An approximation theorem in classical mechanics
نویسندگان
چکیده
منابع مشابه
Quantum mechanics as an approximation of classical statistical mechanics
We show that the probabilistic formalism of QM can be obtained as a special projection of classical statistical mechanics for systems with an infinite number of degrees of freedom. Such systems can be interpreted as classical fields. Thus in our approach QM is a projection of (prequantum) classical statistical field theory (PCSFT). This projection is based on the Taylor expansion of classical p...
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Classical mechanics is formulated in Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Classical mechanics can now be viewed as a deformation of quantum mechanics. The forms of sem...
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Let An,m(ψ) denote the set of ψ-approximable points in R mn. Under the assumption that the approximating function ψ is monotonic, the classical KhintchineGroshev theorem provides an elegant probabilistic criterion for the Lebesgue measure of An,m(ψ). The famous Duffin-Schaeffer counterexample shows that the monotonicity assumption on ψ is absolutely necessary when m = n = 1. On the other hand, ...
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We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical variables. The quantum contribution is given by the term of the second order. To escape technical difficulties related to the infinite dimension of phase space f...
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ژورنال
عنوان ژورنال: Journal of Geometric Mechanics
سال: 2016
ISSN: 1941-4889
DOI: 10.3934/jgm.2016011