of Heisenberg uncertainty relation in prequantum classical field theory
• Partial scaling transform of multiqubit states as a criterion of separability
• Detection model based on representation of quantum particles by classical random fields: Born's rule and beyond
• A probabilistic approach to quantum mechanics based on tomograms
• Probability Representation of Quantum Mechanics: Comments and Bibliography