By A. L. Kuhl, J. C. Leyer, A. A. Borisov, W. A. Sirignano
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Extra resources for Dynamics of Detonations and Explosions: Detonations (Vol. 133, Progress in Astronautics and Aeronautics)
Equivalently, we can describe the state by giving the values of F=3n position coordinates and F momentum coordinates, again a point in a 2F-dimensional space, called the canonical phase space of the system, More generally, the phase space of a classical Hamiltonian system is a smooth even-dimensional manifold. In the case of an uncountable phase space the family of all subsets of the phase space is much too large as to qualify for a Boolean algebra of experimentally distinguishable events. It is an atomic algebra, and the points of the phase space would correspond to experimentally decidable questions.
The following three "laws of thought" are traditionally treated as basic to classical logic: (i) the law of contradiction saying that nothing can be both F and not-F; (ii) the law of excluded middle, saying that anything must either be F or not-F; (iii) the law of identity, saying that if anything is F, then it i& F. According to Boole's (1847, 1854) third law, the propositions of classical logic form a Boolean algebra. 1 for any FEB. 1, which fulfills E=FvpJ. for every FEB. 1} defined by the propositional calculus of classical logic is called a Boolean algebra, and will be discussed in more detail in the next section.
Nat. Acad. Sci. ~, 1 13. J. , 1970, Molec. Phys. 19, 433. , 1978, "On the Molecular Vibration-Rotation Problem", Dissertation, Copenhagen. , 1937, "The Fundamental Principles of Quantum Mechanics", McGraw-Hill (Rep. Dover 1955). , 1978, Phys. Rev. A18, 2150. , 1976, J. Molec. Spec:-61, 107. D. , 1976, Rev. Mod. Phys. 48, 69. Makushkin, Yu. S. , 1977, J. Mol. Spe~ 18, I. M. , 1971a, Molec. , 21, 635. M. , 1971b, Molec. , 22, 809. Meyer, R. , 1968, J. Chem. ~9, 1510. , 1951, Rev. Mod. Phys. 23, 90.